Daily Papers

In this work, we introduce a generative approach for pose-free reconstruction of 360^{circ} scenes from a limited number of uncalibrated 2D images. Pose-free scene reconstruction from incomplete, unposed observations is usually regularized with depth estimation or 3D foundational priors. While recent advances have enabled sparse-view reconstruction of unbounded scenes with known camera poses using diffusion priors, these methods rely on explicit camera embeddings for extrapolating unobserved regions. This reliance limits their application in pose-free settings, where view-specific data is only implicitly available. To address this, we propose an instruction-following RGBD diffusion model designed to inpaint missing details and remove artifacts in novel view renders and depth maps of a 3D scene. We also propose a novel confidence measure for Gaussian representations to allow for better detection of these artifacts. By progressively integrating these novel views in a Gaussian-SLAM-inspired process, we achieve a multi-view-consistent Gaussian representation. Evaluations on the MipNeRF360 dataset demonstrate that our method surpasses existing pose-free techniques and performs competitively with state-of-the-art posed reconstruction methods in complex 360^{circ} scenes.

Reconstructing high-fidelity, animatable 3D head avatars from effortlessly captured monocular videos is a pivotal yet formidable challenge. Although significant progress has been made in rendering performance and manipulation capabilities, notable challenges remain, including incomplete reconstruction and inefficient Gaussian representation. To address these challenges, we introduce FATE, a novel method for reconstructing an editable full-head avatar from a single monocular video. FATE integrates a sampling-based densification strategy to ensure optimal positional distribution of points, improving rendering efficiency. A neural baking technique is introduced to convert discrete Gaussian representations into continuous attribute maps, facilitating intuitive appearance editing. Furthermore, we propose a universal completion framework to recover non-frontal appearance, culminating in a 360^circ-renderable 3D head avatar. FATE outperforms previous approaches in both qualitative and quantitative evaluations, achieving state-of-the-art performance. To the best of our knowledge, FATE is the first animatable and 360^circ full-head monocular reconstruction method for a 3D head avatar. The code will be publicly released upon publication.

We present L4GM, the first 4D Large Reconstruction Model that produces animated objects from a single-view video input -- in a single feed-forward pass that takes only a second. Key to our success is a novel dataset of multiview videos containing curated, rendered animated objects from Objaverse. This dataset depicts 44K diverse objects with 110K animations rendered in 48 viewpoints, resulting in 12M videos with a total of 300M frames. We keep our L4GM simple for scalability and build directly on top of LGM, a pretrained 3D Large Reconstruction Model that outputs 3D Gaussian ellipsoids from multiview image input. L4GM outputs a per-frame 3D Gaussian Splatting representation from video frames sampled at a low fps and then upsamples the representation to a higher fps to achieve temporal smoothness. We add temporal self-attention layers to the base LGM to help it learn consistency across time, and utilize a per-timestep multiview rendering loss to train the model. The representation is upsampled to a higher framerate by training an interpolation model which produces intermediate 3D Gaussian representations. We showcase that L4GM that is only trained on synthetic data generalizes extremely well on in-the-wild videos, producing high quality animated 3D assets.

In this paper, we present a self-calibrating framework that jointly optimizes camera parameters, lens distortion and 3D Gaussian representations, enabling accurate and efficient scene reconstruction. In particular, our technique enables high-quality scene reconstruction from Large field-of-view (FOV) imagery taken with wide-angle lenses, allowing the scene to be modeled from a smaller number of images. Our approach introduces a novel method for modeling complex lens distortions using a hybrid network that combines invertible residual networks with explicit grids. This design effectively regularizes the optimization process, achieving greater accuracy than conventional camera models. Additionally, we propose a cubemap-based resampling strategy to support large FOV images without sacrificing resolution or introducing distortion artifacts. Our method is compatible with the fast rasterization of Gaussian Splatting, adaptable to a wide variety of camera lens distortion, and demonstrates state-of-the-art performance on both synthetic and real-world datasets.

Recently, image-to-3D approaches have significantly advanced the generation quality and speed of 3D assets based on large reconstruction models, particularly 3D Gaussian reconstruction models. Existing large 3D Gaussian models directly map 2D image to 3D Gaussian parameters, while regressing 2D image to 3D Gaussian representations is challenging without 3D priors. In this paper, we propose a large Point-to-Gaussian model, that inputs the initial point cloud produced from large 3D diffusion model conditional on 2D image to generate the Gaussian parameters, for image-to-3D generation. The point cloud provides initial 3D geometry prior for Gaussian generation, thus significantly facilitating image-to-3D Generation. Moreover, we present the Attention mechanism, Projection mechanism, and Point feature extractor, dubbed as APP block, for fusing the image features with point cloud features. The qualitative and quantitative experiments extensively demonstrate the effectiveness of the proposed approach on GSO and Objaverse datasets, and show the proposed method achieves state-of-the-art performance.

In this paper, we introduce GS-SLAM that first utilizes 3D Gaussian representation in the Simultaneous Localization and Mapping (SLAM) system. It facilitates a better balance between efficiency and accuracy. Compared to recent SLAM methods employing neural implicit representations, our method utilizes a real-time differentiable splatting rendering pipeline that offers significant speedup to map optimization and RGB-D re-rendering. Specifically, we propose an adaptive expansion strategy that adds new or deletes noisy 3D Gaussian in order to efficiently reconstruct new observed scene geometry and improve the mapping of previously observed areas. This strategy is essential to extend 3D Gaussian representation to reconstruct the whole scene rather than synthesize a static object in existing methods. Moreover, in the pose tracking process, an effective coarse-to-fine technique is designed to select reliable 3D Gaussian representations to optimize camera pose, resulting in runtime reduction and robust estimation. Our method achieves competitive performance compared with existing state-of-the-art real-time methods on the Replica, TUM-RGBD datasets. The source code will be released soon.

We introduce OmniRe, a holistic approach for efficiently reconstructing high-fidelity dynamic urban scenes from on-device logs. Recent methods for modeling driving sequences using neural radiance fields or Gaussian Splatting have demonstrated the potential of reconstructing challenging dynamic scenes, but often overlook pedestrians and other non-vehicle dynamic actors, hindering a complete pipeline for dynamic urban scene reconstruction. To that end, we propose a comprehensive 3DGS framework for driving scenes, named OmniRe, that allows for accurate, full-length reconstruction of diverse dynamic objects in a driving log. OmniRe builds dynamic neural scene graphs based on Gaussian representations and constructs multiple local canonical spaces that model various dynamic actors, including vehicles, pedestrians, and cyclists, among many others. This capability is unmatched by existing methods. OmniRe allows us to holistically reconstruct different objects present in the scene, subsequently enabling the simulation of reconstructed scenarios with all actors participating in real-time (~60Hz). Extensive evaluations on the Waymo dataset show that our approach outperforms prior state-of-the-art methods quantitatively and qualitatively by a large margin. We believe our work fills a critical gap in driving reconstruction.

Generative models have reached an advanced stage where they can produce remarkably realistic images. However, this remarkable generative capability also introduces the risk of disseminating false or misleading information. Notably, existing image detectors for generated images encounter challenges such as low accuracy and limited generalization. This paper seeks to address this issue by seeking a representation with strong generalization capabilities to enhance the detection of generated images. Our investigation has revealed that real and generated images display distinct latent Gaussian representations when subjected to an inverse diffusion process within a pre-trained diffusion model. Exploiting this disparity, we can amplify subtle artifacts in generated images. Building upon this insight, we introduce a novel image representation known as Diffusion Noise Feature (DNF). DNF is extracted from the estimated noise generated during the inverse diffusion process. A simple classifier, e.g., ResNet50, trained on DNF achieves high accuracy, robustness, and generalization capabilities for detecting generated images (even the corresponding generator is built with datasets/structures that are not seen during the classifier's training). We conducted experiments using four training datasets and five testsets, achieving state-of-the-art detection performance.

Previous efforts have managed to generate production-ready 3D assets from text or images. However, these methods primarily employ NeRF or 3D Gaussian representations, which are not adept at producing smooth, high-quality geometries required by modern rendering pipelines. In this paper, we propose LDM, a novel feed-forward framework capable of generating high-fidelity, illumination-decoupled textured mesh from a single image or text prompts. We firstly utilize a multi-view diffusion model to generate sparse multi-view inputs from single images or text prompts, and then a transformer-based model is trained to predict a tensorial SDF field from these sparse multi-view image inputs. Finally, we employ a gradient-based mesh optimization layer to refine this model, enabling it to produce an SDF field from which high-quality textured meshes can be extracted. Extensive experiments demonstrate that our method can generate diverse, high-quality 3D mesh assets with corresponding decomposed RGB textures within seconds.

In recent years, 3D Gaussian splatting has emerged as a powerful technique for 3D reconstruction and generation, known for its fast and high-quality rendering capabilities. To address these shortcomings, this paper introduces a novel diffusion-based framework, GVGEN, designed to efficiently generate 3D Gaussian representations from text input. We propose two innovative techniques:(1) Structured Volumetric Representation. We first arrange disorganized 3D Gaussian points as a structured form GaussianVolume. This transformation allows the capture of intricate texture details within a volume composed of a fixed number of Gaussians. To better optimize the representation of these details, we propose a unique pruning and densifying method named the Candidate Pool Strategy, enhancing detail fidelity through selective optimization. (2) Coarse-to-fine Generation Pipeline. To simplify the generation of GaussianVolume and empower the model to generate instances with detailed 3D geometry, we propose a coarse-to-fine pipeline. It initially constructs a basic geometric structure, followed by the prediction of complete Gaussian attributes. Our framework, GVGEN, demonstrates superior performance in qualitative and quantitative assessments compared to existing 3D generation methods. Simultaneously, it maintains a fast generation speed (sim7 seconds), effectively striking a balance between quality and efficiency.

Open-vocabulary scene understanding using 3D Gaussian (3DGS) representations has garnered considerable attention. However, existing methods mostly lift knowledge from large 2D vision models into 3DGS on a scene-by-scene basis, restricting the capabilities of open-vocabulary querying within their training scenes so that lacking the generalizability to novel scenes. In this work, we propose OVGaussian, a generalizable Open-Vocabulary 3D semantic segmentation framework based on the 3D Gaussian representation. We first construct a large-scale 3D scene dataset based on 3DGS, dubbed SegGaussian, which provides detailed semantic and instance annotations for both Gaussian points and multi-view images. To promote semantic generalization across scenes, we introduce Generalizable Semantic Rasterization (GSR), which leverages a 3D neural network to learn and predict the semantic property for each 3D Gaussian point, where the semantic property can be rendered as multi-view consistent 2D semantic maps. In the next, we propose a Cross-modal Consistency Learning (CCL) framework that utilizes open-vocabulary annotations of 2D images and 3D Gaussians within SegGaussian to train the 3D neural network capable of open-vocabulary semantic segmentation across Gaussian-based 3D scenes. Experimental results demonstrate that OVGaussian significantly outperforms baseline methods, exhibiting robust cross-scene, cross-domain, and novel-view generalization capabilities. Code and the SegGaussian dataset will be released. (https://github.com/runnanchen/OVGaussian).

We propose RelitLRM, a Large Reconstruction Model (LRM) for generating high-quality Gaussian splatting representations of 3D objects under novel illuminations from sparse (4-8) posed images captured under unknown static lighting. Unlike prior inverse rendering methods requiring dense captures and slow optimization, often causing artifacts like incorrect highlights or shadow baking, RelitLRM adopts a feed-forward transformer-based model with a novel combination of a geometry reconstructor and a relightable appearance generator based on diffusion. The model is trained end-to-end on synthetic multi-view renderings of objects under varying known illuminations. This architecture design enables to effectively decompose geometry and appearance, resolve the ambiguity between material and lighting, and capture the multi-modal distribution of shadows and specularity in the relit appearance. We show our sparse-view feed-forward RelitLRM offers competitive relighting results to state-of-the-art dense-view optimization-based baselines while being significantly faster. Our project page is available at: https://relit-lrm.github.io/.

Simultaneous localization and mapping is essential for position tracking and scene understanding. 3D Gaussian-based map representations enable photorealistic reconstruction and real-time rendering of scenes using multiple posed cameras. We show for the first time that using 3D Gaussians for map representation with unposed camera images and inertial measurements can enable accurate SLAM. Our method, MM3DGS, addresses the limitations of prior neural radiance field-based representations by enabling faster rendering, scale awareness, and improved trajectory tracking. Our framework enables keyframe-based mapping and tracking utilizing loss functions that incorporate relative pose transformations from pre-integrated inertial measurements, depth estimates, and measures of photometric rendering quality. We also release a multi-modal dataset, UT-MM, collected from a mobile robot equipped with a camera and an inertial measurement unit. Experimental evaluation on several scenes from the dataset shows that MM3DGS achieves 3x improvement in tracking and 5% improvement in photometric rendering quality compared to the current 3DGS SLAM state-of-the-art, while allowing real-time rendering of a high-resolution dense 3D map. Project Webpage: https://vita-group.github.io/MM3DGS-SLAM

Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?" These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we show how these questions can have compact, closed form solutions in terms of learned representations. The key idea is to apply a variant of contrastive learning to time series data. Prior work already shows that the representations learned by contrastive learning encode a probability ratio. By extending prior work to show that the marginal distribution over representations is Gaussian, we can then prove that joint distribution of representations is also Gaussian. Taken together, these results show that representations learned via temporal contrastive learning follow a Gauss-Markov chain, a graphical model where inference (e.g., prediction, planning) over representations corresponds to inverting a low-dimensional matrix. In one special case, inferring intermediate representations will be equivalent to interpolating between the learned representations. We validate our theory using numerical simulations on tasks up to 46-dimensions.

We present Bidirectional Gaussian Primitives, an image-based novel view synthesis technique designed to represent and render 3D objects with surface and volumetric materials under dynamic illumination. Our approach integrates light intrinsic decomposition into the Gaussian splatting framework, enabling real-time relighting of 3D objects. To unify surface and volumetric material within a cohesive appearance model, we adopt a light- and view-dependent scattering representation via bidirectional spherical harmonics. Our model does not use a specific surface normal-related reflectance function, making it more compatible with volumetric representations like Gaussian splatting, where the normals are undefined. We demonstrate our method by reconstructing and rendering objects with complex materials. Using One-Light-At-a-Time (OLAT) data as input, we can reproduce photorealistic appearances under novel lighting conditions in real time.

Over the past two decades, research in the field of Simultaneous Localization and Mapping (SLAM) has undergone a significant evolution, highlighting its critical role in enabling autonomous exploration of unknown environments. This evolution ranges from hand-crafted methods, through the era of deep learning, to more recent developments focused on Neural Radiance Fields (NeRFs) and 3D Gaussian Splatting (3DGS) representations. Recognizing the growing body of research and the absence of a comprehensive survey on the topic, this paper aims to provide the first comprehensive overview of SLAM progress through the lens of the latest advancements in radiance fields. It sheds light on the background, evolutionary path, inherent strengths and limitations, and serves as a fundamental reference to highlight the dynamic progress and specific challenges.

We propose the Multi-Head Gaussian Adaptive Attention Mechanism (GAAM), a novel probabilistic attention framework, and the Gaussian Adaptive Transformer (GAT), designed to enhance information aggregation across multiple modalities, including Speech, Text and Vision. GAAM integrates learnable mean and variance into its attention mechanism, implemented in a Multi-Headed framework enabling it to collectively model any Probability Distribution for dynamic recalibration of feature significance. This method demonstrates significant improvements, especially with highly non-stationary data, surpassing the state-of-the-art attention techniques in model performance (up to approximately +20% in accuracy) by identifying key elements within the feature space. GAAM's compatibility with dot-product-based attention models and relatively low number of parameters showcases its adaptability and potential to boost existing attention frameworks. Empirically, GAAM exhibits superior adaptability and efficacy across a diverse range of tasks, including emotion recognition in speech, image classification, and text classification, thereby establishing its robustness and versatility in handling multi-modal data. Furthermore, we introduce the Importance Factor (IF), a new learning-based metric that enhances the explainability of models trained with GAAM-based methods. Overall, GAAM represents an advancement towards development of better performing and more explainable attention models across multiple modalities.

Video representation is a long-standing problem that is crucial for various down-stream tasks, such as tracking,depth prediction,segmentation,view synthesis,and editing. However, current methods either struggle to model complex motions due to the absence of 3D structure or rely on implicit 3D representations that are ill-suited for manipulation tasks. To address these challenges, we introduce a novel explicit 3D representation-video Gaussian representation -- that embeds a video into 3D Gaussians. Our proposed representation models video appearance in a 3D canonical space using explicit Gaussians as proxies and associates each Gaussian with 3D motions for video motion. This approach offers a more intrinsic and explicit representation than layered atlas or volumetric pixel matrices. To obtain such a representation, we distill 2D priors, such as optical flow and depth, from foundation models to regularize learning in this ill-posed setting. Extensive applications demonstrate the versatility of our new video representation. It has been proven effective in numerous video processing tasks, including tracking, consistent video depth and feature refinement, motion and appearance editing, and stereoscopic video generation. Project page: https://sunyangtian.github.io/spatter_a_video_web/

3D Gaussian Splatting has demonstrated notable success in large-scale scene reconstruction, but challenges persist due to high training memory consumption and storage overhead. Hybrid representations that integrate implicit and explicit features offer a way to mitigate these limitations. However, when applied in parallelized block-wise training, two critical issues arise since reconstruction accuracy deteriorates due to reduced data diversity when training each block independently, and parallel training restricts the number of divided blocks to the available number of GPUs. To address these issues, we propose Momentum-GS, a novel approach that leverages momentum-based self-distillation to promote consistency and accuracy across the blocks while decoupling the number of blocks from the physical GPU count. Our method maintains a teacher Gaussian decoder updated with momentum, ensuring a stable reference during training. This teacher provides each block with global guidance in a self-distillation manner, promoting spatial consistency in reconstruction. To further ensure consistency across the blocks, we incorporate block weighting, dynamically adjusting each block's weight according to its reconstruction accuracy. Extensive experiments on large-scale scenes show that our method consistently outperforms existing techniques, achieving a 12.8% improvement in LPIPS over CityGaussian with much fewer divided blocks and establishing a new state of the art. Project page: https://jixuan-fan.github.io/Momentum-GS_Page/

Particle-based representations of radiance fields such as 3D Gaussian Splatting have found great success for reconstructing and re-rendering of complex scenes. Most existing methods render particles via rasterization, projecting them to screen space tiles for processing in a sorted order. This work instead considers ray tracing the particles, building a bounding volume hierarchy and casting a ray for each pixel using high-performance GPU ray tracing hardware. To efficiently handle large numbers of semi-transparent particles, we describe a specialized rendering algorithm which encapsulates particles with bounding meshes to leverage fast ray-triangle intersections, and shades batches of intersections in depth-order. The benefits of ray tracing are well-known in computer graphics: processing incoherent rays for secondary lighting effects such as shadows and reflections, rendering from highly-distorted cameras common in robotics, stochastically sampling rays, and more. With our renderer, this flexibility comes at little cost compared to rasterization. Experiments demonstrate the speed and accuracy of our approach, as well as several applications in computer graphics and vision. We further propose related improvements to the basic Gaussian representation, including a simple use of generalized kernel functions which significantly reduces particle hit counts.

Implicit Neural Representations (INRs) employ neural networks to approximate discrete data as continuous functions. In the context of video data, such models can be utilized to transform the coordinates of pixel locations along with frame occurrence times (or indices) into RGB color values. Although INRs facilitate effective compression, they are unsuitable for editing purposes. One potential solution is to use a 3D Gaussian Splatting (3DGS) based model, such as the Video Gaussian Representation (VGR), which is capable of encoding video as a multitude of 3D Gaussians and is applicable for numerous video processing operations, including editing. Nevertheless, in this case, the capacity for modification is constrained to a limited set of basic transformations. To address this issue, we introduce the Video Gaussian Splatting (VeGaS) model, which enables realistic modifications of video data. To construct VeGaS, we propose a novel family of Folded-Gaussian distributions designed to capture nonlinear dynamics in a video stream and model consecutive frames by 2D Gaussians obtained as respective conditional distributions. Our experiments demonstrate that VeGaS outperforms state-of-the-art solutions in frame reconstruction tasks and allows realistic modifications of video data. The code is available at: https://github.com/gmum/VeGaS.

3D scene representations have gained immense popularity in recent years. Methods that use Neural Radiance fields are versatile for traditional tasks such as novel view synthesis. In recent times, some work has emerged that aims to extend the functionality of NeRF beyond view synthesis, for semantically aware tasks such as editing and segmentation using 3D feature field distillation from 2D foundation models. However, these methods have two major limitations: (a) they are limited by the rendering speed of NeRF pipelines, and (b) implicitly represented feature fields suffer from continuity artifacts reducing feature quality. Recently, 3D Gaussian Splatting has shown state-of-the-art performance on real-time radiance field rendering. In this work, we go one step further: in addition to radiance field rendering, we enable 3D Gaussian splatting on arbitrary-dimension semantic features via 2D foundation model distillation. This translation is not straightforward: naively incorporating feature fields in the 3DGS framework leads to warp-level divergence. We propose architectural and training changes to efficiently avert this problem. Our proposed method is general, and our experiments showcase novel view semantic segmentation, language-guided editing and segment anything through learning feature fields from state-of-the-art 2D foundation models such as SAM and CLIP-LSeg. Across experiments, our distillation method is able to provide comparable or better results, while being significantly faster to both train and render. Additionally, to the best of our knowledge, we are the first method to enable point and bounding-box prompting for radiance field manipulation, by leveraging the SAM model. Project website at: https://feature-3dgs.github.io/

Neural implicit representations, including Neural Distance Fields and Neural Radiance Fields, have demonstrated significant capabilities for reconstructing surfaces with complicated geometry and topology, and generating novel views of a scene. Nevertheless, it is challenging for users to directly deform or manipulate these implicit representations with large deformations in the real-time fashion. Gaussian Splatting(GS) has recently become a promising method with explicit geometry for representing static scenes and facilitating high-quality and real-time synthesis of novel views. However,it cannot be easily deformed due to the use of discrete Gaussians and lack of explicit topology. To address this, we develop a novel GS-based method that enables interactive deformation. Our key idea is to design an innovative mesh-based GS representation, which is integrated into Gaussian learning and manipulation. 3D Gaussians are defined over an explicit mesh, and they are bound with each other: the rendering of 3D Gaussians guides the mesh face split for adaptive refinement, and the mesh face split directs the splitting of 3D Gaussians. Moreover, the explicit mesh constraints help regularize the Gaussian distribution, suppressing poor-quality Gaussians(e.g. misaligned Gaussians,long-narrow shaped Gaussians), thus enhancing visual quality and avoiding artifacts during deformation. Based on this representation, we further introduce a large-scale Gaussian deformation technique to enable deformable GS, which alters the parameters of 3D Gaussians according to the manipulation of the associated mesh. Our method benefits from existing mesh deformation datasets for more realistic data-driven Gaussian deformation. Extensive experiments show that our approach achieves high-quality reconstruction and effective deformation, while maintaining the promising rendering results at a high frame rate(65 FPS on average).

Efficient neural representations for dynamic video scenes are critical for applications ranging from video compression to interactive simulations. Yet, existing methods often face challenges related to high memory usage, lengthy training times, and temporal consistency. To address these issues, we introduce a novel neural video representation that combines 3D Gaussian splatting with continuous camera motion modeling. By leveraging Neural ODEs, our approach learns smooth camera trajectories while maintaining an explicit 3D scene representation through Gaussians. Additionally, we introduce a spatiotemporal hierarchical learning strategy, progressively refining spatial and temporal features to enhance reconstruction quality and accelerate convergence. This memory-efficient approach achieves high-quality rendering at impressive speeds. Experimental results show that our hierarchical learning, combined with robust camera motion modeling, captures complex dynamic scenes with strong temporal consistency, achieving state-of-the-art performance across diverse video datasets in both high- and low-motion scenarios.

3D occupancy prediction is important for autonomous driving due to its comprehensive perception of the surroundings. To incorporate sequential inputs, most existing methods fuse representations from previous frames to infer the current 3D occupancy. However, they fail to consider the continuity of driving scenarios and ignore the strong prior provided by the evolution of 3D scenes (e.g., only dynamic objects move). In this paper, we propose a world-model-based framework to exploit the scene evolution for perception. We reformulate 3D occupancy prediction as a 4D occupancy forecasting problem conditioned on the current sensor input. We decompose the scene evolution into three factors: 1) ego motion alignment of static scenes; 2) local movements of dynamic objects; and 3) completion of newly-observed scenes. We then employ a Gaussian world model (GaussianWorld) to explicitly exploit these priors and infer the scene evolution in the 3D Gaussian space considering the current RGB observation. We evaluate the effectiveness of our framework on the widely used nuScenes dataset. Our GaussianWorld improves the performance of the single-frame counterpart by over 2% in mIoU without introducing additional computations. Code: https://github.com/zuosc19/GaussianWorld.

Conventional uncertainty-aware temporal difference (TD) learning methods often rely on simplistic assumptions, typically including a zero-mean Gaussian distribution for TD errors. Such oversimplification can lead to inaccurate error representations and compromised uncertainty estimation. In this paper, we introduce a novel framework for generalized Gaussian error modeling in deep reinforcement learning, applicable to both discrete and continuous control settings. Our framework enhances the flexibility of error distribution modeling by incorporating additional higher-order moment, particularly kurtosis, thereby improving the estimation and mitigation of data-dependent noise, i.e., aleatoric uncertainty. We examine the influence of the shape parameter of the generalized Gaussian distribution (GGD) on aleatoric uncertainty and provide a closed-form expression that demonstrates an inverse relationship between uncertainty and the shape parameter. Additionally, we propose a theoretically grounded weighting scheme to fully leverage the GGD. To address epistemic uncertainty, we enhance the batch inverse variance weighting by incorporating bias reduction and kurtosis considerations, resulting in improved robustness. Extensive experimental evaluations using policy gradient algorithms demonstrate the consistent efficacy of our method, showcasing significant performance improvements.

Recent approaches representing 3D objects and scenes using Gaussian splats show increased rendering speed across a variety of platforms and devices. While rendering such representations is indeed extremely efficient, storing and transmitting them is often prohibitively expensive. To represent large-scale scenes, one often needs to store millions of 3D Gaussians, occupying gigabytes of disk space. This poses a very practical limitation, prohibiting widespread adoption.Several solutions have been proposed to strike a balance between disk size and rendering quality, noticeably reducing the visual quality. In this work, we propose a new representation that dramatically reduces the hard drive footprint while featuring similar or improved quality when compared to the standard 3D Gaussian splats. When compared to other compact solutions, ours offers higher quality renderings with significantly reduced storage, being able to efficiently run on a mobile device in real-time. Our key observation is that nearby points in the scene can share similar representations. Hence, only a small ratio of 3D points needs to be stored. We introduce an approach to identify such points which are called parent points. The discarded points called children points along with attributes can be efficiently predicted by tiny MLPs.

Implicit neural representations (INRs) recently achieved great success in image representation and compression, offering high visual quality and fast rendering speeds with 10-1000 FPS, assuming sufficient GPU resources are available. However, this requirement often hinders their use on low-end devices with limited memory. In response, we propose a groundbreaking paradigm of image representation and compression by 2D Gaussian Splatting, named GaussianImage. We first introduce 2D Gaussian to represent the image, where each Gaussian has 8 parameters including position, covariance and color. Subsequently, we unveil a novel rendering algorithm based on accumulated summation. Remarkably, our method with a minimum of 3times lower GPU memory usage and 5times faster fitting time not only rivals INRs (e.g., WIRE, I-NGP) in representation performance, but also delivers a faster rendering speed of 1500-2000 FPS regardless of parameter size. Furthermore, we integrate existing vector quantization technique to build an image codec. Experimental results demonstrate that our codec attains rate-distortion performance comparable to compression-based INRs such as COIN and COIN++, while facilitating decoding speeds of approximately 1000 FPS. Additionally, preliminary proof of concept shows that our codec surpasses COIN and COIN++ in performance when using partial bits-back coding.

In this paper we present a novel method for efficient and effective 3D surface reconstruction in open scenes. Existing Neural Radiance Fields (NeRF) based works typically require extensive training and rendering time due to the adopted implicit representations. In contrast, 3D Gaussian splatting (3DGS) uses an explicit and discrete representation, hence the reconstructed surface is built by the huge number of Gaussian primitives, which leads to excessive memory consumption and rough surface details in sparse Gaussian areas. To address these issues, we propose Gaussian Voxel Kernel Functions (GVKF), which establish a continuous scene representation based on discrete 3DGS through kernel regression. The GVKF integrates fast 3DGS rasterization and highly effective scene implicit representations, achieving high-fidelity open scene surface reconstruction. Experiments on challenging scene datasets demonstrate the efficiency and effectiveness of our proposed GVKF, featuring with high reconstruction quality, real-time rendering speed, significant savings in storage and training memory consumption.

With their meaningful geometry and their omnipresence in the 3D world, edges are extremely useful primitives in computer vision. 3D edges comprise of lines and curves, and methods to reconstruct them use either multi-view images or point clouds as input. State-of-the-art image-based methods first learn a 3D edge point cloud then fit 3D edges to it. The edge point cloud is obtained by learning a 3D neural implicit edge field from which the 3D edge points are sampled on a specific level set (0 or 1). However, such methods present two important drawbacks: i) it is not realistic to sample points on exact level sets due to float imprecision and training inaccuracies. Instead, they are sampled within a range of levels so the points do not lie accurately on the 3D edges and require further processing. ii) Such implicit representations are computationally expensive and require long training times. In this paper, we address these two limitations and propose a 3D edge mapping that is simpler, more efficient, and preserves accuracy. Our method learns explicitly the 3D edge points and their edge direction hence bypassing the need for point sampling. It casts a 3D edge point as the center of a 3D Gaussian and the edge direction as the principal axis of the Gaussian. Such a representation has the advantage of being not only geometrically meaningful but also compatible with the efficient training optimization defined in Gaussian Splatting. Results show that the proposed method produces edges as accurate and complete as the state-of-the-art while being an order of magnitude faster. Code is released at https://github.com/kunalchelani/EdgeGaussians.

3D Gaussian Splatting (3DGS) integrates the strengths of primitive-based representations and volumetric rendering techniques, enabling real-time, high-quality rendering. However, 3DGS models typically overfit to single-scene training and are highly sensitive to the initialization of Gaussian ellipsoids, heuristically derived from Structure from Motion (SfM) point clouds, which limits both generalization and practicality. To address these limitations, we propose GS-Net, a generalizable, plug-and-play 3DGS module that densifies Gaussian ellipsoids from sparse SfM point clouds, enhancing geometric structure representation. To the best of our knowledge, GS-Net is the first plug-and-play 3DGS module with cross-scene generalization capabilities. Additionally, we introduce the CARLA-NVS dataset, which incorporates additional camera viewpoints to thoroughly evaluate reconstruction and rendering quality. Extensive experiments demonstrate that applying GS-Net to 3DGS yields a PSNR improvement of 2.08 dB for conventional viewpoints and 1.86 dB for novel viewpoints, confirming the method's effectiveness and robustness.

Animatable clothing transfer, aiming at dressing and animating garments across characters, is a challenging problem. Most human avatar works entangle the representations of the human body and clothing together, which leads to difficulties for virtual try-on across identities. What's worse, the entangled representations usually fail to exactly track the sliding motion of garments. To overcome these limitations, we present Layered Gaussian Avatars (LayGA), a new representation that formulates body and clothing as two separate layers for photorealistic animatable clothing transfer from multi-view videos. Our representation is built upon the Gaussian map-based avatar for its excellent representation power of garment details. However, the Gaussian map produces unstructured 3D Gaussians distributed around the actual surface. The absence of a smooth explicit surface raises challenges in accurate garment tracking and collision handling between body and garments. Therefore, we propose two-stage training involving single-layer reconstruction and multi-layer fitting. In the single-layer reconstruction stage, we propose a series of geometric constraints to reconstruct smooth surfaces and simultaneously obtain the segmentation between body and clothing. Next, in the multi-layer fitting stage, we train two separate models to represent body and clothing and utilize the reconstructed clothing geometries as 3D supervision for more accurate garment tracking. Furthermore, we propose geometry and rendering layers for both high-quality geometric reconstruction and high-fidelity rendering. Overall, the proposed LayGA realizes photorealistic animations and virtual try-on, and outperforms other baseline methods. Our project page is https://jsnln.github.io/layga/index.html.

Realistic 3D human generation from text prompts is a desirable yet challenging task. Existing methods optimize 3D representations like mesh or neural fields via score distillation sampling (SDS), which suffers from inadequate fine details or excessive training time. In this paper, we propose an efficient yet effective framework, HumanGaussian, that generates high-quality 3D humans with fine-grained geometry and realistic appearance. Our key insight is that 3D Gaussian Splatting is an efficient renderer with periodic Gaussian shrinkage or growing, where such adaptive density control can be naturally guided by intrinsic human structures. Specifically, 1) we first propose a Structure-Aware SDS that simultaneously optimizes human appearance and geometry. The multi-modal score function from both RGB and depth space is leveraged to distill the Gaussian densification and pruning process. 2) Moreover, we devise an Annealed Negative Prompt Guidance by decomposing SDS into a noisier generative score and a cleaner classifier score, which well addresses the over-saturation issue. The floating artifacts are further eliminated based on Gaussian size in a prune-only phase to enhance generation smoothness. Extensive experiments demonstrate the superior efficiency and competitive quality of our framework, rendering vivid 3D humans under diverse scenarios. Project Page: https://alvinliu0.github.io/projects/HumanGaussian

We propose GS-IR, a novel inverse rendering approach based on 3D Gaussian Splatting (GS) that leverages forward mapping volume rendering to achieve photorealistic novel view synthesis and relighting results. Unlike previous works that use implicit neural representations and volume rendering (e.g. NeRF), which suffer from low expressive power and high computational complexity, we extend GS, a top-performance representation for novel view synthesis, to estimate scene geometry, surface material, and environment illumination from multi-view images captured under unknown lighting conditions. There are two main problems when introducing GS to inverse rendering: 1) GS does not support producing plausible normal natively; 2) forward mapping (e.g. rasterization and splatting) cannot trace the occlusion like backward mapping (e.g. ray tracing). To address these challenges, our GS-IR proposes an efficient optimization scheme that incorporates a depth-derivation-based regularization for normal estimation and a baking-based occlusion to model indirect lighting. The flexible and expressive GS representation allows us to achieve fast and compact geometry reconstruction, photorealistic novel view synthesis, and effective physically-based rendering. We demonstrate the superiority of our method over baseline methods through qualitative and quantitative evaluations on various challenging scenes.

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions.

The fidelity of relighting is bounded by both geometry and appearance representations. For geometry, both mesh and volumetric approaches have difficulty modeling intricate structures like 3D hair geometry. For appearance, existing relighting models are limited in fidelity and often too slow to render in real-time with high-resolution continuous environments. In this work, we present Relightable Gaussian Codec Avatars, a method to build high-fidelity relightable head avatars that can be animated to generate novel expressions. Our geometry model based on 3D Gaussians can capture 3D-consistent sub-millimeter details such as hair strands and pores on dynamic face sequences. To support diverse materials of human heads such as the eyes, skin, and hair in a unified manner, we present a novel relightable appearance model based on learnable radiance transfer. Together with global illumination-aware spherical harmonics for the diffuse components, we achieve real-time relighting with spatially all-frequency reflections using spherical Gaussians. This appearance model can be efficiently relit under both point light and continuous illumination. We further improve the fidelity of eye reflections and enable explicit gaze control by introducing relightable explicit eye models. Our method outperforms existing approaches without compromising real-time performance. We also demonstrate real-time relighting of avatars on a tethered consumer VR headset, showcasing the efficiency and fidelity of our avatars.

While neural rendering has led to impressive advances in scene reconstruction and novel view synthesis, it relies heavily on accurately pre-computed camera poses. To relax this constraint, multiple efforts have been made to train Neural Radiance Fields (NeRFs) without pre-processed camera poses. However, the implicit representations of NeRFs provide extra challenges to optimize the 3D structure and camera poses at the same time. On the other hand, the recently proposed 3D Gaussian Splatting provides new opportunities given its explicit point cloud representations. This paper leverages both the explicit geometric representation and the continuity of the input video stream to perform novel view synthesis without any SfM preprocessing. We process the input frames in a sequential manner and progressively grow the 3D Gaussians set by taking one input frame at a time, without the need to pre-compute the camera poses. Our method significantly improves over previous approaches in view synthesis and camera pose estimation under large motion changes. Our project page is https://oasisyang.github.io/colmap-free-3dgs

We introduce pixelSplat, a feed-forward model that learns to reconstruct 3D radiance fields parameterized by 3D Gaussian primitives from pairs of images. Our model features real-time and memory-efficient rendering for scalable training as well as fast 3D reconstruction at inference time. To overcome local minima inherent to sparse and locally supported representations, we predict a dense probability distribution over 3D and sample Gaussian means from that probability distribution. We make this sampling operation differentiable via a reparameterization trick, allowing us to back-propagate gradients through the Gaussian splatting representation. We benchmark our method on wide-baseline novel view synthesis on the real-world RealEstate10k and ACID datasets, where we outperform state-of-the-art light field transformers and accelerate rendering by 2.5 orders of magnitude while reconstructing an interpretable and editable 3D radiance field.

Advancements in neural implicit representations and differentiable rendering have markedly improved the ability to learn animatable 3D avatars from sparse multi-view RGB videos. However, current methods that map observation space to canonical space often face challenges in capturing pose-dependent details and generalizing to novel poses. While diffusion models have demonstrated remarkable zero-shot capabilities in 2D image generation, their potential for creating animatable 3D avatars from 2D inputs remains underexplored. In this work, we introduce 3D^2-Actor, a novel approach featuring a pose-conditioned 3D-aware human modeling pipeline that integrates iterative 2D denoising and 3D rectifying steps. The 2D denoiser, guided by pose cues, generates detailed multi-view images that provide the rich feature set necessary for high-fidelity 3D reconstruction and pose rendering. Complementing this, our Gaussian-based 3D rectifier renders images with enhanced 3D consistency through a two-stage projection strategy and a novel local coordinate representation. Additionally, we propose an innovative sampling strategy to ensure smooth temporal continuity across frames in video synthesis. Our method effectively addresses the limitations of traditional numerical solutions in handling ill-posed mappings, producing realistic and animatable 3D human avatars. Experimental results demonstrate that 3D^2-Actor excels in high-fidelity avatar modeling and robustly generalizes to novel poses. Code is available at: https://github.com/silence-tang/GaussianActor.

This paper aims to address the challenge of reconstructing long volumetric videos from multi-view RGB videos. Recent dynamic view synthesis methods leverage powerful 4D representations, like feature grids or point cloud sequences, to achieve high-quality rendering results. However, they are typically limited to short (1~2s) video clips and often suffer from large memory footprints when dealing with longer videos. To solve this issue, we propose a novel 4D representation, named Temporal Gaussian Hierarchy, to compactly model long volumetric videos. Our key observation is that there are generally various degrees of temporal redundancy in dynamic scenes, which consist of areas changing at different speeds. Motivated by this, our approach builds a multi-level hierarchy of 4D Gaussian primitives, where each level separately describes scene regions with different degrees of content change, and adaptively shares Gaussian primitives to represent unchanged scene content over different temporal segments, thus effectively reducing the number of Gaussian primitives. In addition, the tree-like structure of the Gaussian hierarchy allows us to efficiently represent the scene at a particular moment with a subset of Gaussian primitives, leading to nearly constant GPU memory usage during the training or rendering regardless of the video length. Extensive experimental results demonstrate the superiority of our method over alternative methods in terms of training cost, rendering speed, and storage usage. To our knowledge, this work is the first approach capable of efficiently handling minutes of volumetric video data while maintaining state-of-the-art rendering quality. Our project page is available at: https://zju3dv.github.io/longvolcap.

Gaussian splatting has emerged as a powerful 3D representation that harnesses the advantages of both explicit (mesh) and implicit (NeRF) 3D representations. In this paper, we seek to leverage Gaussian splatting to generate realistic animatable avatars from textual descriptions, addressing the limitations (e.g., flexibility and efficiency) imposed by mesh or NeRF-based representations. However, a naive application of Gaussian splatting cannot generate high-quality animatable avatars and suffers from learning instability; it also cannot capture fine avatar geometries and often leads to degenerate body parts. To tackle these problems, we first propose a primitive-based 3D Gaussian representation where Gaussians are defined inside pose-driven primitives to facilitate animation. Second, to stabilize and amortize the learning of millions of Gaussians, we propose to use neural implicit fields to predict the Gaussian attributes (e.g., colors). Finally, to capture fine avatar geometries and extract detailed meshes, we propose a novel SDF-based implicit mesh learning approach for 3D Gaussians that regularizes the underlying geometries and extracts highly detailed textured meshes. Our proposed method, GAvatar, enables the large-scale generation of diverse animatable avatars using only text prompts. GAvatar significantly surpasses existing methods in terms of both appearance and geometry quality, and achieves extremely fast rendering (100 fps) at 1K resolution.

Current visual foundation models are trained purely on unstructured 2D data, limiting their understanding of 3D structure of objects and scenes. In this work, we show that fine-tuning on 3D-aware data improves the quality of emerging semantic features. We design a method to lift semantic 2D features into an efficient 3D Gaussian representation, which allows us to re-render them for arbitrary views. Using the rendered 3D-aware features, we design a fine-tuning strategy to transfer such 3D awareness into a 2D foundation model. We demonstrate that models fine-tuned in that way produce features that readily improve downstream task performance in semantic segmentation and depth estimation through simple linear probing. Notably, though fined-tuned on a single indoor dataset, the improvement is transferable to a variety of indoor datasets and out-of-domain datasets. We hope our study encourages the community to consider injecting 3D awareness when training 2D foundation models. Project page: https://ywyue.github.io/FiT3D.

This work addresses the problem of real-time rendering of photorealistic human body avatars learned from multi-view videos. While the classical approaches to model and render virtual humans generally use a textured mesh, recent research has developed neural body representations that achieve impressive visual quality. However, these models are difficult to render in real-time and their quality degrades when the character is animated with body poses different than the training observations. We propose an animatable human model based on 3D Gaussian Splatting, that has recently emerged as a very efficient alternative to neural radiance fields. The body is represented by a set of gaussian primitives in a canonical space which is deformed with a coarse to fine approach that combines forward skinning and local non-rigid refinement. We describe how to learn our Human Gaussian Splatting (HuGS) model in an end-to-end fashion from multi-view observations, and evaluate it against the state-of-the-art approaches for novel pose synthesis of clothed body. Our method achieves 1.5 dB PSNR improvement over the state-of-the-art on THuman4 dataset while being able to render in real-time (80 fps for 512x512 resolution).

Recent advancements in 3D scene editing have been propelled by the rapid development of generative models. Existing methods typically utilize generative models to perform text-guided editing on 3D representations, such as 3D Gaussian Splatting (3DGS). However, these methods are often limited to texture modifications and fail when addressing geometric changes, such as editing a character's head to turn around. Moreover, such methods lack accurate control over the spatial position of editing results, as language struggles to precisely describe the extent of edits. To overcome these limitations, we introduce DYG, an effective 3D drag-based editing method for 3D Gaussian Splatting. It enables users to conveniently specify the desired editing region and the desired dragging direction through the input of 3D masks and pairs of control points, thereby enabling precise control over the extent of editing. DYG integrates the strengths of the implicit triplane representation to establish the geometric scaffold of the editing results, effectively overcoming suboptimal editing outcomes caused by the sparsity of 3DGS in the desired editing regions. Additionally, we incorporate a drag-based Latent Diffusion Model into our method through the proposed Drag-SDS loss function, enabling flexible, multi-view consistent, and fine-grained editing. Extensive experiments demonstrate that DYG conducts effective drag-based editing guided by control point prompts, surpassing other baselines in terms of editing effect and quality, both qualitatively and quantitatively. Visit our project page at https://quyans.github.io/Drag-Your-Gaussian.

We present GSD, a diffusion model approach based on Gaussian Splatting (GS) representation for 3D object reconstruction from a single view. Prior works suffer from inconsistent 3D geometry or mediocre rendering quality due to improper representations. We take a step towards resolving these shortcomings by utilizing the recent state-of-the-art 3D explicit representation, Gaussian Splatting, and an unconditional diffusion model. This model learns to generate 3D objects represented by sets of GS ellipsoids. With these strong generative 3D priors, though learning unconditionally, the diffusion model is ready for view-guided reconstruction without further model fine-tuning. This is achieved by propagating fine-grained 2D features through the efficient yet flexible splatting function and the guided denoising sampling process. In addition, a 2D diffusion model is further employed to enhance rendering fidelity, and improve reconstructed GS quality by polishing and re-using the rendered images. The final reconstructed objects explicitly come with high-quality 3D structure and texture, and can be efficiently rendered in arbitrary views. Experiments on the challenging real-world CO3D dataset demonstrate the superiority of our approach. Project page: https://yxmu.foo/GSD/{this https URL}

The approximation of Partial Differential Equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and flexibility in implementing various PDEs, PINNs often suffer from limited accuracy due to the spectral bias of Multi-Layer Perceptrons (MLPs), which struggle to effectively learn high-frequency and non-linear components. Recently, parametric mesh representations in combination with neural networks have been investigated as a promising approach to eliminate the inductive biases of neural networks. However, they usually require very high-resolution grids and a large number of collocation points to achieve high accuracy while avoiding overfitting issues. In addition, the fixed positions of the mesh parameters restrict their flexibility, making it challenging to accurately approximate complex PDEs. To overcome these limitations, we propose Physics-Informed Gaussians (PIGs), which combine feature embeddings using Gaussian functions with a lightweight neural network. Our approach uses trainable parameters for the mean and variance of each Gaussian, allowing for dynamic adjustment of their positions and shapes during training. This adaptability enables our model to optimally approximate PDE solutions, unlike models with fixed parameter positions. Furthermore, the proposed approach maintains the same optimization framework used in PINNs, allowing us to benefit from their excellent properties. Experimental results show the competitive performance of our model across various PDEs, demonstrating its potential as a robust tool for solving complex PDEs. Our project page is available at https://namgyukang.github.io/Physics-Informed-Gaussians/

Recent advances in view synthesis and real-time rendering have achieved photorealistic quality at impressive rendering speeds. While Radiance Field-based methods achieve state-of-the-art quality in challenging scenarios such as in-the-wild captures and large-scale scenes, they often suffer from excessively high compute requirements linked to volumetric rendering. Gaussian Splatting-based methods, on the other hand, rely on rasterization and naturally achieve real-time rendering but suffer from brittle optimization heuristics that underperform on more challenging scenes. In this work, we present RadSplat, a lightweight method for robust real-time rendering of complex scenes. Our main contributions are threefold. First, we use radiance fields as a prior and supervision signal for optimizing point-based scene representations, leading to improved quality and more robust optimization. Next, we develop a novel pruning technique reducing the overall point count while maintaining high quality, leading to smaller and more compact scene representations with faster inference speeds. Finally, we propose a novel test-time filtering approach that further accelerates rendering and allows to scale to larger, house-sized scenes. We find that our method enables state-of-the-art synthesis of complex captures at 900+ FPS.

We propose SelfSplat, a novel 3D Gaussian Splatting model designed to perform pose-free and 3D prior-free generalizable 3D reconstruction from unposed multi-view images. These settings are inherently ill-posed due to the lack of ground-truth data, learned geometric information, and the need to achieve accurate 3D reconstruction without finetuning, making it difficult for conventional methods to achieve high-quality results. Our model addresses these challenges by effectively integrating explicit 3D representations with self-supervised depth and pose estimation techniques, resulting in reciprocal improvements in both pose accuracy and 3D reconstruction quality. Furthermore, we incorporate a matching-aware pose estimation network and a depth refinement module to enhance geometry consistency across views, ensuring more accurate and stable 3D reconstructions. To present the performance of our method, we evaluated it on large-scale real-world datasets, including RealEstate10K, ACID, and DL3DV. SelfSplat achieves superior results over previous state-of-the-art methods in both appearance and geometry quality, also demonstrates strong cross-dataset generalization capabilities. Extensive ablation studies and analysis also validate the effectiveness of our proposed methods. Code and pretrained models are available at https://gynjn.github.io/selfsplat/

Recent advancements in 3D reconstruction from single images have been driven by the evolution of generative models. Prominent among these are methods based on Score Distillation Sampling (SDS) and the adaptation of diffusion models in the 3D domain. Despite their progress, these techniques often face limitations due to slow optimization or rendering processes, leading to extensive training and optimization times. In this paper, we introduce a novel approach for single-view reconstruction that efficiently generates a 3D model from a single image via feed-forward inference. Our method utilizes two transformer-based networks, namely a point decoder and a triplane decoder, to reconstruct 3D objects using a hybrid Triplane-Gaussian intermediate representation. This hybrid representation strikes a balance, achieving a faster rendering speed compared to implicit representations while simultaneously delivering superior rendering quality than explicit representations. The point decoder is designed for generating point clouds from single images, offering an explicit representation which is then utilized by the triplane decoder to query Gaussian features for each point. This design choice addresses the challenges associated with directly regressing explicit 3D Gaussian attributes characterized by their non-structural nature. Subsequently, the 3D Gaussians are decoded by an MLP to enable rapid rendering through splatting. Both decoders are built upon a scalable, transformer-based architecture and have been efficiently trained on large-scale 3D datasets. The evaluations conducted on both synthetic datasets and real-world images demonstrate that our method not only achieves higher quality but also ensures a faster runtime in comparison to previous state-of-the-art techniques. Please see our project page at https://zouzx.github.io/TriplaneGaussian/.

In this paper, we introduce GaussianMotion, a novel human rendering model that generates fully animatable scenes aligned with textual descriptions using Gaussian Splatting. Although existing methods achieve reasonable text-to-3D generation of human bodies using various 3D representations, they often face limitations in fidelity and efficiency, or primarily focus on static models with limited pose control. In contrast, our method generates fully animatable 3D avatars by combining deformable 3D Gaussian Splatting with text-to-3D score distillation, achieving high fidelity and efficient rendering for arbitrary poses. By densely generating diverse random poses during optimization, our deformable 3D human model learns to capture a wide range of natural motions distilled from a pose-conditioned diffusion model in an end-to-end manner. Furthermore, we propose Adaptive Score Distillation that effectively balances realistic detail and smoothness to achieve optimal 3D results. Experimental results demonstrate that our approach outperforms existing baselines by producing high-quality textures in both static and animated results, and by generating diverse 3D human models from various textual inputs.

Creating high-fidelity 3D human head avatars is crucial for applications in VR/AR, telepresence, digital human interfaces, and film production. Recent advances have leveraged morphable face models to generate animated head avatars from easily accessible data, representing varying identities and expressions within a low-dimensional parametric space. However, existing methods often struggle with modeling complex appearance details, e.g., hairstyles and accessories, and suffer from low rendering quality and efficiency. This paper introduces a novel approach, 3D Gaussian Parametric Head Model, which employs 3D Gaussians to accurately represent the complexities of the human head, allowing precise control over both identity and expression. Additionally, it enables seamless face portrait interpolation and the reconstruction of detailed head avatars from a single image. Unlike previous methods, the Gaussian model can handle intricate details, enabling realistic representations of varying appearances and complex expressions. Furthermore, this paper presents a well-designed training framework to ensure smooth convergence, providing a guarantee for learning the rich content. Our method achieves high-quality, photo-realistic rendering with real-time efficiency, making it a valuable contribution to the field of parametric head models.

The 3D Gaussian Splatting (3DGS) gained its popularity recently by combining the advantages of both primitive-based and volumetric 3D representations, resulting in improved quality and efficiency for 3D scene rendering. However, 3DGS is not alias-free, and its rendering at varying resolutions could produce severe blurring or jaggies. This is because 3DGS treats each pixel as an isolated, single point rather than as an area, causing insensitivity to changes in the footprints of pixels. Consequently, this discrete sampling scheme inevitably results in aliasing, owing to the restricted sampling bandwidth. In this paper, we derive an analytical solution to address this issue. More specifically, we use a conditioned logistic function as the analytic approximation of the cumulative distribution function (CDF) in a one-dimensional Gaussian signal and calculate the Gaussian integral by subtracting the CDFs. We then introduce this approximation in the two-dimensional pixel shading, and present Analytic-Splatting, which analytically approximates the Gaussian integral within the 2D-pixel window area to better capture the intensity response of each pixel. Moreover, we use the approximated response of the pixel window integral area to participate in the transmittance calculation of volume rendering, making Analytic-Splatting sensitive to the changes in pixel footprint at different resolutions. Experiments on various datasets validate that our approach has better anti-aliasing capability that gives more details and better fidelity.

3D editing plays a crucial role in many areas such as gaming and virtual reality. Traditional 3D editing methods, which rely on representations like meshes and point clouds, often fall short in realistically depicting complex scenes. On the other hand, methods based on implicit 3D representations, like Neural Radiance Field (NeRF), render complex scenes effectively but suffer from slow processing speeds and limited control over specific scene areas. In response to these challenges, our paper presents GaussianEditor, an innovative and efficient 3D editing algorithm based on Gaussian Splatting (GS), a novel 3D representation. GaussianEditor enhances precision and control in editing through our proposed Gaussian semantic tracing, which traces the editing target throughout the training process. Additionally, we propose Hierarchical Gaussian splatting (HGS) to achieve stabilized and fine results under stochastic generative guidance from 2D diffusion models. We also develop editing strategies for efficient object removal and integration, a challenging task for existing methods. Our comprehensive experiments demonstrate GaussianEditor's superior control, efficacy, and rapid performance, marking a significant advancement in 3D editing. Project Page: https://buaacyw.github.io/gaussian-editor/

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

Nuanced expressiveness, particularly through fine-grained hand and facial expressions, is pivotal for enhancing the realism and vitality of digital human representations. In this work, we focus on investigating the expressiveness of human avatars when learned from monocular RGB video; a setting that introduces new challenges in capturing and animating fine-grained details. To this end, we introduce EVA, a drivable human model that meticulously sculpts fine details based on 3D Gaussians and SMPL-X, an expressive parametric human model. Focused on enhancing expressiveness, our work makes three key contributions. First, we highlight the critical importance of aligning the SMPL-X model with RGB frames for effective avatar learning. Recognizing the limitations of current SMPL-X prediction methods for in-the-wild videos, we introduce a plug-and-play module that significantly ameliorates misalignment issues. Second, we propose a context-aware adaptive density control strategy, which is adaptively adjusting the gradient thresholds to accommodate the varied granularity across body parts. Last but not least, we develop a feedback mechanism that predicts per-pixel confidence to better guide the learning of 3D Gaussians. Extensive experiments on two benchmarks demonstrate the superiority of our framework both quantitatively and qualitatively, especially on the fine-grained hand and facial details. See the project website at https://evahuman.github.io

Recent advancements in real-time neural rendering using point-based techniques have paved the way for the widespread adoption of 3D representations. However, foundational approaches like 3D Gaussian Splatting come with a substantial storage overhead caused by growing the SfM points to millions, often demanding gigabyte-level disk space for a single unbounded scene, posing significant scalability challenges and hindering the splatting efficiency. To address this challenge, we introduce LightGaussian, a novel method designed to transform 3D Gaussians into a more efficient and compact format. Drawing inspiration from the concept of Network Pruning, LightGaussian identifies Gaussians that are insignificant in contributing to the scene reconstruction and adopts a pruning and recovery process, effectively reducing redundancy in Gaussian counts while preserving visual effects. Additionally, LightGaussian employs distillation and pseudo-view augmentation to distill spherical harmonics to a lower degree, allowing knowledge transfer to more compact representations while maintaining reflectance. Furthermore, we propose a hybrid scheme, VecTree Quantization, to quantize all attributes, resulting in lower bitwidth representations with minimal accuracy losses. In summary, LightGaussian achieves an averaged compression rate over 15x while boosting the FPS from 139 to 215, enabling an efficient representation of complex scenes on Mip-NeRF 360, Tank and Temple datasets. Project website: https://lightgaussian.github.io/

While novel view synthesis (NVS) has made substantial progress in 3D computer vision, it typically requires an initial estimation of camera intrinsics and extrinsics from dense viewpoints. This pre-processing is usually conducted via a Structure-from-Motion (SfM) pipeline, a procedure that can be slow and unreliable, particularly in sparse-view scenarios with insufficient matched features for accurate reconstruction. In this work, we integrate the strengths of point-based representations (e.g., 3D Gaussian Splatting, 3D-GS) with end-to-end dense stereo models (DUSt3R) to tackle the complex yet unresolved issues in NVS under unconstrained settings, which encompasses pose-free and sparse view challenges. Our framework, InstantSplat, unifies dense stereo priors with 3D-GS to build 3D Gaussians of large-scale scenes from sparseview & pose-free images in less than 1 minute. Specifically, InstantSplat comprises a Coarse Geometric Initialization (CGI) module that swiftly establishes a preliminary scene structure and camera parameters across all training views, utilizing globally-aligned 3D point maps derived from a pre-trained dense stereo pipeline. This is followed by the Fast 3D-Gaussian Optimization (F-3DGO) module, which jointly optimizes the 3D Gaussian attributes and the initialized poses with pose regularization. Experiments conducted on the large-scale outdoor Tanks & Temples datasets demonstrate that InstantSplat significantly improves SSIM (by 32%) while concurrently reducing Absolute Trajectory Error (ATE) by 80%. These establish InstantSplat as a viable solution for scenarios involving posefree and sparse-view conditions. Project page: instantsplat.github.io.

3D Semantic Occupancy Prediction is fundamental for spatial understanding as it provides a comprehensive semantic cognition of surrounding environments. However, prevalent approaches primarily rely on extensive labeled data and computationally intensive voxel-based modeling, restricting the scalability and generalizability of 3D representation learning. In this paper, we introduce GaussTR, a novel Gaussian Transformer that leverages alignment with foundation models to advance self-supervised 3D spatial understanding. GaussTR adopts a Transformer architecture to predict sparse sets of 3D Gaussians that represent scenes in a feed-forward manner. Through aligning rendered Gaussian features with diverse knowledge from pre-trained foundation models, GaussTR facilitates the learning of versatile 3D representations and enables open-vocabulary occupancy prediction without explicit annotations. Empirical evaluations on the Occ3D-nuScenes dataset showcase GaussTR's state-of-the-art zero-shot performance, achieving 11.70 mIoU while reducing training duration by approximately 50%. These experimental results highlight the significant potential of GaussTR for scalable and holistic 3D spatial understanding, with promising implications for autonomous driving and embodied agents. Code is available at https://github.com/hustvl/GaussTR.

In computer graphics, there is a need to recover easily modifiable representations of 3D geometry and appearance from image data. We introduce a novel method for this task using 3D Gaussian Splatting, which enables intuitive scene editing through mesh adjustments. Starting with input images and camera poses, we reconstruct the underlying geometry using a neural Signed Distance Field and extract a high-quality mesh. Our model then estimates a set of Gaussians, where each component is flat, and the opacity is conditioned on the recovered neural surface. To facilitate editing, we produce a proxy representation that encodes information about the Gaussians' shape and position. Unlike other methods, our pipeline allows modifications applied to the extracted mesh to be propagated to the proxy representation, from which we recover the updated parameters of the Gaussians. This effectively transfers the mesh edits back to the recovered appearance representation. By leveraging mesh-guided transformations, our approach simplifies 3D scene editing and offers improvements over existing methods in terms of usability and visual fidelity of edits. The complete source code for this project can be accessed at https://github.com/WJakubowska/NeuralSurfacePriors

Recently, 3D Gaussian splatting has gained attention for its capability to generate high-fidelity rendering results. At the same time, most applications such as games, animation, and AR/VR use mesh-based representations to represent and render 3D scenes. We propose a novel approach that integrates mesh representation with 3D Gaussian splats to perform high-quality rendering of reconstructed real-world scenes. In particular, we introduce a distance-based Gaussian splatting technique to align the Gaussian splats with the mesh surface and remove redundant Gaussian splats that do not contribute to the rendering. We consider the distance between each Gaussian splat and the mesh surface to distinguish between tightly-bound and loosely-bound Gaussian splats. The tightly-bound splats are flattened and aligned well with the mesh geometry. The loosely-bound Gaussian splats are used to account for the artifacts in reconstructed 3D meshes in terms of rendering. We present a training strategy of binding Gaussian splats to the mesh geometry, and take into account both types of splats. In this context, we introduce several regularization techniques aimed at precisely aligning tightly-bound Gaussian splats with the mesh surface during the training process. We validate the effectiveness of our method on large and unbounded scene from mip-NeRF 360 and Deep Blending datasets. Our method surpasses recent mesh-based neural rendering techniques by achieving a 2dB higher PSNR, and outperforms mesh-based Gaussian splatting methods by 1.3 dB PSNR, particularly on the outdoor mip-NeRF 360 dataset, demonstrating better rendering quality. We provide analyses for each type of Gaussian splat and achieve a reduction in the number of Gaussian splats by 30% compared to the original 3D Gaussian splatting.

Novel view synthesis has advanced significantly with the development of neural radiance fields (NeRF) and 3D Gaussian splatting (3DGS). However, achieving high quality without compromising real-time rendering remains challenging, particularly for physically-based ray tracing with view-dependent effects. Recently, N-dimensional Gaussians (N-DG) introduced a 6D spatial-angular representation to better incorporate view-dependent effects, but the Gaussian representation and control scheme are sub-optimal. In this paper, we revisit 6D Gaussians and introduce 6D Gaussian Splatting (6DGS), which enhances color and opacity representations and leverages the additional directional information in the 6D space for optimized Gaussian control. Our approach is fully compatible with the 3DGS framework and significantly improves real-time radiance field rendering by better modeling view-dependent effects and fine details. Experiments demonstrate that 6DGS significantly outperforms 3DGS and N-DG, achieving up to a 15.73 dB improvement in PSNR with a reduction of 66.5% Gaussian points compared to 3DGS. The project page is: https://gaozhongpai.github.io/6dgs/

A key property of deep neural networks (DNNs) is their ability to learn new features during training. This intriguing aspect of deep learning stands out most clearly in recently reported Grokking phenomena. While mainly reflected as a sudden increase in test accuracy, Grokking is also believed to be a beyond lazy-learning/Gaussian Process (GP) phenomenon involving feature learning. Here we apply a recent development in the theory of feature learning, the adaptive kernel approach, to two teacher-student models with cubic-polynomial and modular addition teachers. We provide analytical predictions on feature learning and Grokking properties of these models and demonstrate a mapping between Grokking and the theory of phase transitions. We show that after Grokking, the state of the DNN is analogous to the mixed phase following a first-order phase transition. In this mixed phase, the DNN generates useful internal representations of the teacher that are sharply distinct from those before the transition.

Autoencoders and their variants are among the most widely used models in representation learning and generative modeling. However, autoencoder-based models usually assume that the learned representations are i.i.d. and fail to capture the correlations between the data samples. To address this issue, we propose a novel Sparse Gaussian Process Bayesian Autoencoder (SGPBAE) model in which we impose fully Bayesian sparse Gaussian Process priors on the latent space of a Bayesian Autoencoder. We perform posterior estimation for this model via stochastic gradient Hamiltonian Monte Carlo. We evaluate our approach qualitatively and quantitatively on a wide range of representation learning and generative modeling tasks and show that our approach consistently outperforms multiple alternatives relying on Variational Autoencoders.

Remarkable progress has been made in 4D content generation recently. However, existing methods suffer from long optimization time, lack of motion controllability, and a low level of detail. In this paper, we introduce DreamGaussian4D, an efficient 4D generation framework that builds on 4D Gaussian Splatting representation. Our key insight is that the explicit modeling of spatial transformations in Gaussian Splatting makes it more suitable for the 4D generation setting compared with implicit representations. DreamGaussian4D reduces the optimization time from several hours to just a few minutes, allows flexible control of the generated 3D motion, and produces animated meshes that can be efficiently rendered in 3D engines.

Novel-view synthesis aims to generate novel views of a scene from multiple input images or videos, and recent advancements like 3D Gaussian splatting (3DGS) have achieved notable success in producing photorealistic renderings with efficient pipelines. However, generating high-quality novel views under challenging settings, such as sparse input views, remains difficult due to insufficient information in under-sampled areas, often resulting in noticeable artifacts. This paper presents 3DGS-Enhancer, a novel pipeline for enhancing the representation quality of 3DGS representations. We leverage 2D video diffusion priors to address the challenging 3D view consistency problem, reformulating it as achieving temporal consistency within a video generation process. 3DGS-Enhancer restores view-consistent latent features of rendered novel views and integrates them with the input views through a spatial-temporal decoder. The enhanced views are then used to fine-tune the initial 3DGS model, significantly improving its rendering performance. Extensive experiments on large-scale datasets of unbounded scenes demonstrate that 3DGS-Enhancer yields superior reconstruction performance and high-fidelity rendering results compared to state-of-the-art methods. The project webpage is https://xiliu8006.github.io/3DGS-Enhancer-project .

Creating high-fidelity head avatars from multi-view videos is a core issue for many AR/VR applications. However, existing methods usually struggle to obtain high-quality renderings for all different head components simultaneously since they use one single representation to model components with drastically different characteristics (e.g., skin vs. hair). In this paper, we propose a Hybrid Mesh-Gaussian Head Avatar (MeGA) that models different head components with more suitable representations. Specifically, we select an enhanced FLAME mesh as our facial representation and predict a UV displacement map to provide per-vertex offsets for improved personalized geometric details. To achieve photorealistic renderings, we obtain facial colors using deferred neural rendering and disentangle neural textures into three meaningful parts. For hair modeling, we first build a static canonical hair using 3D Gaussian Splatting. A rigid transformation and an MLP-based deformation field are further applied to handle complex dynamic expressions. Combined with our occlusion-aware blending, MeGA generates higher-fidelity renderings for the whole head and naturally supports more downstream tasks. Experiments on the NeRSemble dataset demonstrate the effectiveness of our designs, outperforming previous state-of-the-art methods and supporting various editing functionalities, including hairstyle alteration and texture editing.

Text-to-3D scene generation holds immense potential for the gaming, film, and architecture sectors. Despite significant progress, existing methods struggle with maintaining high quality, consistency, and editing flexibility. In this paper, we propose DreamScene, a 3D Gaussian-based novel text-to-3D scene generation framework, to tackle the aforementioned three challenges mainly via two strategies. First, DreamScene employs Formation Pattern Sampling (FPS), a multi-timestep sampling strategy guided by the formation patterns of 3D objects, to form fast, semantically rich, and high-quality representations. FPS uses 3D Gaussian filtering for optimization stability, and leverages reconstruction techniques to generate plausible textures. Second, DreamScene employs a progressive three-stage camera sampling strategy, specifically designed for both indoor and outdoor settings, to effectively ensure object-environment integration and scene-wide 3D consistency. Last, DreamScene enhances scene editing flexibility by integrating objects and environments, enabling targeted adjustments. Extensive experiments validate DreamScene's superiority over current state-of-the-art techniques, heralding its wide-ranging potential for diverse applications. Code and demos will be released at https://dreamscene-project.github.io .

Text-based generation and editing of 3D scenes hold significant potential for streamlining content creation through intuitive user interactions. While recent advances leverage 3D Gaussian Splatting (3DGS) for high-fidelity and real-time rendering, existing methods are often specialized and task-focused, lacking a unified framework for both generation and editing. In this paper, we introduce SplatFlow, a comprehensive framework that addresses this gap by enabling direct 3DGS generation and editing. SplatFlow comprises two main components: a multi-view rectified flow (RF) model and a Gaussian Splatting Decoder (GSDecoder). The multi-view RF model operates in latent space, generating multi-view images, depths, and camera poses simultaneously, conditioned on text prompts, thus addressing challenges like diverse scene scales and complex camera trajectories in real-world settings. Then, the GSDecoder efficiently translates these latent outputs into 3DGS representations through a feed-forward 3DGS method. Leveraging training-free inversion and inpainting techniques, SplatFlow enables seamless 3DGS editing and supports a broad range of 3D tasks-including object editing, novel view synthesis, and camera pose estimation-within a unified framework without requiring additional complex pipelines. We validate SplatFlow's capabilities on the MVImgNet and DL3DV-7K datasets, demonstrating its versatility and effectiveness in various 3D generation, editing, and inpainting-based tasks.

Efficiently synthesizing novel views from sparse inputs while maintaining accuracy remains a critical challenge in 3D reconstruction. While advanced techniques like radiance fields and 3D Gaussian Splatting achieve rendering quality and impressive efficiency with dense view inputs, they suffer from significant geometric reconstruction errors when applied to sparse input views. Moreover, although recent methods leverage monocular depth estimation to enhance geometric learning, their dependence on single-view estimated depth often leads to view inconsistency issues across different viewpoints. Consequently, this reliance on absolute depth can introduce inaccuracies in geometric information, ultimately compromising the quality of scene reconstruction with Gaussian splats. In this paper, we present RDG-GS, a novel sparse-view 3D rendering framework with Relative Depth Guidance based on 3D Gaussian Splatting. The core innovation lies in utilizing relative depth guidance to refine the Gaussian field, steering it towards view-consistent spatial geometric representations, thereby enabling the reconstruction of accurate geometric structures and capturing intricate textures. First, we devise refined depth priors to rectify the coarse estimated depth and insert global and fine-grained scene information to regular Gaussians. Building on this, to address spatial geometric inaccuracies from absolute depth, we propose relative depth guidance by optimizing the similarity between spatially correlated patches of depth and images. Additionally, we also directly deal with the sparse areas challenging to converge by the adaptive sampling for quick densification. Across extensive experiments on Mip-NeRF360, LLFF, DTU, and Blender, RDG-GS demonstrates state-of-the-art rendering quality and efficiency, making a significant advancement for real-world application.

Despite their many desirable properties, Gaussian processes (GPs) are often compared unfavorably to deep neural networks (NNs) for lacking the ability to learn representations. Recent efforts to bridge the gap between GPs and deep NNs have yielded a new class of inter-domain variational GPs in which the inducing variables correspond to hidden units of a feedforward NN. In this work, we examine some practical issues associated with this approach and propose an extension that leverages the orthogonal decomposition of GPs to mitigate these limitations. In particular, we introduce spherical inter-domain features to construct more flexible data-dependent basis functions for both the principal and orthogonal components of the GP approximation and show that incorporating NN activation features under this framework not only alleviates these shortcomings but is more scalable than alternative strategies. Experiments on multiple benchmark datasets demonstrate the effectiveness of our approach.

Video generative models are receiving particular attention given their ability to generate realistic and imaginative frames. Besides, these models are also observed to exhibit strong 3D consistency, significantly enhancing their potential to act as world simulators. In this work, we present Vidu4D, a novel reconstruction model that excels in accurately reconstructing 4D (i.e., sequential 3D) representations from single generated videos, addressing challenges associated with non-rigidity and frame distortion. This capability is pivotal for creating high-fidelity virtual contents that maintain both spatial and temporal coherence. At the core of Vidu4D is our proposed Dynamic Gaussian Surfels (DGS) technique. DGS optimizes time-varying warping functions to transform Gaussian surfels (surface elements) from a static state to a dynamically warped state. This transformation enables a precise depiction of motion and deformation over time. To preserve the structural integrity of surface-aligned Gaussian surfels, we design the warped-state geometric regularization based on continuous warping fields for estimating normals. Additionally, we learn refinements on rotation and scaling parameters of Gaussian surfels, which greatly alleviates texture flickering during the warping process and enhances the capture of fine-grained appearance details. Vidu4D also contains a novel initialization state that provides a proper start for the warping fields in DGS. Equipping Vidu4D with an existing video generative model, the overall framework demonstrates high-fidelity text-to-4D generation in both appearance and geometry.

While text-to-3D and image-to-3D generation tasks have received considerable attention, one important but under-explored field between them is controllable text-to-3D generation, which we mainly focus on in this work. To address this task, 1) we introduce Multi-view ControlNet (MVControl), a novel neural network architecture designed to enhance existing pre-trained multi-view diffusion models by integrating additional input conditions, such as edge, depth, normal, and scribble maps. Our innovation lies in the introduction of a conditioning module that controls the base diffusion model using both local and global embeddings, which are computed from the input condition images and camera poses. Once trained, MVControl is able to offer 3D diffusion guidance for optimization-based 3D generation. And, 2) we propose an efficient multi-stage 3D generation pipeline that leverages the benefits of recent large reconstruction models and score distillation algorithm. Building upon our MVControl architecture, we employ a unique hybrid diffusion guidance method to direct the optimization process. In pursuit of efficiency, we adopt 3D Gaussians as our representation instead of the commonly used implicit representations. We also pioneer the use of SuGaR, a hybrid representation that binds Gaussians to mesh triangle faces. This approach alleviates the issue of poor geometry in 3D Gaussians and enables the direct sculpting of fine-grained geometry on the mesh. Extensive experiments demonstrate that our method achieves robust generalization and enables the controllable generation of high-quality 3D content.

We present a novel stochastic variational Gaussian process (GP) inference method, based on a posterior over a learnable set of weighted pseudo input-output points (coresets). Instead of a free-form variational family, the proposed coreset-based, variational tempered family for GPs (CVTGP) is defined in terms of the GP prior and the data-likelihood; hence, accommodating the modeling inductive biases. We derive CVTGP's lower bound for the log-marginal likelihood via marginalization of the proposed posterior over latent GP coreset variables, and show it is amenable to stochastic optimization. CVTGP reduces the learnable parameter size to O(M), enjoys numerical stability, and maintains O(M^3) time- and O(M^2) space-complexity, by leveraging a coreset-based tempered posterior that, in turn, provides sparse and explainable representations of the data. Results on simulated and real-world regression problems with Gaussian observation noise validate that CVTGP provides better evidence lower-bound estimates and predictive root mean squared error than alternative stochastic GP inference methods.

The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation learning. However, standard theoretical approaches (formally NNGPs) involving infinite width limits eliminate representation learning. We therefore develop a new infinite width limit, the Bayesian representation learning limit, that exhibits representation learning mirroring that in finite-width models, yet at the same time, retains some of the simplicity of standard infinite-width limits. In particular, we show that Deep Gaussian processes (DGPs) in the Bayesian representation learning limit have exactly multivariate Gaussian posteriors, and the posterior covariances can be obtained by optimizing an interpretable objective combining a log-likelihood to improve performance with a series of KL-divergences which keep the posteriors close to the prior. We confirm these results experimentally in wide but finite DGPs. Next, we introduce the possibility of using this limit and objective as a flexible, deep generalisation of kernel methods, that we call deep kernel machines (DKMs). Like most naive kernel methods, DKMs scale cubically in the number of datapoints. We therefore use methods from the Gaussian process inducing point literature to develop a sparse DKM that scales linearly in the number of datapoints. Finally, we extend these approaches to NNs (which have non-Gaussian posteriors) in the Appendices.

Effective image tokenization is crucial for both multi-modal understanding and generation tasks due to the necessity of the alignment with discrete text data. To this end, existing approaches utilize vector quantization (VQ) to project pixels onto a discrete codebook and reconstruct images from the discrete representation. However, compared with the continuous latent space, the limited discrete codebook space significantly restrict the representational ability of these image tokenizers. In this paper, we propose GaussianToken: An Effective Image Tokenizer with 2D Gaussian Splatting as a solution. We first represent the encoded samples as multiple flexible featured 2D Gaussians characterized by positions, rotation angles, scaling factors, and feature coefficients. We adopt the standard quantization for the Gaussian features and then concatenate the quantization results with the other intrinsic Gaussian parameters before the corresponding splatting operation and the subsequent decoding module. In general, GaussianToken integrates the local influence of 2D Gaussian distribution into the discrete space and thus enhances the representation capability of the image tokenizer. Competitive reconstruction performances on CIFAR, Mini-ImageNet, and ImageNet-1K demonstrate the effectiveness of our framework. Our code is available at: https://github.com/ChrisDong-THU/GaussianToken.

Scene representations using 3D Gaussian primitives have produced excellent results in modeling the appearance of static and dynamic 3D scenes. Many graphics applications, however, demand the ability to manipulate both the appearance and the physical properties of objects. We introduce Feature Splatting, an approach that unifies physics-based dynamic scene synthesis with rich semantics from vision language foundation models that are grounded by natural language. Our first contribution is a way to distill high-quality, object-centric vision-language features into 3D Gaussians, that enables semi-automatic scene decomposition using text queries. Our second contribution is a way to synthesize physics-based dynamics from an otherwise static scene using a particle-based simulator, in which material properties are assigned automatically via text queries. We ablate key techniques used in this pipeline, to illustrate the challenge and opportunities in using feature-carrying 3D Gaussians as a unified format for appearance, geometry, material properties and semantics grounded on natural language. Project website: https://feature-splatting.github.io/

3D Gaussian Splatting (3DGS) has become the de facto method of 3D representation in many vision tasks. This calls for the 3D understanding directly in this representation space. To facilitate the research in this direction, we first build a large-scale dataset of 3DGS using the commonly used ShapeNet and ModelNet datasets. Our dataset ShapeSplat consists of 65K objects from 87 unique categories, whose labels are in accordance with the respective datasets. The creation of this dataset utilized the compute equivalent of 2 GPU years on a TITAN XP GPU. We utilize our dataset for unsupervised pretraining and supervised finetuning for classification and segmentation tasks. To this end, we introduce \textit{Gaussian-MAE}, which highlights the unique benefits of representation learning from Gaussian parameters. Through exhaustive experiments, we provide several valuable insights. In particular, we show that (1) the distribution of the optimized GS centroids significantly differs from the uniformly sampled point cloud (used for initialization) counterpart; (2) this change in distribution results in degradation in classification but improvement in segmentation tasks when using only the centroids; (3) to leverage additional Gaussian parameters, we propose Gaussian feature grouping in a normalized feature space, along with splats pooling layer, offering a tailored solution to effectively group and embed similar Gaussians, which leads to notable improvement in finetuning tasks.

Transition videos play a crucial role in media production, enhancing the flow and coherence of visual narratives. Traditional methods like morphing often lack artistic appeal and require specialized skills, limiting their effectiveness. Recent advances in diffusion model-based video generation offer new possibilities for creating transitions but face challenges such as poor inter-frame relationship modeling and abrupt content changes. We propose a novel training-free Transition Video Generation (TVG) approach using video-level diffusion models that addresses these limitations without additional training. Our method leverages Gaussian Process Regression (GPR) to model latent representations, ensuring smooth and dynamic transitions between frames. Additionally, we introduce interpolation-based conditional controls and a Frequency-aware Bidirectional Fusion (FBiF) architecture to enhance temporal control and transition reliability. Evaluations of benchmark datasets and custom image pairs demonstrate the effectiveness of our approach in generating high-quality smooth transition videos. The code are provided in https://sobeymil.github.io/tvg.com.

The recent 3D Gaussian splatting (3D-GS) has shown remarkable rendering fidelity and efficiency compared to NeRF-based neural scene representations. While demonstrating the potential for real-time rendering, 3D-GS encounters rendering bottlenecks in large scenes with complex details due to an excessive number of Gaussian primitives located within the viewing frustum. This limitation is particularly noticeable in zoom-out views and can lead to inconsistent rendering speeds in scenes with varying details. Moreover, it often struggles to capture the corresponding level of details at different scales with its heuristic density control operation. Inspired by the Level-of-Detail (LOD) techniques, we introduce Octree-GS, featuring an LOD-structured 3D Gaussian approach supporting level-of-detail decomposition for scene representation that contributes to the final rendering results. Our model dynamically selects the appropriate level from the set of multi-resolution anchor points, ensuring consistent rendering performance with adaptive LOD adjustments while maintaining high-fidelity rendering results.

Neural rendering methods have significantly advanced photo-realistic 3D scene rendering in various academic and industrial applications. The recent 3D Gaussian Splatting method has achieved the state-of-the-art rendering quality and speed combining the benefits of both primitive-based representations and volumetric representations. However, it often leads to heavily redundant Gaussians that try to fit every training view, neglecting the underlying scene geometry. Consequently, the resulting model becomes less robust to significant view changes, texture-less area and lighting effects. We introduce Scaffold-GS, which uses anchor points to distribute local 3D Gaussians, and predicts their attributes on-the-fly based on viewing direction and distance within the view frustum. Anchor growing and pruning strategies are developed based on the importance of neural Gaussians to reliably improve the scene coverage. We show that our method effectively reduces redundant Gaussians while delivering high-quality rendering. We also demonstrates an enhanced capability to accommodate scenes with varying levels-of-detail and view-dependent observations, without sacrificing the rendering speed.

Anomaly Detection (AD) in images is a fundamental computer vision problem and refers to identifying images and image substructures that deviate significantly from the norm. Popular AD algorithms commonly try to learn a model of normality from scratch using task specific datasets, but are limited to semi-supervised approaches employing mostly normal data due to the inaccessibility of anomalies on a large scale combined with the ambiguous nature of anomaly appearance. We follow an alternative approach and demonstrate that deep feature representations learned by discriminative models on large natural image datasets are well suited to describe normality and detect even subtle anomalies in a transfer learning setting. Our model of normality is established by fitting a multivariate Gaussian (MVG) to deep feature representations of classification networks trained on ImageNet using normal data only. By subsequently applying the Mahalanobis distance as the anomaly score we outperform the current state of the art on the public MVTec AD dataset, achieving an AUROC value of 95.8 pm 1.2 (mean pm SEM) over all 15 classes. We further investigate why the learned representations are discriminative to the AD task using Principal Component Analysis. We find that the principal components containing little variance in normal data are the ones crucial for discriminating between normal and anomalous instances. This gives a possible explanation to the often sub-par performance of AD approaches trained from scratch using normal data only. By selectively fitting a MVG to these most relevant components only, we are able to further reduce model complexity while retaining AD performance. We also investigate setting the working point by selecting acceptable False Positive Rate thresholds based on the MVG assumption. Code available at https://github.com/ORippler/gaussian-ad-mvtec

Given the growing need for automatic 3D content creation pipelines, various 3D representations have been studied to generate 3D objects from a single image. Due to its superior rendering efficiency, 3D Gaussian splatting-based models have recently excelled in both 3D reconstruction and generation. 3D Gaussian splatting approaches for image to 3D generation are often optimization-based, requiring many computationally expensive score-distillation steps. To overcome these challenges, we introduce an Amortized Generative 3D Gaussian framework (AGG) that instantly produces 3D Gaussians from a single image, eliminating the need for per-instance optimization. Utilizing an intermediate hybrid representation, AGG decomposes the generation of 3D Gaussian locations and other appearance attributes for joint optimization. Moreover, we propose a cascaded pipeline that first generates a coarse representation of the 3D data and later upsamples it with a 3D Gaussian super-resolution module. Our method is evaluated against existing optimization-based 3D Gaussian frameworks and sampling-based pipelines utilizing other 3D representations, where AGG showcases competitive generation abilities both qualitatively and quantitatively while being several orders of magnitude faster. Project page: https://ir1d.github.io/AGG/

Generalized feed-forward Gaussian models have achieved significant progress in sparse-view 3D reconstruction by leveraging prior knowledge from large multi-view datasets. However, these models often struggle to represent high-frequency details due to the limited number of Gaussians. While the densification strategy used in per-scene 3D Gaussian splatting (3D-GS) optimization can be adapted to the feed-forward models, it may not be ideally suited for generalized scenarios. In this paper, we propose Generative Densification, an efficient and generalizable method to densify Gaussians generated by feed-forward models. Unlike the 3D-GS densification strategy, which iteratively splits and clones raw Gaussian parameters, our method up-samples feature representations from the feed-forward models and generates their corresponding fine Gaussians in a single forward pass, leveraging the embedded prior knowledge for enhanced generalization. Experimental results on both object-level and scene-level reconstruction tasks demonstrate that our method outperforms state-of-the-art approaches with comparable or smaller model sizes, achieving notable improvements in representing fine details.

3D characters are essential to modern creative industries, but making them animatable often demands extensive manual work in tasks like rigging and skinning. Existing automatic rigging tools face several limitations, including the necessity for manual annotations, rigid skeleton topologies, and limited generalization across diverse shapes and poses. An alternative approach is to generate animatable avatars pre-bound to a rigged template mesh. However, this method often lacks flexibility and is typically limited to realistic human shapes. To address these issues, we present Make-It-Animatable, a novel data-driven method to make any 3D humanoid model ready for character animation in less than one second, regardless of its shapes and poses. Our unified framework generates high-quality blend weights, bones, and pose transformations. By incorporating a particle-based shape autoencoder, our approach supports various 3D representations, including meshes and 3D Gaussian splats. Additionally, we employ a coarse-to-fine representation and a structure-aware modeling strategy to ensure both accuracy and robustness, even for characters with non-standard skeleton structures. We conducted extensive experiments to validate our framework's effectiveness. Compared to existing methods, our approach demonstrates significant improvements in both quality and speed.

Real-world large-scale datasets are both noisily labeled and class-imbalanced. The issues seriously hurt the generalization of trained models. It is hence significant to address the simultaneous incorrect labeling and class-imbalance, i.e., the problem of learning with noisy labels on long-tailed data. Previous works develop several methods for the problem. However, they always rely on strong assumptions that are invalid or hard to be checked in practice. In this paper, to handle the problem and address the limitations of prior works, we propose a representation calibration method RCAL. Specifically, RCAL works with the representations extracted by unsupervised contrastive learning. We assume that without incorrect labeling and class imbalance, the representations of instances in each class conform to a multivariate Gaussian distribution, which is much milder and easier to be checked. Based on the assumption, we recover underlying representation distributions from polluted ones resulting from mislabeled and class-imbalanced data. Additional data points are then sampled from the recovered distributions to help generalization. Moreover, during classifier training, representation learning takes advantage of representation robustness brought by contrastive learning, which further improves the classifier performance. We derive theoretical results to discuss the effectiveness of our representation calibration. Experiments on multiple benchmarks justify our claims and confirm the superiority of the proposed method.

We introduce PhysGaussian, a new method that seamlessly integrates physically grounded Newtonian dynamics within 3D Gaussians to achieve high-quality novel motion synthesis. Employing a custom Material Point Method (MPM), our approach enriches 3D Gaussian kernels with physically meaningful kinematic deformation and mechanical stress attributes, all evolved in line with continuum mechanics principles. A defining characteristic of our method is the seamless integration between physical simulation and visual rendering: both components utilize the same 3D Gaussian kernels as their discrete representations. This negates the necessity for triangle/tetrahedron meshing, marching cubes, "cage meshes," or any other geometry embedding, highlighting the principle of "what you see is what you simulate (WS^2)." Our method demonstrates exceptional versatility across a wide variety of materials--including elastic entities, metals, non-Newtonian fluids, and granular materials--showcasing its strong capabilities in creating diverse visual content with novel viewpoints and movements. Our project page is at: https://xpandora.github.io/PhysGaussian/

We propose TextToon, a method to generate a drivable toonified avatar. Given a short monocular video sequence and a written instruction about the avatar style, our model can generate a high-fidelity toonified avatar that can be driven in real-time by another video with arbitrary identities. Existing related works heavily rely on multi-view modeling to recover geometry via texture embeddings, presented in a static manner, leading to control limitations. The multi-view video input also makes it difficult to deploy these models in real-world applications. To address these issues, we adopt a conditional embedding Tri-plane to learn realistic and stylized facial representations in a Gaussian deformation field. Additionally, we expand the stylization capabilities of 3D Gaussian Splatting by introducing an adaptive pixel-translation neural network and leveraging patch-aware contrastive learning to achieve high-quality images. To push our work into consumer applications, we develop a real-time system that can operate at 48 FPS on a GPU machine and 15-18 FPS on a mobile machine. Extensive experiments demonstrate the efficacy of our approach in generating textual avatars over existing methods in terms of quality and real-time animation. Please refer to our project page for more details: https://songluchuan.github.io/TextToon/.

Token embeddings, a mapping from discrete lexical symbols to continuous vectors, are at the heart of any language model (LM). However, lexical symbol meanings can also be determined and even redefined by their structural role in a long context. In this paper, we ask: is it possible for a language model to be performant without any fixed token embeddings? Such a language model would have to rely entirely on the co-occurence and repetition of tokens in the context rather than the a priori identity of any token. To answer this, we study lexinvariantlanguage models that are invariant to lexical symbols and therefore do not need fixed token embeddings in practice. First, we prove that we can construct a lexinvariant LM to converge to the true language model at a uniform rate that is polynomial in terms of the context length, with a constant factor that is sublinear in the vocabulary size. Second, to build a lexinvariant LM, we simply encode tokens using random Gaussian vectors, such that each token maps to the same representation within each sequence but different representations across sequences. Empirically, we demonstrate that it can indeed attain perplexity comparable to that of a standard language model, given a sufficiently long context. We further explore two properties of the lexinvariant language models: First, given text generated from a substitution cipher of English, it implicitly implements Bayesian in-context deciphering and infers the mapping to the underlying real tokens with high accuracy. Second, it has on average 4X better accuracy over synthetic in-context reasoning tasks. Finally, we discuss regularizing standard language models towards lexinvariance and potential practical applications.

Addressing imbalanced or long-tailed data is a major challenge in visual recognition tasks due to disparities between training and testing distributions and issues with data noise. We propose the Wrapped Cauchy Distributed Angular Softmax (WCDAS), a novel softmax function that incorporates data-wise Gaussian-based kernels into the angular correlation between feature representations and classifier weights, effectively mitigating noise and sparse sampling concerns. The class-wise distribution of angular representation becomes a sum of these kernels. Our theoretical analysis reveals that the wrapped Cauchy distribution excels the Gaussian distribution in approximating mixed distributions. Additionally, WCDAS uses trainable concentration parameters to dynamically adjust the compactness and margin of each class. Empirical results confirm label-aware behavior in these parameters and demonstrate WCDAS's superiority over other state-of-the-art softmax-based methods in handling long-tailed visual recognition across multiple benchmark datasets. The code is public available.

Self-supervised representation learning is heavily dependent on data augmentations to specify the invariances encoded in representations. Previous work has shown that applying diverse data augmentations is crucial to downstream performance, but augmentation techniques remain under-explored. In this work, we propose a new family of local transformations based on Gaussian random fields to generate image augmentations for self-supervised representation learning. These transformations generalize the well-established affine and color transformations (translation, rotation, color jitter, etc.) and greatly increase the space of augmentations by allowing transformation parameter values to vary from pixel to pixel. The parameters are treated as continuous functions of spatial coordinates, and modeled as independent Gaussian random fields. Empirical results show the effectiveness of the new transformations for self-supervised representation learning. Specifically, we achieve a 1.7% top-1 accuracy improvement over baseline on ImageNet downstream classification, and a 3.6% improvement on out-of-distribution iNaturalist downstream classification. However, due to the flexibility of the new transformations, learned representations are sensitive to hyperparameters. While mild transformations improve representations, we observe that strong transformations can degrade the structure of an image, indicating that balancing the diversity and strength of augmentations is important for improving generalization of learned representations.

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a family of sub-Gaussian probability distributions. We introduce a notion of complexity for probability distributions in terms of their relative density with respect to the standard Gaussian measure. We prove that if the log-relative density can be locally approximated by a neural network whose parameters can be suitably bounded, then the distribution generated by empirical score matching approximates the target distribution in total variation with a dimension-independent rate. We illustrate our theory through examples, which include certain mixtures of Gaussians. An essential ingredient of our proof is to derive a dimension-free deep neural network approximation rate for the true score function associated with the forward process, which is interesting in its own right.

The field of 3D reconstruction from images has rapidly evolved in the past few years, first with the introduction of Neural Radiance Field (NeRF) and more recently with 3D Gaussian Splatting (3DGS). The latter provides a significant edge over NeRF in terms of the training and inference speed, as well as the reconstruction quality. Although 3DGS works well for dense input images, the unstructured point-cloud like representation quickly overfits to the more challenging setup of extremely sparse input images (e.g., 3 images), creating a representation that appears as a jumble of needles from novel views. To address this issue, we propose regularized optimization and depth-based initialization. Our key idea is to introduce a structured Gaussian representation that can be controlled in 2D image space. We then constraint the Gaussians, in particular their position, and prevent them from moving independently during optimization. Specifically, we introduce single and multiview constraints through an implicit convolutional decoder and a total variation loss, respectively. With the coherency introduced to the Gaussians, we further constrain the optimization through a flow-based loss function. To support our regularized optimization, we propose an approach to initialize the Gaussians using monocular depth estimates at each input view. We demonstrate significant improvements compared to the state-of-the-art sparse-view NeRF-based approaches on a variety of scenes.

In learned image compression, probabilistic models play an essential role in characterizing the distribution of latent variables. The Gaussian model with mean and scale parameters has been widely used for its simplicity and effectiveness. Probabilistic models with more parameters, such as the Gaussian mixture models, can fit the distribution of latent variables more precisely, but the corresponding complexity will also be higher. To balance between compression performance and complexity, we extend the Gaussian model to the generalized Gaussian model for more flexible latent distribution modeling, introducing only one additional shape parameter, beta, than the Gaussian model. To enhance the performance of the generalized Gaussian model by alleviating the train-test mismatch, we propose improved training methods, including beta-dependent lower bounds for scale parameters and gradient rectification. Our proposed generalized Gaussian model, coupled with the improved training methods, is demonstrated to outperform the Gaussian and Gaussian mixture models on a variety of learned image compression methods.

Neural Radiance Fields (NeRFs) have demonstrated remarkable potential in capturing complex 3D scenes with high fidelity. However, one persistent challenge that hinders the widespread adoption of NeRFs is the computational bottleneck due to the volumetric rendering. On the other hand, 3D Gaussian splatting (3DGS) has recently emerged as an alternative representation that leverages a 3D Gaussisan-based representation and adopts the rasterization pipeline to render the images rather than volumetric rendering, achieving very fast rendering speed and promising image quality. However, a significant drawback arises as 3DGS entails a substantial number of 3D Gaussians to maintain the high fidelity of the rendered images, which requires a large amount of memory and storage. To address this critical issue, we place a specific emphasis on two key objectives: reducing the number of Gaussian points without sacrificing performance and compressing the Gaussian attributes, such as view-dependent color and covariance. To this end, we propose a learnable mask strategy that significantly reduces the number of Gaussians while preserving high performance. In addition, we propose a compact but effective representation of view-dependent color by employing a grid-based neural field rather than relying on spherical harmonics. Finally, we learn codebooks to compactly represent the geometric attributes of Gaussian by vector quantization. In our extensive experiments, we consistently show over 10times reduced storage and enhanced rendering speed, while maintaining the quality of the scene representation, compared to 3DGS. Our work provides a comprehensive framework for 3D scene representation, achieving high performance, fast training, compactness, and real-time rendering. Our project page is available at https://maincold2.github.io/c3dgs/.

In novel view synthesis of scenes from multiple input views, 3D Gaussian splatting emerges as a viable alternative to existing radiance field approaches, delivering great visual quality and real-time rendering. While successful in static scenes, the present advancement of 3D Gaussian representation, however, faces challenges in dynamic scenes in terms of memory consumption and the need for numerous observations per time step, due to the onus of storing 3D Gaussian parameters per time step. In this study, we present an efficient 3D Gaussian representation tailored for dynamic scenes in which we define positions and rotations as functions of time while leaving other time-invariant properties of the static 3D Gaussian unchanged. Notably, our representation reduces memory usage, which is consistent regardless of the input sequence length. Additionally, it mitigates the risk of overfitting observed frames by accounting for temporal changes. The optimization of our Gaussian representation based on image and flow reconstruction results in a powerful framework for dynamic scene view synthesis in both monocular and multi-view cases. We obtain the highest rendering speed of 118 frames per second (FPS) at a resolution of 1352 times 1014 with a single GPU, showing the practical usability and effectiveness of our proposed method in dynamic scene rendering scenarios.

3D Gaussian Splatting (3DGS) has become an emerging technique with remarkable potential in 3D representation and image rendering. However, the substantial storage overhead of 3DGS significantly impedes its practical applications. In this work, we formulate the compact 3D Gaussian learning as an end-to-end Rate-Distortion Optimization (RDO) problem and propose RDO-Gaussian that can achieve flexible and continuous rate control. RDO-Gaussian addresses two main issues that exist in current schemes: 1) Different from prior endeavors that minimize the rate under the fixed distortion, we introduce dynamic pruning and entropy-constrained vector quantization (ECVQ) that optimize the rate and distortion at the same time. 2) Previous works treat the colors of each Gaussian equally, while we model the colors of different regions and materials with learnable numbers of parameters. We verify our method on both real and synthetic scenes, showcasing that RDO-Gaussian greatly reduces the size of 3D Gaussian over 40x, and surpasses existing methods in rate-distortion performance.

Novel View Synthesis (NVS) from unconstrained photo collections is challenging in computer graphics. Recently, 3D Gaussian Splatting (3DGS) has shown promise for photorealistic and real-time NVS of static scenes. Building on 3DGS, we propose an efficient point-based differentiable rendering framework for scene reconstruction from photo collections. Our key innovation is a residual-based spherical harmonic coefficients transfer module that adapts 3DGS to varying lighting conditions and photometric post-processing. This lightweight module can be pre-computed and ensures efficient gradient propagation from rendered images to 3D Gaussian attributes. Additionally, we observe that the appearance encoder and the transient mask predictor, the two most critical parts of NVS from unconstrained photo collections, can be mutually beneficial. We introduce a plug-and-play lightweight spatial attention module to simultaneously predict transient occluders and latent appearance representation for each image. After training and preprocessing, our method aligns with the standard 3DGS format and rendering pipeline, facilitating seamlessly integration into various 3DGS applications. Extensive experiments on diverse datasets show our approach outperforms existing approaches on the rendering quality of novel view and appearance synthesis with high converge and rendering speed.

In recent times, the generation of 3D assets from text prompts has shown impressive results. Both 2D and 3D diffusion models can generate decent 3D objects based on prompts. 3D diffusion models have good 3D consistency, but their quality and generalization are limited as trainable 3D data is expensive and hard to obtain. 2D diffusion models enjoy strong abilities of generalization and fine generation, but the 3D consistency is hard to guarantee. This paper attempts to bridge the power from the two types of diffusion models via the recent explicit and efficient 3D Gaussian splatting representation. A fast 3D generation framework, named as \name, is proposed, where the 3D diffusion model provides point cloud priors for initialization and the 2D diffusion model enriches the geometry and appearance. Operations of noisy point growing and color perturbation are introduced to enhance the initialized Gaussians. Our \name can generate a high-quality 3D instance within 25 minutes on one GPU, much faster than previous methods, while the generated instances can be directly rendered in real time. Demos and code are available at https://taoranyi.com/gaussiandreamer/.

This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact representation, as data is only stored where details exist. Convolution kernels and data are Gaussian mixtures with unconstrained weights, positions, and covariance matrices. Similar to discrete convolutional networks, each convolution step produces several feature channels, represented by independent Gaussian mixtures. Since traditional transfer functions like ReLUs do not produce Gaussian mixtures, we propose using a fitting of these functions instead. This fitting step also acts as a pooling layer if the number of Gaussian components is reduced appropriately. We demonstrate that networks based on this architecture reach competitive accuracy on Gaussian mixtures fitted to the MNIST and ModelNet data sets.

While 3D Gaussian Splatting has recently become popular for neural rendering, current methods rely on carefully engineered cloning and splitting strategies for placing Gaussians, which can lead to poor-quality renderings, and reliance on a good initialization. In this work, we rethink the set of 3D Gaussians as a random sample drawn from an underlying probability distribution describing the physical representation of the scene-in other words, Markov Chain Monte Carlo (MCMC) samples. Under this view, we show that the 3D Gaussian updates can be converted as Stochastic Gradient Langevin Dynamics (SGLD) updates by simply introducing noise. We then rewrite the densification and pruning strategies in 3D Gaussian Splatting as simply a deterministic state transition of MCMC samples, removing these heuristics from the framework. To do so, we revise the 'cloning' of Gaussians into a relocalization scheme that approximately preserves sample probability. To encourage efficient use of Gaussians, we introduce a regularizer that promotes the removal of unused Gaussians. On various standard evaluation scenes, we show that our method provides improved rendering quality, easy control over the number of Gaussians, and robustness to initialization.

3D Gaussian Splatting has recently emerged as a highly promising technique for modeling of static 3D scenes. In contrast to Neural Radiance Fields, it utilizes efficient rasterization allowing for very fast rendering at high-quality. However, the storage size is significantly higher, which hinders practical deployment, e.g.~on resource constrained devices. In this paper, we introduce a compact scene representation organizing the parameters of 3D Gaussian Splatting (3DGS) into a 2D grid with local homogeneity, ensuring a drastic reduction in storage requirements without compromising visual quality during rendering. Central to our idea is the explicit exploitation of perceptual redundancies present in natural scenes. In essence, the inherent nature of a scene allows for numerous permutations of Gaussian parameters to equivalently represent it. To this end, we propose a novel highly parallel algorithm that regularly arranges the high-dimensional Gaussian parameters into a 2D grid while preserving their neighborhood structure. During training, we further enforce local smoothness between the sorted parameters in the grid. The uncompressed Gaussians use the same structure as 3DGS, ensuring a seamless integration with established renderers. Our method achieves a reduction factor of 8x to 26x in size for complex scenes with no increase in training time, marking a substantial leap forward in the domain of 3D scene distribution and consumption. Additional information can be found on our project page: https://fraunhoferhhi.github.io/Self-Organizing-Gaussians/

We introduce a parametric nonlinear transformation that is well-suited for Gaussianizing data from natural images. The data are linearly transformed, and each component is then normalized by a pooled activity measure, computed by exponentiating a weighted sum of rectified and exponentiated components and a constant. We optimize the parameters of the full transformation (linear transform, exponents, weights, constant) over a database of natural images, directly minimizing the negentropy of the responses. The optimized transformation substantially Gaussianizes the data, achieving a significantly smaller mutual information between transformed components than alternative methods including ICA and radial Gaussianization. The transformation is differentiable and can be efficiently inverted, and thus induces a density model on images. We show that samples of this model are visually similar to samples of natural image patches. We demonstrate the use of the model as a prior probability density that can be used to remove additive noise. Finally, we show that the transformation can be cascaded, with each layer optimized using the same Gaussianization objective, thus offering an unsupervised method of optimizing a deep network architecture.

Modeling animatable human avatars from RGB videos is a long-standing and challenging problem. Recent works usually adopt MLP-based neural radiance fields (NeRF) to represent 3D humans, but it remains difficult for pure MLPs to regress pose-dependent garment details. To this end, we introduce Animatable Gaussians, a new avatar representation that leverages powerful 2D CNNs and 3D Gaussian splatting to create high-fidelity avatars. To associate 3D Gaussians with the animatable avatar, we learn a parametric template from the input videos, and then parameterize the template on two front \& back canonical Gaussian maps where each pixel represents a 3D Gaussian. The learned template is adaptive to the wearing garments for modeling looser clothes like dresses. Such template-guided 2D parameterization enables us to employ a powerful StyleGAN-based CNN to learn the pose-dependent Gaussian maps for modeling detailed dynamic appearances. Furthermore, we introduce a pose projection strategy for better generalization given novel poses. Overall, our method can create lifelike avatars with dynamic, realistic and generalized appearances. Experiments show that our method outperforms other state-of-the-art approaches. Code: https://github.com/lizhe00/AnimatableGaussians

We show that taking the width and depth to infinity in a deep neural network with skip connections, when branches are scaled by 1/depth (the only nontrivial scaling), result in the same covariance structure no matter how that limit is taken. This explains why the standard infinite-width-then-depth approach provides practical insights even for networks with depth of the same order as width. We also demonstrate that the pre-activations, in this case, have Gaussian distributions which has direct applications in Bayesian deep learning. We conduct extensive simulations that show an excellent match with our theoretical findings.

We present latentSplat, a method to predict semantic Gaussians in a 3D latent space that can be splatted and decoded by a light-weight generative 2D architecture. Existing methods for generalizable 3D reconstruction either do not scale to large scenes and resolutions, or are limited to interpolation of close input views. latentSplat combines the strengths of regression-based and generative approaches while being trained purely on readily available real video data. The core of our method are variational 3D Gaussians, a representation that efficiently encodes varying uncertainty within a latent space consisting of 3D feature Gaussians. From these Gaussians, specific instances can be sampled and rendered via efficient splatting and a fast, generative decoder. We show that latentSplat outperforms previous works in reconstruction quality and generalization, while being fast and scalable to high-resolution data.

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However, existing methods are often computationally expensive, or demand costly retraining when priors change, limiting their utility, particularly in sequential inference problems such as real-time sensor fusion. To address these challenges, we introduce the Distribution Transformer -- a novel architecture that can learn arbitrary distribution-to-distribution mappings. Our method can be trained to map a prior to the corresponding posterior, conditioned on some dataset -- thus performing approximate Bayesian inference. Our novel architecture represents a prior distribution as a (universally-approximating) Gaussian Mixture Model (GMM), and transforms it into a GMM representation of the posterior. The components of the GMM attend to each other via self-attention, and to the datapoints via cross-attention. We demonstrate that Distribution Transformers both maintain flexibility to vary the prior, and significantly reduces computation times-from minutes to milliseconds-while achieving log-likelihood performance on par with or superior to existing approximate inference methods across tasks such as sequential inference, quantum system parameter inference, and Gaussian Process predictive posterior inference with hyperpriors.

3D Gaussian Splatting is a new method for modeling and rendering 3D radiance fields that achieves much faster learning and rendering time compared to SOTA NeRF methods. However, it comes with a drawback in the much larger storage demand compared to NeRF methods since it needs to store the parameters for several 3D Gaussians. We notice that many Gaussians may share similar parameters, so we introduce a simple vector quantization method based on \kmeans algorithm to quantize the Gaussian parameters. Then, we store the small codebook along with the index of the code for each Gaussian. Moreover, we compress the indices further by sorting them and using a method similar to run-length encoding. We do extensive experiments on standard benchmarks as well as a new benchmark which is an order of magnitude larger than the standard benchmarks. We show that our simple yet effective method can reduce the storage cost for the original 3D Gaussian Splatting method by a factor of almost 20times with a very small drop in the quality of rendered images.

The recent Gaussian Splatting achieves high-quality and real-time novel-view synthesis of the 3D scenes. However, it is solely concentrated on the appearance and geometry modeling, while lacking in fine-grained object-level scene understanding. To address this issue, we propose Gaussian Grouping, which extends Gaussian Splatting to jointly reconstruct and segment anything in open-world 3D scenes. We augment each Gaussian with a compact Identity Encoding, allowing the Gaussians to be grouped according to their object instance or stuff membership in the 3D scene. Instead of resorting to expensive 3D labels, we supervise the Identity Encodings during the differentiable rendering by leveraging the 2D mask predictions by SAM, along with introduced 3D spatial consistency regularization. Comparing to the implicit NeRF representation, we show that the discrete and grouped 3D Gaussians can reconstruct, segment and edit anything in 3D with high visual quality, fine granularity and efficiency. Based on Gaussian Grouping, we further propose a local Gaussian Editing scheme, which shows efficacy in versatile scene editing applications, including 3D object removal, inpainting, colorization and scene recomposition. Our code and models will be at https://github.com/lkeab/gaussian-grouping.

Open-vocabulary querying in 3D space is challenging but essential for scene understanding tasks such as object localization and segmentation. Language-embedded scene representations have made progress by incorporating language features into 3D spaces. However, their efficacy heavily depends on neural networks that are resource-intensive in training and rendering. Although recent 3D Gaussians offer efficient and high-quality novel view synthesis, directly embedding language features in them leads to prohibitive memory usage and decreased performance. In this work, we introduce Language Embedded 3D Gaussians, a novel scene representation for open-vocabulary query tasks. Instead of embedding high-dimensional raw semantic features on 3D Gaussians, we propose a dedicated quantization scheme that drastically alleviates the memory requirement, and a novel embedding procedure that achieves smoother yet high accuracy query, countering the multi-view feature inconsistencies and the high-frequency inductive bias in point-based representations. Our comprehensive experiments show that our representation achieves the best visual quality and language querying accuracy across current language-embedded representations, while maintaining real-time rendering frame rates on a single desktop GPU.

Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed over non-Euclidean domains, including smooth manifolds appearing in numerous fields such as computer vision, dynamical systems, and neuroscience. However, these approaches assume that the manifold underlying the data is known, limiting their practical utility. We introduce RVGP, a generalisation of GPs for learning vector signals over latent Riemannian manifolds. Our method uses positional encoding with eigenfunctions of the connection Laplacian, associated with the tangent bundle, readily derived from common graph-based approximation of data. We demonstrate that RVGP possesses global regularity over the manifold, which allows it to super-resolve and inpaint vector fields while preserving singularities. Furthermore, we use RVGP to reconstruct high-density neural dynamics derived from low-density EEG recordings in healthy individuals and Alzheimer's patients. We show that vector field singularities are important disease markers and that their reconstruction leads to a comparable classification accuracy of disease states to high-density recordings. Thus, our method overcomes a significant practical limitation in experimental and clinical applications.

A neural architecture with randomly initialized weights, in the infinite width limit, is equivalent to a Gaussian Random Field whose covariance function is the so-called Neural Network Gaussian Process kernel (NNGP). We prove that a reproducing kernel Hilbert space (RKHS) defined by the NNGP contains only functions that can be approximated by the architecture. To achieve a certain approximation error the required number of neurons in each layer is defined by the RKHS norm of the target function. Moreover, the approximation can be constructed from a supervised dataset by a random multi-layer representation of an input vector, together with training of the last layer's weights. For a 2-layer NN and a domain equal to an n-1-dimensional sphere in {mathbb R}^n, we compare the number of neurons required by Barron's theorem and by the multi-layer features construction. We show that if eigenvalues of the integral operator of the NNGP decay slower than k^{-n-2{3}} where k is an order of an eigenvalue, then our theorem guarantees a more succinct neural network approximation than Barron's theorem. We also make some computational experiments to verify our theoretical findings. Our experiments show that realistic neural networks easily learn target functions even when both theorems do not give any guarantees.

Advancements in 3D Gaussian Splatting have significantly accelerated 3D reconstruction and generation. However, it may require a large number of Gaussians, which creates a substantial memory footprint. This paper introduces GES (Generalized Exponential Splatting), a novel representation that employs Generalized Exponential Function (GEF) to model 3D scenes, requiring far fewer particles to represent a scene and thus significantly outperforming Gaussian Splatting methods in efficiency with a plug-and-play replacement ability for Gaussian-based utilities. GES is validated theoretically and empirically in both principled 1D setup and realistic 3D scenes. It is shown to represent signals with sharp edges more accurately, which are typically challenging for Gaussians due to their inherent low-pass characteristics. Our empirical analysis demonstrates that GEF outperforms Gaussians in fitting natural-occurring signals (e.g. squares, triangles, and parabolic signals), thereby reducing the need for extensive splitting operations that increase the memory footprint of Gaussian Splatting. With the aid of a frequency-modulated loss, GES achieves competitive performance in novel-view synthesis benchmarks while requiring less than half the memory storage of Gaussian Splatting and increasing the rendering speed by up to 39%. The code is available on the project website https://abdullahamdi.com/ges .

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

Recently, 3D Gaussian splatting (3D-GS) has achieved great success in reconstructing and rendering real-world scenes. To transfer the high rendering quality to generation tasks, a series of research works attempt to generate 3D-Gaussian assets from text. However, the generated assets have not achieved the same quality as those in reconstruction tasks. We observe that Gaussians tend to grow without control as the generation process may cause indeterminacy. Aiming at highly enhancing the generation quality, we propose a novel framework named GaussianDreamerPro. The main idea is to bind Gaussians to reasonable geometry, which evolves over the whole generation process. Along different stages of our framework, both the geometry and appearance can be enriched progressively. The final output asset is constructed with 3D Gaussians bound to mesh, which shows significantly enhanced details and quality compared with previous methods. Notably, the generated asset can also be seamlessly integrated into downstream manipulation pipelines, e.g. animation, composition, and simulation etc., greatly promoting its potential in wide applications. Demos are available at https://taoranyi.com/gaussiandreamerpro/.

Rendering dynamic scenes from monocular videos is a crucial yet challenging task. The recent deformable Gaussian Splatting has emerged as a robust solution to represent real-world dynamic scenes. However, it often leads to heavily redundant Gaussians, attempting to fit every training view at various time steps, leading to slower rendering speeds. Additionally, the attributes of Gaussians in static areas are time-invariant, making it unnecessary to model every Gaussian, which can cause jittering in static regions. In practice, the primary bottleneck in rendering speed for dynamic scenes is the number of Gaussians. In response, we introduce Efficient Dynamic Gaussian Splatting (EDGS), which represents dynamic scenes via sparse time-variant attribute modeling. Our approach formulates dynamic scenes using a sparse anchor-grid representation, with the motion flow of dense Gaussians calculated via a classical kernel representation. Furthermore, we propose an unsupervised strategy to efficiently filter out anchors corresponding to static areas. Only anchors associated with deformable objects are input into MLPs to query time-variant attributes. Experiments on two real-world datasets demonstrate that our EDGS significantly improves the rendering speed with superior rendering quality compared to previous state-of-the-art methods.

Reconstructing photo-realistic drivable human avatars from multi-view image sequences has been a popular and challenging topic in the field of computer vision and graphics. While existing NeRF-based methods can achieve high-quality novel view rendering of human models, both training and inference processes are time-consuming. Recent approaches have utilized 3D Gaussians to represent the human body, enabling faster training and rendering. However, they undermine the importance of the mesh guidance and directly predict Gaussians in 3D space with coarse mesh guidance. This hinders the learning procedure of the Gaussians and tends to produce blurry textures. Therefore, we propose UV Gaussians, which models the 3D human body by jointly learning mesh deformations and 2D UV-space Gaussian textures. We utilize the embedding of UV map to learn Gaussian textures in 2D space, leveraging the capabilities of powerful 2D networks to extract features. Additionally, through an independent Mesh network, we optimize pose-dependent geometric deformations, thereby guiding Gaussian rendering and significantly enhancing rendering quality. We collect and process a new dataset of human motion, which includes multi-view images, scanned models, parametric model registration, and corresponding texture maps. Experimental results demonstrate that our method achieves state-of-the-art synthesis of novel view and novel pose. The code and data will be made available on the homepage https://alex-jyj.github.io/UV-Gaussians/ once the paper is accepted.

Most advances in 3D Generative Adversarial Networks (3D GANs) largely depend on ray casting-based volume rendering, which incurs demanding rendering costs. One promising alternative is rasterization-based 3D Gaussian Splatting (3D-GS), providing a much faster rendering speed and explicit 3D representation. In this paper, we exploit Gaussian as a 3D representation for 3D GANs by leveraging its efficient and explicit characteristics. However, in an adversarial framework, we observe that a na\"ive generator architecture suffers from training instability and lacks the capability to adjust the scale of Gaussians. This leads to model divergence and visual artifacts due to the absence of proper guidance for initialized positions of Gaussians and densification to manage their scales adaptively. To address these issues, we introduce a generator architecture with a hierarchical multi-scale Gaussian representation that effectively regularizes the position and scale of generated Gaussians. Specifically, we design a hierarchy of Gaussians where finer-level Gaussians are parameterized by their coarser-level counterparts; the position of finer-level Gaussians would be located near their coarser-level counterparts, and the scale would monotonically decrease as the level becomes finer, modeling both coarse and fine details of the 3D scene. Experimental results demonstrate that ours achieves a significantly faster rendering speed (x100) compared to state-of-the-art 3D consistent GANs with comparable 3D generation capability. Project page: https://hse1032.github.io/gsgan.

Gaussian splatting, renowned for its exceptional rendering quality and efficiency, has emerged as a prominent technique in 3D scene representation. However, the substantial data volume of Gaussian splatting impedes its practical utility in real-world applications. Herein, we propose an efficient 3D scene representation, named Compressed Gaussian Splatting (CompGS), which harnesses compact Gaussian primitives for faithful 3D scene modeling with a remarkably reduced data size. To ensure the compactness of Gaussian primitives, we devise a hybrid primitive structure that captures predictive relationships between each other. Then, we exploit a small set of anchor primitives for prediction, allowing the majority of primitives to be encapsulated into highly compact residual forms. Moreover, we develop a rate-constrained optimization scheme to eliminate redundancies within such hybrid primitives, steering our CompGS towards an optimal trade-off between bitrate consumption and representation efficacy. Experimental results show that the proposed CompGS significantly outperforms existing methods, achieving superior compactness in 3D scene representation without compromising model accuracy and rendering quality. Our code will be released on GitHub for further research.

Modeling latent variables with priors and hyperpriors is an essential problem in variational image compression. Formally, trade-off between rate and distortion is handled well if priors and hyperpriors precisely describe latent variables. Current practices only adopt univariate priors and process each variable individually. However, we find inter-correlations and intra-correlations exist when observing latent variables in a vectorized perspective. These findings reveal visual redundancies to improve rate-distortion performance and parallel processing ability to speed up compression. This encourages us to propose a novel vectorized prior. Specifically, a multivariate Gaussian mixture is proposed with means and covariances to be estimated. Then, a novel probabilistic vector quantization is utilized to effectively approximate means, and remaining covariances are further induced to a unified mixture and solved by cascaded estimation without context models involved. Furthermore, codebooks involved in quantization are extended to multi-codebooks for complexity reduction, which formulates an efficient compression procedure. Extensive experiments on benchmark datasets against state-of-the-art indicate our model has better rate-distortion performance and an impressive 3.18times compression speed up, giving us the ability to perform real-time, high-quality variational image compression in practice. Our source code is publicly available at https://github.com/xiaosu-zhu/McQuic.

Reconstructing dynamic objects from monocular videos is a severely underconstrained and challenging problem, and recent work has approached it in various directions. However, owing to the ill-posed nature of this problem, there has been no solution that can provide consistent, high-quality novel views from camera positions that are significantly different from the training views. In this work, we introduce Neural Parametric Gaussians (NPGs) to take on this challenge by imposing a two-stage approach: first, we fit a low-rank neural deformation model, which then is used as regularization for non-rigid reconstruction in the second stage. The first stage learns the object's deformations such that it preserves consistency in novel views. The second stage obtains high reconstruction quality by optimizing 3D Gaussians that are driven by the coarse model. To this end, we introduce a local 3D Gaussian representation, where temporally shared Gaussians are anchored in and deformed by local oriented volumes. The resulting combined model can be rendered as radiance fields, resulting in high-quality photo-realistic reconstructions of the non-rigidly deforming objects, maintaining 3D consistency across novel views. We demonstrate that NPGs achieve superior results compared to previous works, especially in challenging scenarios with few multi-view cues.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

Standard infinite-width limits of neural networks sacrifice the ability for intermediate layers to learn representations from data. Recent work (A theory of representation learning gives a deep generalisation of kernel methods, Yang et al. 2023) modified the Neural Network Gaussian Process (NNGP) limit of Bayesian neural networks so that representation learning is retained. Furthermore, they found that applying this modified limit to a deep Gaussian process gives a practical learning algorithm which they dubbed the deep kernel machine (DKM). However, they only considered the simplest possible setting: regression in small, fully connected networks with e.g. 10 input features. Here, we introduce convolutional deep kernel machines. This required us to develop a novel inter-domain inducing point approximation, as well as introducing and experimentally assessing a number of techniques not previously seen in DKMs, including analogues to batch normalisation, different likelihoods, and different types of top-layer. The resulting model trains in roughly 77 GPU hours, achieving around 99% test accuracy on MNIST, 72% on CIFAR-100, and 92.7% on CIFAR-10, which is SOTA for kernel methods.

We propose a method for dynamic scene reconstruction using deformable 3D Gaussians that is tailored for monocular video. Building upon the efficiency of Gaussian splatting, our approach extends the representation to accommodate dynamic elements via a deformable set of Gaussians residing in a canonical space, and a time-dependent deformation field defined by a multi-layer perceptron (MLP). Moreover, under the assumption that most natural scenes have large regions that remain static, we allow the MLP to focus its representational power by additionally including a static Gaussian point cloud. The concatenated dynamic and static point clouds form the input for the Gaussian Splatting rasterizer, enabling real-time rendering. The differentiable pipeline is optimized end-to-end with a self-supervised rendering loss. Our method achieves results that are comparable to state-of-the-art dynamic neural radiance field methods while allowing much faster optimization and rendering. Project website: https://lynl7130.github.io/gaufre/index.html

There has been a recent surge of interest in modeling neural networks (NNs) as Gaussian processes. In the limit of a NN of infinite width the NN becomes equivalent to a Gaussian process. Here we demonstrate that for an ensemble of large, finite, fully connected networks with a single hidden layer the distribution of outputs at initialization is well described by a Gaussian perturbed by the fourth Hermite polynomial for weights drawn from a symmetric distribution. We show that the scale of the perturbation is inversely proportional to the number of units in the NN and that higher order terms decay more rapidly, thereby recovering the Edgeworth expansion. We conclude by observing that understanding how this perturbation changes under training would reveal the regimes in which the Gaussian process framework is valid to model NN behavior.

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning.

Autoencoders are a popular model in many branches of machine learning and lossy data compression. However, their fundamental limits, the performance of gradient methods and the features learnt during optimization remain poorly understood, even in the two-layer setting. In fact, earlier work has considered either linear autoencoders or specific training regimes (leading to vanishing or diverging compression rates). Our paper addresses this gap by focusing on non-linear two-layer autoencoders trained in the challenging proportional regime in which the input dimension scales linearly with the size of the representation. Our results characterize the minimizers of the population risk, and show that such minimizers are achieved by gradient methods; their structure is also unveiled, thus leading to a concise description of the features obtained via training. For the special case of a sign activation function, our analysis establishes the fundamental limits for the lossy compression of Gaussian sources via (shallow) autoencoders. Finally, while the results are proved for Gaussian data, numerical simulations on standard datasets display the universality of the theoretical predictions.

3D Gaussians have recently emerged as an efficient representation for novel view synthesis. This work studies its editability with a particular focus on the inpainting task, which aims to supplement an incomplete set of 3D Gaussians with additional points for visually harmonious rendering. Compared to 2D inpainting, the crux of inpainting 3D Gaussians is to figure out the rendering-relevant properties of the introduced points, whose optimization largely benefits from their initial 3D positions. To this end, we propose to guide the point initialization with an image-conditioned depth completion model, which learns to directly restore the depth map based on the observed image. Such a design allows our model to fill in depth values at an aligned scale with the original depth, and also to harness strong generalizability from largescale diffusion prior. Thanks to the more accurate depth completion, our approach, dubbed InFusion, surpasses existing alternatives with sufficiently better fidelity and efficiency under various complex scenarios. We further demonstrate the effectiveness of InFusion with several practical applications, such as inpainting with user-specific texture or with novel object insertion.

Videos of robots interacting with objects encode rich information about the objects' dynamics. However, existing video prediction approaches typically do not explicitly account for the 3D information from videos, such as robot actions and objects' 3D states, limiting their use in real-world robotic applications. In this work, we introduce a framework to learn object dynamics directly from multi-view RGB videos by explicitly considering the robot's action trajectories and their effects on scene dynamics. We utilize the 3D Gaussian representation of 3D Gaussian Splatting (3DGS) to train a particle-based dynamics model using Graph Neural Networks. This model operates on sparse control particles downsampled from the densely tracked 3D Gaussian reconstructions. By learning the neural dynamics model on offline robot interaction data, our method can predict object motions under varying initial configurations and unseen robot actions. The 3D transformations of Gaussians can be interpolated from the motions of control particles, enabling the rendering of predicted future object states and achieving action-conditioned video prediction. The dynamics model can also be applied to model-based planning frameworks for object manipulation tasks. We conduct experiments on various kinds of deformable materials, including ropes, clothes, and stuffed animals, demonstrating our framework's ability to model complex shapes and dynamics. Our project page is available at https://gs-dynamics.github.io.

We propose L3DG, the first approach for generative 3D modeling of 3D Gaussians through a latent 3D Gaussian diffusion formulation. This enables effective generative 3D modeling, scaling to generation of entire room-scale scenes which can be very efficiently rendered. To enable effective synthesis of 3D Gaussians, we propose a latent diffusion formulation, operating in a compressed latent space of 3D Gaussians. This compressed latent space is learned by a vector-quantized variational autoencoder (VQ-VAE), for which we employ a sparse convolutional architecture to efficiently operate on room-scale scenes. This way, the complexity of the costly generation process via diffusion is substantially reduced, allowing higher detail on object-level generation, as well as scalability to large scenes. By leveraging the 3D Gaussian representation, the generated scenes can be rendered from arbitrary viewpoints in real-time. We demonstrate that our approach significantly improves visual quality over prior work on unconditional object-level radiance field synthesis and showcase its applicability to room-scale scene generation.

Reconstructing deformable tissues from endoscopic videos is essential in many downstream surgical applications. However, existing methods suffer from slow rendering speed, greatly limiting their practical use. In this paper, we introduce EndoGaussian, a real-time endoscopic scene reconstruction framework built on 3D Gaussian Splatting (3DGS). By integrating the efficient Gaussian representation and highly-optimized rendering engine, our framework significantly boosts the rendering speed to a real-time level. To adapt 3DGS for endoscopic scenes, we propose two strategies, Holistic Gaussian Initialization (HGI) and Spatio-temporal Gaussian Tracking (SGT), to handle the non-trivial Gaussian initialization and tissue deformation problems, respectively. In HGI, we leverage recent depth estimation models to predict depth maps of input binocular/monocular image sequences, based on which pixels are re-projected and combined for holistic initialization. In SPT, we propose to model surface dynamics using a deformation field, which is composed of an efficient encoding voxel and a lightweight deformation decoder, allowing for Gaussian tracking with minor training and rendering burden. Experiments on public datasets demonstrate our efficacy against prior SOTAs in many aspects, including better rendering speed (195 FPS real-time, 100times gain), better rendering quality (37.848 PSNR), and less training overhead (within 2 min/scene), showing significant promise for intraoperative surgery applications. Code is available at: https://yifliu3.github.io/EndoGaussian/.

Recent 3D large reconstruction models (LRMs) can generate high-quality 3D content in sub-seconds by integrating multi-view diffusion models with scalable multi-view reconstructors. Current works further leverage 3D Gaussian Splatting as 3D representation for improved visual quality and rendering efficiency. However, we observe that existing Gaussian reconstruction models often suffer from multi-view inconsistency and blurred textures. We attribute this to the compromise of multi-view information propagation in favor of adopting powerful yet computationally intensive architectures (e.g., Transformers). To address this issue, we introduce MVGamba, a general and lightweight Gaussian reconstruction model featuring a multi-view Gaussian reconstructor based on the RNN-like State Space Model (SSM). Our Gaussian reconstructor propagates causal context containing multi-view information for cross-view self-refinement while generating a long sequence of Gaussians for fine-detail modeling with linear complexity. With off-the-shelf multi-view diffusion models integrated, MVGamba unifies 3D generation tasks from a single image, sparse images, or text prompts. Extensive experiments demonstrate that MVGamba outperforms state-of-the-art baselines in all 3D content generation scenarios with approximately only 0.1times of the model size.

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student t mixture or Gaussian mixture. We apply the inverse Fourier transform to obtain the covariance function (by Wiener-Khinchin theorem). The covariance derived from the Gaussian mixture spectrum corresponds to the known spectral mixture kernel. Next, we estimate the mixture weights in the log domain, which we show is equivalent to placing a Jeffreys prior. It automatically induces sparsity, prunes excessive frequencies, and adjusts the remaining toward the ground truth. Third, to enable efficient and scalable computation on massive collocation points, which are critical to capture high frequencies, we place the collocation points on a grid, and multiply our covariance function at each input dimension. We use the GP conditional mean to predict the solution and its derivatives so as to fit the boundary condition and the equation itself. As a result, we can derive a Kronecker product structure in the covariance matrix. We use Kronecker product properties and multilinear algebra to promote computational efficiency and scalability, without low-rank approximations. We show the advantage of our method in systematic experiments. The code is released at https://github.com/xuangu-fang/Gaussian-Process-Slover-for-High-Freq-PDE.

This paper presents a Surface-Aligned Gaussian representation for creating animatable human avatars from monocular videos,aiming at improving the novel view and pose synthesis performance while ensuring fast training and real-time rendering. Recently,3DGS has emerged as a more efficient and expressive alternative to NeRF, and has been used for creating dynamic human avatars. However,when applied to the severely ill-posed task of monocular dynamic reconstruction, the Gaussians tend to overfit the constantly changing regions such as clothes wrinkles or shadows since these regions cannot provide consistent supervision, resulting in noisy geometry and abrupt deformation that typically fail to generalize under novel views and poses.To address these limitations, we present SAGA,i.e.,Surface-Aligned Gaussian Avatar,which aligns the Gaussians with a mesh to enforce well-defined geometry and consistent deformation, thereby improving generalization under novel views and poses. Unlike existing strict alignment methods that suffer from limited expressive power and low realism,SAGA employs a two-stage alignment strategy where the Gaussians are first adhered on while then detached from the mesh, thus facilitating both good geometry and high expressivity. In the Adhered Stage, we improve the flexibility of Adhered-on-Mesh Gaussians by allowing them to flow on the mesh, in contrast to existing methods that rigidly bind Gaussians to fixed location. In the second Detached Stage, we introduce a Gaussian-Mesh Alignment regularization, which allows us to unleash the expressivity by detaching the Gaussians but maintain the geometric alignment by minimizing their location and orientation offsets from the bound triangles. Finally, since the Gaussians may drift outside the bound triangles during optimization, an efficient Walking-on-Mesh strategy is proposed to dynamically update the bound triangles.

The field of novel-view synthesis has recently witnessed the emergence of 3D Gaussian Splatting, which represents scenes in a point-based manner and renders through rasterization. This methodology, in contrast to Radiance Fields that rely on ray tracing, demonstrates superior rendering quality and speed. However, the explicit and unstructured nature of 3D Gaussians poses a significant storage challenge, impeding its broader application. To address this challenge, we introduce the Gaussian-Forest modeling framework, which hierarchically represents a scene as a forest of hybrid 3D Gaussians. Each hybrid Gaussian retains its unique explicit attributes while sharing implicit ones with its sibling Gaussians, thus optimizing parameterization with significantly fewer variables. Moreover, adaptive growth and pruning strategies are designed, ensuring detailed representation in complex regions and a notable reduction in the number of required Gaussians. Extensive experiments demonstrate that Gaussian-Forest not only maintains comparable speed and quality but also achieves a compression rate surpassing 10 times, marking a significant advancement in efficient scene modeling. Codes will be available at https://github.com/Xian-Bei/GaussianForest.

3D content creation has achieved significant progress in terms of both quality and speed. Although current feed-forward models can produce 3D objects in seconds, their resolution is constrained by the intensive computation required during training. In this paper, we introduce Large Multi-View Gaussian Model (LGM), a novel framework designed to generate high-resolution 3D models from text prompts or single-view images. Our key insights are two-fold: 1) 3D Representation: We propose multi-view Gaussian features as an efficient yet powerful representation, which can then be fused together for differentiable rendering. 2) 3D Backbone: We present an asymmetric U-Net as a high-throughput backbone operating on multi-view images, which can be produced from text or single-view image input by leveraging multi-view diffusion models. Extensive experiments demonstrate the high fidelity and efficiency of our approach. Notably, we maintain the fast speed to generate 3D objects within 5 seconds while boosting the training resolution to 512, thereby achieving high-resolution 3D content generation.

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the high-dimensional regime. Motivated by the recent stream of results on the Gaussian universality of the test and training errors in generalized linear estimation, we ask ourselves the question: "when is a single Gaussian enough to characterize the error?". Our formula allow us to give sharp answers to this question, both in the positive and negative directions. More precisely, we show that the sufficient conditions for Gaussian universality (or lack of thereof) crucially depend on the alignment between the target weights and the means and covariances of the mixture clusters, which we precisely quantify. In the particular case of least-squares interpolation, we prove a strong universality property of the training error, and show it follows a simple, closed-form expression. Finally, we apply our results to real datasets, clarifying some recent discussion in the literature about Gaussian universality of the errors in this context.

We have recently seen tremendous progress in photo-real human modeling and rendering. Yet, efficiently rendering realistic human performance and integrating it into the rasterization pipeline remains challenging. In this paper, we present HiFi4G, an explicit and compact Gaussian-based approach for high-fidelity human performance rendering from dense footage. Our core intuition is to marry the 3D Gaussian representation with non-rigid tracking, achieving a compact and compression-friendly representation. We first propose a dual-graph mechanism to obtain motion priors, with a coarse deformation graph for effective initialization and a fine-grained Gaussian graph to enforce subsequent constraints. Then, we utilize a 4D Gaussian optimization scheme with adaptive spatial-temporal regularizers to effectively balance the non-rigid prior and Gaussian updating. We also present a companion compression scheme with residual compensation for immersive experiences on various platforms. It achieves a substantial compression rate of approximately 25 times, with less than 2MB of storage per frame. Extensive experiments demonstrate the effectiveness of our approach, which significantly outperforms existing approaches in terms of optimization speed, rendering quality, and storage overhead.

This manuscript considers the problem of learning a random Gaussian network function using a fully connected network with frozen intermediate layers and trainable readout layer. This problem can be seen as a natural generalization of the widely studied random features model to deeper architectures. First, we prove Gaussian universality of the test error in a ridge regression setting where the learner and target networks share the same intermediate layers, and provide a sharp asymptotic formula for it. Establishing this result requires proving a deterministic equivalent for traces of the deep random features sample covariance matrices which can be of independent interest. Second, we conjecture the asymptotic Gaussian universality of the test error in the more general setting of arbitrary convex losses and generic learner/target architectures. We provide extensive numerical evidence for this conjecture, which requires the derivation of closed-form expressions for the layer-wise post-activation population covariances. In light of our results, we investigate the interplay between architecture design and implicit regularization.

Representation learning has significantly driven the field to develop pretrained models that can act as a valuable starting point when transferring to new datasets. With the rising demand for reliable machine learning and uncertainty quantification, there is a need for pretrained models that not only provide embeddings but also transferable uncertainty estimates. To guide the development of such models, we propose the Uncertainty-aware Representation Learning (URL) benchmark. Besides the transferability of the representations, it also measures the zero-shot transferability of the uncertainty estimate using a novel metric. We apply URL to evaluate eleven uncertainty quantifiers that are pretrained on ImageNet and transferred to eight downstream datasets. We find that approaches that focus on the uncertainty of the representation itself or estimate the prediction risk directly outperform those that are based on the probabilities of upstream classes. Yet, achieving transferable uncertainty quantification remains an open challenge. Our findings indicate that it is not necessarily in conflict with traditional representation learning goals. Code is provided under https://github.com/mkirchhof/url .

Recent works have revealed that infinitely-wide feed-forward or recurrent neural networks of any architecture correspond to Gaussian processes referred to as Neural Network Gaussian Processes (NNGPs). While these works have extended the class of neural networks converging to Gaussian processes significantly, however, there has been little focus on broadening the class of stochastic processes that such neural networks converge to. In this work, inspired by the scale mixture of Gaussian random variables, we propose the scale mixture of NNGPs for which we introduce a prior distribution on the scale of the last-layer parameters. We show that simply introducing a scale prior on the last-layer parameters can turn infinitely-wide neural networks of any architecture into a richer class of stochastic processes. With certain scale priors, we obtain heavy-tailed stochastic processes, and in the case of inverse gamma priors, we recover Student's t processes. We further analyze the distributions of the neural networks initialized with our prior setting and trained with gradient descents and obtain similar results as for NNGPs. We present a practical posterior-inference algorithm for the scale mixture of NNGPs and empirically demonstrate its usefulness on regression and classification tasks. In particular, we show that in both tasks, the heavy-tailed stochastic processes obtained from our framework are robust to out-of-distribution data.

While neural rendering has demonstrated impressive capabilities in 3D scene reconstruction and novel view synthesis, it heavily relies on high-quality sharp images and accurate camera poses. Numerous approaches have been proposed to train Neural Radiance Fields (NeRF) with motion-blurred images, commonly encountered in real-world scenarios such as low-light or long-exposure conditions. However, the implicit representation of NeRF struggles to accurately recover intricate details from severely motion-blurred images and cannot achieve real-time rendering. In contrast, recent advancements in 3D Gaussian Splatting achieve high-quality 3D scene reconstruction and real-time rendering by explicitly optimizing point clouds as Gaussian spheres. In this paper, we introduce a novel approach, named BAD-Gaussians (Bundle Adjusted Deblur Gaussian Splatting), which leverages explicit Gaussian representation and handles severe motion-blurred images with inaccurate camera poses to achieve high-quality scene reconstruction. Our method models the physical image formation process of motion-blurred images and jointly learns the parameters of Gaussians while recovering camera motion trajectories during exposure time. In our experiments, we demonstrate that BAD-Gaussians not only achieves superior rendering quality compared to previous state-of-the-art deblur neural rendering methods on both synthetic and real datasets but also enables real-time rendering capabilities. Our project page and source code is available at https://lingzhezhao.github.io/BAD-Gaussians/

We present GALA3D, generative 3D GAussians with LAyout-guided control, for effective compositional text-to-3D generation. We first utilize large language models (LLMs) to generate the initial layout and introduce a layout-guided 3D Gaussian representation for 3D content generation with adaptive geometric constraints. We then propose an object-scene compositional optimization mechanism with conditioned diffusion to collaboratively generate realistic 3D scenes with consistent geometry, texture, scale, and accurate interactions among multiple objects while simultaneously adjusting the coarse layout priors extracted from the LLMs to align with the generated scene. Experiments show that GALA3D is a user-friendly, end-to-end framework for state-of-the-art scene-level 3D content generation and controllable editing while ensuring the high fidelity of object-level entities within the scene. Source codes and models will be available at https://gala3d.github.io/.

Precise camera tracking, high-fidelity 3D tissue reconstruction, and real-time online visualization are critical for intrabody medical imaging devices such as endoscopes and capsule robots. However, existing SLAM (Simultaneous Localization and Mapping) methods often struggle to achieve both complete high-quality surgical field reconstruction and efficient computation, restricting their intraoperative applications among endoscopic surgeries. In this paper, we introduce EndoGSLAM, an efficient SLAM approach for endoscopic surgeries, which integrates streamlined Gaussian representation and differentiable rasterization to facilitate over 100 fps rendering speed during online camera tracking and tissue reconstructing. Extensive experiments show that EndoGSLAM achieves a better trade-off between intraoperative availability and reconstruction quality than traditional or neural SLAM approaches, showing tremendous potential for endoscopic surgeries. The project page is at https://EndoGSLAM.loping151.com

Reconstructing and rendering 3D objects from highly sparse views is of critical importance for promoting applications of 3D vision techniques and improving user experience. However, images from sparse views only contain very limited 3D information, leading to two significant challenges: 1) Difficulty in building multi-view consistency as images for matching are too few; 2) Partially omitted or highly compressed object information as view coverage is insufficient. To tackle these challenges, we propose GaussianObject, a framework to represent and render the 3D object with Gaussian splatting, that achieves high rendering quality with only 4 input images. We first introduce techniques of visual hull and floater elimination which explicitly inject structure priors into the initial optimization process for helping build multi-view consistency, yielding a coarse 3D Gaussian representation. Then we construct a Gaussian repair model based on diffusion models to supplement the omitted object information, where Gaussians are further refined. We design a self-generating strategy to obtain image pairs for training the repair model. Our GaussianObject is evaluated on several challenging datasets, including MipNeRF360, OmniObject3D, and OpenIllumination, achieving strong reconstruction results from only 4 views and significantly outperforming previous state-of-the-art methods.

Constructing a 3D scene capable of accommodating open-ended language queries, is a pivotal pursuit, particularly within the domain of robotics. Such technology facilitates robots in executing object manipulations based on human language directives. To tackle this challenge, some research efforts have been dedicated to the development of language-embedded implicit fields. However, implicit fields (e.g. NeRF) encounter limitations due to the necessity of processing a large number of input views for reconstruction, coupled with their inherent inefficiencies in inference. Thus, we present the GaussianGrasper, which utilizes 3D Gaussian Splatting to explicitly represent the scene as a collection of Gaussian primitives. Our approach takes a limited set of RGB-D views and employs a tile-based splatting technique to create a feature field. In particular, we propose an Efficient Feature Distillation (EFD) module that employs contrastive learning to efficiently and accurately distill language embeddings derived from foundational models. With the reconstructed geometry of the Gaussian field, our method enables the pre-trained grasping model to generate collision-free grasp pose candidates. Furthermore, we propose a normal-guided grasp module to select the best grasp pose. Through comprehensive real-world experiments, we demonstrate that GaussianGrasper enables robots to accurately query and grasp objects with language instructions, providing a new solution for language-guided manipulation tasks. Data and codes can be available at https://github.com/MrSecant/GaussianGrasper.

3D Gaussian splatting (3DGS) has recently emerged as an alternative representation that leverages a 3D Gaussian-based representation and introduces an approximated volumetric rendering, achieving very fast rendering speed and promising image quality. Furthermore, subsequent studies have successfully extended 3DGS to dynamic 3D scenes, demonstrating its wide range of applications. However, a significant drawback arises as 3DGS and its following methods entail a substantial number of Gaussians to maintain the high fidelity of the rendered images, which requires a large amount of memory and storage. To address this critical issue, we place a specific emphasis on two key objectives: reducing the number of Gaussian points without sacrificing performance and compressing the Gaussian attributes, such as view-dependent color and covariance. To this end, we propose a learnable mask strategy that significantly reduces the number of Gaussians while preserving high performance. In addition, we propose a compact but effective representation of view-dependent color by employing a grid-based neural field rather than relying on spherical harmonics. Finally, we learn codebooks to compactly represent the geometric and temporal attributes by residual vector quantization. With model compression techniques such as quantization and entropy coding, we consistently show over 25x reduced storage and enhanced rendering speed compared to 3DGS for static scenes, while maintaining the quality of the scene representation. For dynamic scenes, our approach achieves more than 12x storage efficiency and retains a high-quality reconstruction compared to the existing state-of-the-art methods. Our work provides a comprehensive framework for 3D scene representation, achieving high performance, fast training, compactness, and real-time rendering. Our project page is available at https://maincold2.github.io/c3dgs/.

Generating high-quality 3D content requires models capable of learning robust distributions of complex scenes and the real-world objects within them. Recent Gaussian-based 3D reconstruction techniques have achieved impressive results in recovering high-fidelity 3D assets from sparse input images by predicting 3D Gaussians in a feed-forward manner. However, these techniques often lack the extensive priors and expressiveness offered by Diffusion Models. On the other hand, 2D Diffusion Models, which have been successfully applied to denoise multiview images, show potential for generating a wide range of photorealistic 3D outputs but still fall short on explicit 3D priors and consistency. In this work, we aim to bridge these two approaches by introducing DSplats, a novel method that directly denoises multiview images using Gaussian Splat-based Reconstructors to produce a diverse array of realistic 3D assets. To harness the extensive priors of 2D Diffusion Models, we incorporate a pretrained Latent Diffusion Model into the reconstructor backbone to predict a set of 3D Gaussians. Additionally, the explicit 3D representation embedded in the denoising network provides a strong inductive bias, ensuring geometrically consistent novel view generation. Our qualitative and quantitative experiments demonstrate that DSplats not only produces high-quality, spatially consistent outputs, but also sets a new standard in single-image to 3D reconstruction. When evaluated on the Google Scanned Objects dataset, DSplats achieves a PSNR of 20.38, an SSIM of 0.842, and an LPIPS of 0.109.

In this paper, we contend that the objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a mixture of low-dimensional Gaussian distributions supported on incoherent subspaces. The quality of the final representation can be measured by a unified objective function called sparse rate reduction. From this perspective, popular deep networks such as transformers can be naturally viewed as realizing iterative schemes to optimize this objective incrementally. Particularly, we show that the standard transformer block can be derived from alternating optimization on complementary parts of this objective: the multi-head self-attention operator can be viewed as a gradient descent step to compress the token sets by minimizing their lossy coding rate, and the subsequent multi-layer perceptron can be viewed as attempting to sparsify the representation of the tokens. This leads to a family of white-box transformer-like deep network architectures which are mathematically fully interpretable. Despite their simplicity, experiments show that these networks indeed learn to optimize the designed objective: they compress and sparsify representations of large-scale real-world vision datasets such as ImageNet, and achieve performance very close to thoroughly engineered transformers such as ViT. Code is at https://github.com/Ma-Lab-Berkeley/CRATE.

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package.

By equipping the most recent 3D Gaussian Splatting representation with head 3D morphable models (3DMM), existing methods manage to create head avatars with high fidelity. However, most existing methods only reconstruct a head without the body, substantially limiting their application scenarios. We found that naively applying Gaussians to model the clothed chest and shoulders tends to result in blurry reconstruction and noisy floaters under novel poses. This is because of the fundamental limitation of Gaussians and point clouds -- each Gaussian or point can only have a single directional radiance without spatial variance, therefore an unnecessarily large number of them is required to represent complicated spatially varying texture, even for simple geometry. In contrast, we propose to model the body part with a neural texture that consists of coarse and pose-dependent fine colors. To properly render the body texture for each view and pose without accurate geometry nor UV mapping, we optimize another sparse set of Gaussians as anchors that constrain the neural warping field that maps image plane coordinates to the texture space. We demonstrate that Gaussian Head & Shoulders can fit the high-frequency details on the clothed upper body with high fidelity and potentially improve the accuracy and fidelity of the head region. We evaluate our method with casual phone-captured and internet videos and show our method archives superior reconstruction quality and robustness in both self and cross reenactment tasks. To fully utilize the efficient rendering speed of Gaussian splatting, we additionally propose an accelerated inference method of our trained model without Multi-Layer Perceptron (MLP) queries and reach a stable rendering speed of around 130 FPS for any subjects.

We introduce RMAvatar, a novel human avatar representation with Gaussian splatting embedded on mesh to learn clothed avatar from a monocular video. We utilize the explicit mesh geometry to represent motion and shape of a virtual human and implicit appearance rendering with Gaussian Splatting. Our method consists of two main modules: Gaussian initialization module and Gaussian rectification module. We embed Gaussians into triangular faces and control their motion through the mesh, which ensures low-frequency motion and surface deformation of the avatar. Due to the limitations of LBS formula, the human skeleton is hard to control complex non-rigid transformations. We then design a pose-related Gaussian rectification module to learn fine-detailed non-rigid deformations, further improving the realism and expressiveness of the avatar. We conduct extensive experiments on public datasets, RMAvatar shows state-of-the-art performance on both rendering quality and quantitative evaluations. Please see our project page at https://rm-avatar.github.io.

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at https://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition.

We present SplattingAvatar, a hybrid 3D representation of photorealistic human avatars with Gaussian Splatting embedded on a triangle mesh, which renders over 300 FPS on a modern GPU and 30 FPS on a mobile device. We disentangle the motion and appearance of a virtual human with explicit mesh geometry and implicit appearance modeling with Gaussian Splatting. The Gaussians are defined by barycentric coordinates and displacement on a triangle mesh as Phong surfaces. We extend lifted optimization to simultaneously optimize the parameters of the Gaussians while walking on the triangle mesh. SplattingAvatar is a hybrid representation of virtual humans where the mesh represents low-frequency motion and surface deformation, while the Gaussians take over the high-frequency geometry and detailed appearance. Unlike existing deformation methods that rely on an MLP-based linear blend skinning (LBS) field for motion, we control the rotation and translation of the Gaussians directly by mesh, which empowers its compatibility with various animation techniques, e.g., skeletal animation, blend shapes, and mesh editing. Trainable from monocular videos for both full-body and head avatars, SplattingAvatar shows state-of-the-art rendering quality across multiple datasets.

Dictionary learning is a classic representation learning method that has been widely applied in signal processing and data analytics. In this paper, we investigate a family of ell_p-norm (p>2,p in N) maximization approaches for the complete dictionary learning problem from theoretical and algorithmic aspects. Specifically, we prove that the global maximizers of these formulations are very close to the true dictionary with high probability, even when Gaussian noise is present. Based on the generalized power method (GPM), an efficient algorithm is then developed for the ell_p-based formulations. We further show the efficacy of the developed algorithm: for the population GPM algorithm over the sphere constraint, it first quickly enters the neighborhood of a global maximizer, and then converges linearly in this region. Extensive experiments will demonstrate that the ell_p-based approaches enjoy a higher computational efficiency and better robustness than conventional approaches and p=3 performs the best.

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

In this paper, we contend that a natural objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a low-dimensional Gaussian mixture supported on incoherent subspaces. The goodness of such a representation can be evaluated by a principled measure, called sparse rate reduction, that simultaneously maximizes the intrinsic information gain and extrinsic sparsity of the learned representation. From this perspective, popular deep network architectures, including transformers, can be viewed as realizing iterative schemes to optimize this measure. Particularly, we derive a transformer block from alternating optimization on parts of this objective: the multi-head self-attention operator compresses the representation by implementing an approximate gradient descent step on the coding rate of the features, and the subsequent multi-layer perceptron sparsifies the features. This leads to a family of white-box transformer-like deep network architectures, named CRATE, which are mathematically fully interpretable. We show, by way of a novel connection between denoising and compression, that the inverse to the aforementioned compressive encoding can be realized by the same class of CRATE architectures. Thus, the so-derived white-box architectures are universal to both encoders and decoders. Experiments show that these networks, despite their simplicity, indeed learn to compress and sparsify representations of large-scale real-world image and text datasets, and achieve performance very close to highly engineered transformer-based models: ViT, MAE, DINO, BERT, and GPT2. We believe the proposed computational framework demonstrates great potential in bridging the gap between theory and practice of deep learning, from a unified perspective of data compression. Code is available at: https://ma-lab-berkeley.github.io/CRATE .

Recently, 3D Gaussian Splatting, as a novel 3D representation, has garnered attention for its fast rendering speed and high rendering quality. However, this comes with high memory consumption, e.g., a well-trained Gaussian field may utilize three million Gaussian primitives and over 700 MB of memory. We credit this high memory footprint to the lack of consideration for the relationship between primitives. In this paper, we propose a memory-efficient Gaussian field named SUNDAE with spectral pruning and neural compensation. On one hand, we construct a graph on the set of Gaussian primitives to model their relationship and design a spectral down-sampling module to prune out primitives while preserving desired signals. On the other hand, to compensate for the quality loss of pruning Gaussians, we exploit a lightweight neural network head to mix splatted features, which effectively compensates for quality losses while capturing the relationship between primitives in its weights. We demonstrate the performance of SUNDAE with extensive results. For example, SUNDAE can achieve 26.80 PSNR at 145 FPS using 104 MB memory while the vanilla Gaussian splatting algorithm achieves 25.60 PSNR at 160 FPS using 523 MB memory, on the Mip-NeRF360 dataset. Codes are publicly available at https://runyiyang.github.io/projects/SUNDAE/.

Novel view synthesis of dynamic scenes has been an intriguing yet challenging problem. Despite recent advancements, simultaneously achieving high-resolution photorealistic results, real-time rendering, and compact storage remains a formidable task. To address these challenges, we propose Spacetime Gaussian Feature Splatting as a novel dynamic scene representation, composed of three pivotal components. First, we formulate expressive Spacetime Gaussians by enhancing 3D Gaussians with temporal opacity and parametric motion/rotation. This enables Spacetime Gaussians to capture static, dynamic, as well as transient content within a scene. Second, we introduce splatted feature rendering, which replaces spherical harmonics with neural features. These features facilitate the modeling of view- and time-dependent appearance while maintaining small size. Third, we leverage the guidance of training error and coarse depth to sample new Gaussians in areas that are challenging to converge with existing pipelines. Experiments on several established real-world datasets demonstrate that our method achieves state-of-the-art rendering quality and speed, while retaining compact storage. At 8K resolution, our lite-version model can render at 60 FPS on an Nvidia RTX 4090 GPU.

Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural images are highly non-Gaussian so that GMM cannot be applied to perform clustering task on pixel space. To overcome such limitation, we propose a GAN based EM learning framework that can maximize the likelihood of images and estimate the latent variables with only the constraint of L-Lipschitz continuity. We call this model GAN-EM, which is a framework for image clustering, semi-supervised classification and dimensionality reduction. In M-step, we design a novel loss function for discriminator of GAN to perform maximum likelihood estimation (MLE) on data with soft class label assignments. Specifically, a conditional generator captures data distribution for K classes, and a discriminator tells whether a sample is real or fake for each class. Since our model is unsupervised, the class label of real data is regarded as latent variable, which is estimated by an additional network (E-net) in E-step. The proposed GAN-EM achieves state-of-the-art clustering and semi-supervised classification results on MNIST, SVHN and CelebA, as well as comparable quality of generated images to other recently developed generative models.

Recently, impressive results have been achieved in 3D scene editing with text instructions based on a 2D diffusion model. However, current diffusion models primarily generate images by predicting noise in the latent space, and the editing is usually applied to the whole image, which makes it challenging to perform delicate, especially localized, editing for 3D scenes. Inspired by recent 3D Gaussian splatting, we propose a systematic framework, named GaussianEditor, to edit 3D scenes delicately via 3D Gaussians with text instructions. Benefiting from the explicit property of 3D Gaussians, we design a series of techniques to achieve delicate editing. Specifically, we first extract the region of interest (RoI) corresponding to the text instruction, aligning it to 3D Gaussians. The Gaussian RoI is further used to control the editing process. Our framework can achieve more delicate and precise editing of 3D scenes than previous methods while enjoying much faster training speed, i.e. within 20 minutes on a single V100 GPU, more than twice as fast as Instruct-NeRF2NeRF (45 minutes -- 2 hours).

3D Gaussian Splatting (GS) have achieved considerable improvement over Neural Radiance Fields in terms of 3D fitting fidelity and rendering speed. However, this unstructured representation with scattered Gaussians poses a significant challenge for generative modeling. To address the problem, we introduce GaussianCube, a structured GS representation that is both powerful and efficient for generative modeling. We achieve this by first proposing a modified densification-constrained GS fitting algorithm which can yield high-quality fitting results using a fixed number of free Gaussians, and then re-arranging the Gaussians into a predefined voxel grid via Optimal Transport. The structured grid representation allows us to use standard 3D U-Net as our backbone in diffusion generative modeling without elaborate designs. Extensive experiments conducted on ShapeNet and OmniObject3D show that our model achieves state-of-the-art generation results both qualitatively and quantitatively, underscoring the potential of GaussianCube as a powerful and versatile 3D representation.

Recently, 3D Gaussian splatting (3D-GS) has gained popularity in novel-view scene synthesis. It addresses the challenges of lengthy training times and slow rendering speeds associated with Neural Radiance Fields (NeRFs). Through rapid, differentiable rasterization of 3D Gaussians, 3D-GS achieves real-time rendering and accelerated training. They, however, demand substantial memory resources for both training and storage, as they require millions of Gaussians in their point cloud representation for each scene. We present a technique utilizing quantized embeddings to significantly reduce memory storage requirements and a coarse-to-fine training strategy for a faster and more stable optimization of the Gaussian point clouds. Our approach results in scene representations with fewer Gaussians and quantized representations, leading to faster training times and rendering speeds for real-time rendering of high resolution scenes. We reduce memory by more than an order of magnitude all while maintaining the reconstruction quality. We validate the effectiveness of our approach on a variety of datasets and scenes preserving the visual quality while consuming 10-20x less memory and faster training/inference speed. Project page and code is available https://efficientgaussian.github.io

Despite much progress, achieving real-time high-fidelity head avatar animation is still difficult and existing methods have to trade-off between speed and quality. 3DMM based methods often fail to model non-facial structures such as eyeglasses and hairstyles, while neural implicit models suffer from deformation inflexibility and rendering inefficiency. Although 3D Gaussian has been demonstrated to possess promising capability for geometry representation and radiance field reconstruction, applying 3D Gaussian in head avatar creation remains a major challenge since it is difficult for 3D Gaussian to model the head shape variations caused by changing poses and expressions. In this paper, we introduce PSAvatar, a novel framework for animatable head avatar creation that utilizes discrete geometric primitive to create a parametric morphable shape model and employs 3D Gaussian for fine detail representation and high fidelity rendering. The parametric morphable shape model is a Point-based Morphable Shape Model (PMSM) which uses points instead of meshes for 3D representation to achieve enhanced representation flexibility. The PMSM first converts the FLAME mesh to points by sampling on the surfaces as well as off the meshes to enable the reconstruction of not only surface-like structures but also complex geometries such as eyeglasses and hairstyles. By aligning these points with the head shape in an analysis-by-synthesis manner, the PMSM makes it possible to utilize 3D Gaussian for fine detail representation and appearance modeling, thus enabling the creation of high-fidelity avatars. We show that PSAvatar can reconstruct high-fidelity head avatars of a variety of subjects and the avatars can be animated in real-time (ge 25 fps at a resolution of 512 times 512 ).

In crowd counting, each training image contains multiple people, where each person is annotated by a dot. Existing crowd counting methods need to use a Gaussian to smooth each annotated dot or to estimate the likelihood of every pixel given the annotated point. In this paper, we show that imposing Gaussians to annotations hurts generalization performance. Instead, we propose to use Distribution Matching for crowd COUNTing (DM-Count). In DM-Count, we use Optimal Transport (OT) to measure the similarity between the normalized predicted density map and the normalized ground truth density map. To stabilize OT computation, we include a Total Variation loss in our model. We show that the generalization error bound of DM-Count is tighter than that of the Gaussian smoothed methods. In terms of Mean Absolute Error, DM-Count outperforms the previous state-of-the-art methods by a large margin on two large-scale counting datasets, UCF-QNRF and NWPU, and achieves the state-of-the-art results on the ShanghaiTech and UCF-CC50 datasets. DM-Count reduced the error of the state-of-the-art published result by approximately 16%. Code is available at https://github.com/cvlab-stonybrook/DM-Count.

Coordinate-based neural representations have shown significant promise as an alternative to discrete, array-based representations for complex low dimensional signals. However, optimizing a coordinate-based network from randomly initialized weights for each new signal is inefficient. We propose applying standard meta-learning algorithms to learn the initial weight parameters for these fully-connected networks based on the underlying class of signals being represented (e.g., images of faces or 3D models of chairs). Despite requiring only a minor change in implementation, using these learned initial weights enables faster convergence during optimization and can serve as a strong prior over the signal class being modeled, resulting in better generalization when only partial observations of a given signal are available. We explore these benefits across a variety of tasks, including representing 2D images, reconstructing CT scans, and recovering 3D shapes and scenes from 2D image observations.

Dense simultaneous localization and mapping (SLAM) is pivotal for embodied scene understanding. Recent work has shown that 3D Gaussians enable high-quality reconstruction and real-time rendering of scenes using multiple posed cameras. In this light, we show for the first time that representing a scene by 3D Gaussians can enable dense SLAM using a single unposed monocular RGB-D camera. Our method, SplaTAM, addresses the limitations of prior radiance field-based representations, including fast rendering and optimization, the ability to determine if areas have been previously mapped, and structured map expansion by adding more Gaussians. We employ an online tracking and mapping pipeline while tailoring it to specifically use an underlying Gaussian representation and silhouette-guided optimization via differentiable rendering. Extensive experiments show that SplaTAM achieves up to 2X state-of-the-art performance in camera pose estimation, map construction, and novel-view synthesis, demonstrating its superiority over existing approaches, while allowing real-time rendering of a high-resolution dense 3D map.

Sequential learning paradigms pose challenges for gradient-based deep learning due to difficulties incorporating new data and retaining prior knowledge. While Gaussian processes elegantly tackle these problems, they struggle with scalability and handling rich inputs, such as images. To address these issues, we introduce a technique that converts neural networks from weight space to function space, through a dual parameterization. Our parameterization offers: (i) a way to scale function-space methods to large data sets via sparsification, (ii) retention of prior knowledge when access to past data is limited, and (iii) a mechanism to incorporate new data without retraining. Our experiments demonstrate that we can retain knowledge in continual learning and incorporate new data efficiently. We further show its strengths in uncertainty quantification and guiding exploration in model-based RL. Further information and code is available on the project website.

The Bayesian treatment of neural networks dictates that a prior distribution is specified over their weight and bias parameters. This poses a challenge because modern neural networks are characterized by a large number of parameters, and the choice of these priors has an uncontrolled effect on the induced functional prior, which is the distribution of the functions obtained by sampling the parameters from their prior distribution. We argue that this is a hugely limiting aspect of Bayesian deep learning, and this work tackles this limitation in a practical and effective way. Our proposal is to reason in terms of functional priors, which are easier to elicit, and to "tune" the priors of neural network parameters in a way that they reflect such functional priors. Gaussian processes offer a rigorous framework to define prior distributions over functions, and we propose a novel and robust framework to match their prior with the functional prior of neural networks based on the minimization of their Wasserstein distance. We provide vast experimental evidence that coupling these priors with scalable Markov chain Monte Carlo sampling offers systematically large performance improvements over alternative choices of priors and state-of-the-art approximate Bayesian deep learning approaches. We consider this work a considerable step in the direction of making the long-standing challenge of carrying out a fully Bayesian treatment of neural networks, including convolutional neural networks, a concrete possibility.

To achieve scalable and accurate inference for latent Gaussian processes, we propose a variational approximation based on a family of Gaussian distributions whose covariance matrices have sparse inverse Cholesky (SIC) factors. We combine this variational approximation of the posterior with a similar and efficient SIC-restricted Kullback-Leibler-optimal approximation of the prior. We then focus on a particular SIC ordering and nearest-neighbor-based sparsity pattern resulting in highly accurate prior and posterior approximations. For this setting, our variational approximation can be computed via stochastic gradient descent in polylogarithmic time per iteration. We provide numerical comparisons showing that the proposed double-Kullback-Leibler-optimal Gaussian-process approximation (DKLGP) can sometimes be vastly more accurate for stationary kernels than alternative approaches such as inducing-point and mean-field approximations at similar computational complexity.

We introduce GRM, a large-scale reconstructor capable of recovering a 3D asset from sparse-view images in around 0.1s. GRM is a feed-forward transformer-based model that efficiently incorporates multi-view information to translate the input pixels into pixel-aligned Gaussians, which are unprojected to create a set of densely distributed 3D Gaussians representing a scene. Together, our transformer architecture and the use of 3D Gaussians unlock a scalable and efficient reconstruction framework. Extensive experimental results demonstrate the superiority of our method over alternatives regarding both reconstruction quality and efficiency. We also showcase the potential of GRM in generative tasks, i.e., text-to-3D and image-to-3D, by integrating it with existing multi-view diffusion models. Our project website is at: https://justimyhxu.github.io/projects/grm/.

Achieving high-resolution novel view synthesis (HRNVS) from low-resolution input views is a challenging task due to the lack of high-resolution data. Previous methods optimize high-resolution Neural Radiance Field (NeRF) from low-resolution input views but suffer from slow rendering speed. In this work, we base our method on 3D Gaussian Splatting (3DGS) due to its capability of producing high-quality images at a faster rendering speed. To alleviate the shortage of data for higher-resolution synthesis, we propose to leverage off-the-shelf 2D diffusion priors by distilling the 2D knowledge into 3D with Score Distillation Sampling (SDS). Nevertheless, applying SDS directly to Gaussian-based 3D super-resolution leads to undesirable and redundant 3D Gaussian primitives, due to the randomness brought by generative priors. To mitigate this issue, we introduce two simple yet effective techniques to reduce stochastic disturbances introduced by SDS. Specifically, we 1) shrink the range of diffusion timestep in SDS with an annealing strategy; 2) randomly discard redundant Gaussian primitives during densification. Extensive experiments have demonstrated that our proposed GaussainSR can attain high-quality results for HRNVS with only low-resolution inputs on both synthetic and real-world datasets. Project page: https://chchnii.github.io/GaussianSR/

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

In this paper, we present Gaussian Splatting based text-to-3D generation (GSGEN), a novel approach for generating high-quality 3D objects. Previous methods suffer from inaccurate geometry and limited fidelity due to the absence of 3D prior and proper representation. We leverage 3D Gaussian Splatting, a recent state-of-the-art representation, to address existing shortcomings by exploiting the explicit nature that enables the incorporation of 3D prior. Specifically, our method adopts a progressive optimization strategy, which includes a geometry optimization stage and an appearance refinement stage. In geometry optimization, a coarse representation is established under a 3D geometry prior along with the ordinary 2D SDS loss, ensuring a sensible and 3D-consistent rough shape. Subsequently, the obtained Gaussians undergo an iterative refinement to enrich details. In this stage, we increase the number of Gaussians by compactness-based densification to enhance continuity and improve fidelity. With these designs, our approach can generate 3D content with delicate details and more accurate geometry. Extensive evaluations demonstrate the effectiveness of our method, especially for capturing high-frequency components. Video results are provided at https://gsgen3d.github.io. Our code is available at https://github.com/gsgen3d/gsgen

X-ray is widely applied for transmission imaging due to its stronger penetration than natural light. When rendering novel view X-ray projections, existing methods mainly based on NeRF suffer from long training time and slow inference speed. In this paper, we propose a 3D Gaussian splatting-based framework, namely X-Gaussian, for X-ray novel view synthesis. Firstly, we redesign a radiative Gaussian point cloud model inspired by the isotropic nature of X-ray imaging. Our model excludes the influence of view direction when learning to predict the radiation intensity of 3D points. Based on this model, we develop a Differentiable Radiative Rasterization (DRR) with CUDA implementation. Secondly, we customize an Angle-pose Cuboid Uniform Initialization (ACUI) strategy that directly uses the parameters of the X-ray scanner to compute the camera information and then uniformly samples point positions within a cuboid enclosing the scanned object. Experiments show that our X-Gaussian outperforms state-of-the-art methods by 6.5 dB while enjoying less than 15% training time and over 73x inference speed. The application on sparse-view CT reconstruction also reveals the practical values of our method. Code and models will be publicly available at https://github.com/caiyuanhao1998/X-Gaussian . A video demo of the training process visualization is at https://www.youtube.com/watch?v=gDVf_Ngeghg .

The increasing demand for virtual reality applications has highlighted the significance of crafting immersive 3D assets. We present a text-to-3D 360^{circ} scene generation pipeline that facilitates the creation of comprehensive 360^{circ} scenes for in-the-wild environments in a matter of minutes. Our approach utilizes the generative power of a 2D diffusion model and prompt self-refinement to create a high-quality and globally coherent panoramic image. This image acts as a preliminary "flat" (2D) scene representation. Subsequently, it is lifted into 3D Gaussians, employing splatting techniques to enable real-time exploration. To produce consistent 3D geometry, our pipeline constructs a spatially coherent structure by aligning the 2D monocular depth into a globally optimized point cloud. This point cloud serves as the initial state for the centroids of 3D Gaussians. In order to address invisible issues inherent in single-view inputs, we impose semantic and geometric constraints on both synthesized and input camera views as regularizations. These guide the optimization of Gaussians, aiding in the reconstruction of unseen regions. In summary, our method offers a globally consistent 3D scene within a 360^{circ} perspective, providing an enhanced immersive experience over existing techniques. Project website at: http://dreamscene360.github.io/

We propose a novel framework for incorporating unlabeled data into semi-supervised classification problems, where scenarios involving the minimization of either i) adversarially robust or ii) non-robust loss functions have been considered. Notably, we allow the unlabeled samples to deviate slightly (in total variation sense) from the in-domain distribution. The core idea behind our framework is to combine Distributionally Robust Optimization (DRO) with self-supervised training. As a result, we also leverage efficient polynomial-time algorithms for the training stage. From a theoretical standpoint, we apply our framework on the classification problem of a mixture of two Gaussians in R^d, where in addition to the m independent and labeled samples from the true distribution, a set of n (usually with ngg m) out of domain and unlabeled samples are given as well. Using only the labeled data, it is known that the generalization error can be bounded by proptoleft(d/mright)^{1/2}. However, using our method on both isotropic and non-isotropic Gaussian mixture models, one can derive a new set of analytically explicit and non-asymptotic bounds which show substantial improvement on the generalization error compared to ERM. Our results underscore two significant insights: 1) out-of-domain samples, even when unlabeled, can be harnessed to narrow the generalization gap, provided that the true data distribution adheres to a form of the ``cluster assumption", and 2) the semi-supervised learning paradigm can be regarded as a special case of our framework when there are no distributional shifts. We validate our claims through experiments conducted on a variety of synthetic and real-world datasets.

We present a new approach, termed GPS-Gaussian, for synthesizing novel views of a character in a real-time manner. The proposed method enables 2K-resolution rendering under a sparse-view camera setting. Unlike the original Gaussian Splatting or neural implicit rendering methods that necessitate per-subject optimizations, we introduce Gaussian parameter maps defined on the source views and regress directly Gaussian Splatting properties for instant novel view synthesis without any fine-tuning or optimization. To this end, we train our Gaussian parameter regression module on a large amount of human scan data, jointly with a depth estimation module to lift 2D parameter maps to 3D space. The proposed framework is fully differentiable and experiments on several datasets demonstrate that our method outperforms state-of-the-art methods while achieving an exceeding rendering speed.

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

Recent progress in neural rendering has brought forth pioneering methods, such as NeRF and Gaussian Splatting, which revolutionize view rendering across various domains like AR/VR, gaming, and content creation. While these methods excel at interpolating {\em within the training data}, the challenge of generalizing to new scenes and objects from very sparse views persists. Specifically, modeling 3D humans from sparse views presents formidable hurdles due to the inherent complexity of human geometry, resulting in inaccurate reconstructions of geometry and textures. To tackle this challenge, this paper leverages recent advancements in Gaussian Splatting and introduces a new method to learn generalizable human Gaussians that allows photorealistic and accurate view-rendering of a new human subject from a limited set of sparse views in a feed-forward manner. A pivotal innovation of our approach involves reformulating the learning of 3D Gaussian parameters into a regression process defined on the 2D UV space of a human template, which allows leveraging the strong geometry prior and the advantages of 2D convolutions. In addition, a multi-scaffold is proposed to effectively represent the offset details. Our method outperforms recent methods on both within-dataset generalization as well as cross-dataset generalization settings.

We propose a game-based formulation for learning dimensionality-reducing representations of feature vectors, when only a prior knowledge on future prediction tasks is available. In this game, the first player chooses a representation, and then the second player adversarially chooses a prediction task from a given class, representing the prior knowledge. The first player aims is to minimize, and the second player to maximize, the regret: The minimal prediction loss using the representation, compared to the same loss using the original features. For the canonical setting in which the representation, the response to predict and the predictors are all linear functions, and under the mean squared error loss function, we derive the theoretically optimal representation in pure strategies, which shows the effectiveness of the prior knowledge, and the optimal regret in mixed strategies, which shows the usefulness of randomizing the representation. For general representations and loss functions, we propose an efficient algorithm to optimize a randomized representation. The algorithm only requires the gradients of the loss function, and is based on incrementally adding a representation rule to a mixture of such rules.

Implicit neural representation methods have shown impressive advancements in learning 3D scenes from unstructured in-the-wild photo collections but are still limited by the large computational cost of volumetric rendering. More recently, 3D Gaussian Splatting emerged as a much faster alternative with superior rendering quality and training efficiency, especially for small-scale and object-centric scenarios. Nevertheless, this technique suffers from poor performance on unstructured in-the-wild data. To tackle this, we extend over 3D Gaussian Splatting to handle unstructured image collections. We achieve this by modeling appearance to seize photometric variations in the rendered images. Additionally, we introduce a new mechanism to train transient Gaussians to handle the presence of scene occluders in an unsupervised manner. Experiments on diverse photo collection scenes and multi-pass acquisition of outdoor landmarks show the effectiveness of our method over prior works achieving state-of-the-art results with improved efficiency.

For robots to robustly understand and interact with the physical world, it is highly beneficial to have a comprehensive representation - modelling geometry, physics, and visual observations - that informs perception, planning, and control algorithms. We propose a novel dual Gaussian-Particle representation that models the physical world while (i) enabling predictive simulation of future states and (ii) allowing online correction from visual observations in a dynamic world. Our representation comprises particles that capture the geometrical aspect of objects in the world and can be used alongside a particle-based physics system to anticipate physically plausible future states. Attached to these particles are 3D Gaussians that render images from any viewpoint through a splatting process thus capturing the visual state. By comparing the predicted and observed images, our approach generates visual forces that correct the particle positions while respecting known physical constraints. By integrating predictive physical modelling with continuous visually-derived corrections, our unified representation reasons about the present and future while synchronizing with reality. Our system runs in realtime at 30Hz using only 3 cameras. We validate our approach on 2D and 3D tracking tasks as well as photometric reconstruction quality. Videos are found at https://embodied-gaussians.github.io/.

We present a method that simultaneously addresses the tasks of dynamic scene novel-view synthesis and six degree-of-freedom (6-DOF) tracking of all dense scene elements. We follow an analysis-by-synthesis framework, inspired by recent work that models scenes as a collection of 3D Gaussians which are optimized to reconstruct input images via differentiable rendering. To model dynamic scenes, we allow Gaussians to move and rotate over time while enforcing that they have persistent color, opacity, and size. By regularizing Gaussians' motion and rotation with local-rigidity constraints, we show that our Dynamic 3D Gaussians correctly model the same area of physical space over time, including the rotation of that space. Dense 6-DOF tracking and dynamic reconstruction emerges naturally from persistent dynamic view synthesis, without requiring any correspondence or flow as input. We demonstrate a large number of downstream applications enabled by our representation, including first-person view synthesis, dynamic compositional scene synthesis, and 4D video editing.

Denoisers play a central role in many applications, from noise suppression in low-grade imaging sensors, to empowering score-based generative models. The latter category of methods makes use of Tweedie's formula, which links the posterior mean in Gaussian denoising (\ie the minimum MSE denoiser) with the score of the data distribution. Here, we derive a fundamental relation between the higher-order central moments of the posterior distribution, and the higher-order derivatives of the posterior mean. We harness this result for uncertainty quantification of pre-trained denoisers. Particularly, we show how to efficiently compute the principal components of the posterior distribution for any desired region of an image, as well as to approximate the full marginal distribution along those (or any other) one-dimensional directions. Our method is fast and memory-efficient, as it does not explicitly compute or store the high-order moment tensors and it requires no training or fine tuning of the denoiser. Code and examples are available on the project webpage in https://hilamanor.github.io/GaussianDenoisingPosterior/ .

We propose GS-LRM, a scalable large reconstruction model that can predict high-quality 3D Gaussian primitives from 2-4 posed sparse images in 0.23 seconds on single A100 GPU. Our model features a very simple transformer-based architecture; we patchify input posed images, pass the concatenated multi-view image tokens through a sequence of transformer blocks, and decode final per-pixel Gaussian parameters directly from these tokens for differentiable rendering. In contrast to previous LRMs that can only reconstruct objects, by predicting per-pixel Gaussians, GS-LRM naturally handles scenes with large variations in scale and complexity. We show that our model can work on both object and scene captures by training it on Objaverse and RealEstate10K respectively. In both scenarios, the models outperform state-of-the-art baselines by a wide margin. We also demonstrate applications of our model in downstream 3D generation tasks. Our project webpage is available at: https://sai-bi.github.io/project/gs-lrm/ .

Reconstructing realistic 3D human models from monocular images has significant applications in creative industries, human-computer interfaces, and healthcare. We base our work on 3D Gaussian Splatting (3DGS), a scene representation composed of a mixture of Gaussians. Predicting such mixtures for a human from a single input image is challenging, as it is a non-uniform density (with a many-to-one relationship with input pixels) with strict physical constraints. At the same time, it needs to be flexible to accommodate a variety of clothes and poses. Our key observation is that the vertices of standardized human meshes (such as SMPL) can provide an adequate density and approximate initial position for Gaussians. We can then train a transformer model to jointly predict comparatively small adjustments to these positions, as well as the other Gaussians' attributes and the SMPL parameters. We show empirically that this combination (using only multi-view supervision) can achieve fast inference of 3D human models from a single image without test-time optimization, expensive diffusion models, or 3D points supervision. We also show that it can improve 3D pose estimation by better fitting human models that account for clothes and other variations. The code is available on the project website https://abdullahamdi.com/gst/ .

Does the dominant approach to learn representations (as a side effect of optimizing an expected cost for a single training distribution) remain a good approach when we are dealing with multiple distributions? Our thesis is that such scenarios are better served by representations that are richer than those obtained with a single optimization episode. We support this thesis with simple theoretical arguments and with experiments utilizing an apparently na\"{\i}ve ensembling technique: concatenating the representations obtained from multiple training episodes using the same data, model, algorithm, and hyper-parameters, but different random seeds. These independently trained networks perform similarly. Yet, in a number of scenarios involving new distributions, the concatenated representation performs substantially better than an equivalently sized network trained with a single training run. This proves that the representations constructed by multiple training episodes are in fact different. Although their concatenation carries little additional information about the training task under the training distribution, it becomes substantially more informative when tasks or distributions change. Meanwhile, a single training episode is unlikely to yield such a redundant representation because the optimization process has no reason to accumulate features that do not incrementally improve the training performance.

Since the introduction of deep learning, a wide scope of representation properties, such as decorrelation, whitening, disentanglement, rank, isotropy, and mutual information, have been studied to improve the quality of representation. However, manipulating such properties can be challenging in terms of implementational effectiveness and general applicability. To address these limitations, we propose to regularize von Neumann entropy~(VNE) of representation. First, we demonstrate that the mathematical formulation of VNE is superior in effectively manipulating the eigenvalues of the representation autocorrelation matrix. Then, we demonstrate that it is widely applicable in improving state-of-the-art algorithms or popular benchmark algorithms by investigating domain-generalization, meta-learning, self-supervised learning, and generative models. In addition, we formally establish theoretical connections with rank, disentanglement, and isotropy of representation. Finally, we provide discussions on the dimension control of VNE and the relationship with Shannon entropy. Code is available at: https://github.com/jaeill/CVPR23-VNE.

We propose MVSplat, an efficient feed-forward 3D Gaussian Splatting model learned from sparse multi-view images. To accurately localize the Gaussian centers, we propose to build a cost volume representation via plane sweeping in the 3D space, where the cross-view feature similarities stored in the cost volume can provide valuable geometry cues to the estimation of depth. We learn the Gaussian primitives' opacities, covariances, and spherical harmonics coefficients jointly with the Gaussian centers while only relying on photometric supervision. We demonstrate the importance of the cost volume representation in learning feed-forward Gaussian Splatting models via extensive experimental evaluations. On the large-scale RealEstate10K and ACID benchmarks, our model achieves state-of-the-art performance with the fastest feed-forward inference speed (22 fps). Compared to the latest state-of-the-art method pixelSplat, our model uses 10times fewer parameters and infers more than 2times faster while providing higher appearance and geometry quality as well as better cross-dataset generalization.

Representation learning has been a critical topic in machine learning. In Click-through Rate Prediction, most features are represented as embedding vectors and learned simultaneously with other parameters in the model. With the development of CTR models, feature representation learning has become a trending topic and has been extensively studied by both industrial and academic researchers in recent years. This survey aims at summarizing the feature representation learning in a broader picture and pave the way for future research. To achieve such a goal, we first present a taxonomy of current research methods on feature representation learning following two main issues: (i) which feature to represent and (ii) how to represent these features. Then we give a detailed description of each method regarding these two issues. Finally, the review concludes with a discussion on the future directions of this field.

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size n is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in R^K, where samples are assumed to be corrupted by a multi-variate additive Gaussian noise of an arbitrary magnitude. We prove the existence of an algorithm that with high probability outputs a simplex having a ell_2 distance of at most varepsilon from the true simplex (for any varepsilon>0). Also, we theoretically show that in order to achieve this bound, it is sufficient to have ngeleft(K^2/varepsilon^2right)e^{Omegaleft(K/SNR^2right)} samples, where SNR stands for the signal-to-noise ratio. This result solves an important open problem and shows as long as SNRgeOmegaleft(K^{1/2}right), the sample complexity of the noisy regime has the same order to that of the noiseless case. Our proofs are a combination of the so-called sample compression technique in ashtiani2018nearly, mathematical tools from high-dimensional geometry, and Fourier analysis. In particular, we have proposed a general Fourier-based technique for recovery of a more general class of distribution families from additive Gaussian noise, which can be further used in a variety of other related problems.

The Gaussian splatting for radiance field rendering method has recently emerged as an efficient approach for accurate scene representation. It optimizes the location, size, color, and shape of a cloud of 3D Gaussian elements to visually match, after projection, or splatting, a set of given images taken from various viewing directions. And yet, despite the proximity of Gaussian elements to the shape boundaries, direct surface reconstruction of objects in the scene is a challenge. We propose a novel approach for surface reconstruction from Gaussian splatting models. Rather than relying on the Gaussian elements' locations as a prior for surface reconstruction, we leverage the superior novel-view synthesis capabilities of 3DGS. To that end, we use the Gaussian splatting model to render pairs of stereo-calibrated novel views from which we extract depth profiles using a stereo matching method. We then combine the extracted RGB-D images into a geometrically consistent surface. The resulting reconstruction is more accurate and shows finer details when compared to other methods for surface reconstruction from Gaussian splatting models, while requiring significantly less compute time compared to other surface reconstruction methods. We performed extensive testing of the proposed method on in-the-wild scenes, taken by a smartphone, showcasing its superior reconstruction abilities. Additionally, we tested the proposed method on the Tanks and Temples benchmark, and it has surpassed the current leading method for surface reconstruction from Gaussian splatting models. Project page: https://gs2mesh.github.io/.

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

The infinitely wide neural network has been proven a useful and manageable mathematical model that enables the understanding of many phenomena appearing in deep learning. One example is the convergence of random deep networks to Gaussian processes that allows a rigorous analysis of the way the choice of activation function and network weights impacts the training dynamics. In this paper, we extend the seminal proof of Matthews et al. (2018) to a larger class of initial weight distributions (which we call PSEUDO-IID), including the established cases of IID and orthogonal weights, as well as the emerging low-rank and structured sparse settings celebrated for their computational speed-up benefits. We show that fully-connected and convolutional networks initialized with PSEUDO-IID distributions are all effectively equivalent up to their variance. Using our results, one can identify the Edge-of-Chaos for a broader class of neural networks and tune them at criticality in order to enhance their training. Moreover, they enable the posterior distribution of Bayesian Neural Networks to be tractable across these various initialization schemes.

We aim to address sparse-view reconstruction of a 3D scene by leveraging priors from large-scale vision models. While recent advancements such as 3D Gaussian Splatting (3DGS) have demonstrated remarkable successes in 3D reconstruction, these methods typically necessitate hundreds of input images that densely capture the underlying scene, making them time-consuming and impractical for real-world applications. However, sparse-view reconstruction is inherently ill-posed and under-constrained, often resulting in inferior and incomplete outcomes. This is due to issues such as failed initialization, overfitting on input images, and a lack of details. To mitigate these challenges, we introduce LM-Gaussian, a method capable of generating high-quality reconstructions from a limited number of images. Specifically, we propose a robust initialization module that leverages stereo priors to aid in the recovery of camera poses and the reliable point clouds. Additionally, a diffusion-based refinement is iteratively applied to incorporate image diffusion priors into the Gaussian optimization process to preserve intricate scene details. Finally, we utilize video diffusion priors to further enhance the rendered images for realistic visual effects. Overall, our approach significantly reduces the data acquisition requirements compared to previous 3DGS methods. We validate the effectiveness of our framework through experiments on various public datasets, demonstrating its potential for high-quality 360-degree scene reconstruction. Visual results are on our website.

Performing language-conditioned robotic manipulation tasks in unstructured environments is highly demanded for general intelligent robots. Conventional robotic manipulation methods usually learn semantic representation of the observation for action prediction, which ignores the scene-level spatiotemporal dynamics for human goal completion. In this paper, we propose a dynamic Gaussian Splatting method named ManiGaussian for multi-task robotic manipulation, which mines scene dynamics via future scene reconstruction. Specifically, we first formulate the dynamic Gaussian Splatting framework that infers the semantics propagation in the Gaussian embedding space, where the semantic representation is leveraged to predict the optimal robot action. Then, we build a Gaussian world model to parameterize the distribution in our dynamic Gaussian Splatting framework, which provides informative supervision in the interactive environment via future scene reconstruction. We evaluate our ManiGaussian on 10 RLBench tasks with 166 variations, and the results demonstrate our framework can outperform the state-of-the-art methods by 13.1\% in average success rate. Project page: https://guanxinglu.github.io/ManiGaussian/.

Interactive segmentation of 3D Gaussians opens a great opportunity for real-time manipulation of 3D scenes thanks to the real-time rendering capability of 3D Gaussian Splatting. However, the current methods suffer from time-consuming post-processing to deal with noisy segmentation output. Also, they struggle to provide detailed segmentation, which is important for fine-grained manipulation of 3D scenes. In this study, we propose Click-Gaussian, which learns distinguishable feature fields of two-level granularity, facilitating segmentation without time-consuming post-processing. We delve into challenges stemming from inconsistently learned feature fields resulting from 2D segmentation obtained independently from a 3D scene. 3D segmentation accuracy deteriorates when 2D segmentation results across the views, primary cues for 3D segmentation, are in conflict. To overcome these issues, we propose Global Feature-guided Learning (GFL). GFL constructs the clusters of global feature candidates from noisy 2D segments across the views, which smooths out noises when training the features of 3D Gaussians. Our method runs in 10 ms per click, 15 to 130 times as fast as the previous methods, while also significantly improving segmentation accuracy. Our project page is available at https://seokhunchoi.github.io/Click-Gaussian

We present a spatial and angular Gaussian based representation and a triple splatting process, for real-time, high-quality novel lighting-and-view synthesis from multi-view point-lit input images. To describe complex appearance, we employ a Lambertian plus a mixture of angular Gaussians as an effective reflectance function for each spatial Gaussian. To generate self-shadow, we splat all spatial Gaussians towards the light source to obtain shadow values, which are further refined by a small multi-layer perceptron. To compensate for other effects like global illumination, another network is trained to compute and add a per-spatial-Gaussian RGB tuple. The effectiveness of our representation is demonstrated on 30 samples with a wide variation in geometry (from solid to fluffy) and appearance (from translucent to anisotropic), as well as using different forms of input data, including rendered images of synthetic/reconstructed objects, photographs captured with a handheld camera and a flash, or from a professional lightstage. We achieve a training time of 40-70 minutes and a rendering speed of 90 fps on a single commodity GPU. Our results compare favorably with state-of-the-art techniques in terms of quality/performance. Our code and data are publicly available at https://GSrelight.github.io/.

While the Transformer architecture has achieved remarkable success across various domains, a thorough theoretical foundation explaining its optimization dynamics is yet to be fully developed. In this study, we aim to bridge this understanding gap by answering the following two core questions: (1) Which types of Transformer architectures allow Gradient Descent (GD) to achieve guaranteed convergence? and (2) Under what initial conditions and architectural specifics does the Transformer achieve rapid convergence during training? By analyzing the loss landscape of a single Transformer layer using Softmax and Gaussian attention kernels, our work provides concrete answers to these questions. Our findings demonstrate that, with appropriate weight initialization, GD can train a Transformer model (with either kernel type) to achieve a global optimal solution, especially when the input embedding dimension is large. Nonetheless, certain scenarios highlight potential pitfalls: training a Transformer using the Softmax attention kernel may sometimes lead to suboptimal local solutions. In contrast, the Gaussian attention kernel exhibits a much favorable behavior. Our empirical study further validate the theoretical findings.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Estimating physical properties for visual data is a crucial task in computer vision, graphics, and robotics, underpinning applications such as augmented reality, physical simulation, and robotic grasping. However, this area remains under-explored due to the inherent ambiguities in physical property estimation. To address these challenges, we introduce GaussianProperty, a training-free framework that assigns physical properties of materials to 3D Gaussians. Specifically, we integrate the segmentation capability of SAM with the recognition capability of GPT-4V(ision) to formulate a global-local physical property reasoning module for 2D images. Then we project the physical properties from multi-view 2D images to 3D Gaussians using a voting strategy. We demonstrate that 3D Gaussians with physical property annotations enable applications in physics-based dynamic simulation and robotic grasping. For physics-based dynamic simulation, we leverage the Material Point Method (MPM) for realistic dynamic simulation. For robot grasping, we develop a grasping force prediction strategy that estimates a safe force range required for object grasping based on the estimated physical properties. Extensive experiments on material segmentation, physics-based dynamic simulation, and robotic grasping validate the effectiveness of our proposed method, highlighting its crucial role in understanding physical properties from visual data. Online demo, code, more cases and annotated datasets are available on https://Gaussian-Property.github.io{this https URL}.

We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU non-linearity. This allows propagating Gaussian and Cauchy input uncertainties through neural networks to quantify their output uncertainties. To demonstrate the utility of propagating distributions, we apply the proposed method to predicting calibrated confidence intervals and selective prediction on out-of-distribution data. The results demonstrate a broad applicability of propagating distributions and show the advantages of our method over other approaches such as moment matching.

Recent successful generative models are trained by fitting a neural network to an a-priori defined tractable probability density path taking noise to training examples. In this paper we investigate the space of Gaussian probability paths, which includes diffusion paths as an instance, and look for an optimal member in some useful sense. In particular, minimizing the Kinetic Energy (KE) of a path is known to make particles' trajectories simple, hence easier to sample, and empirically improve performance in terms of likelihood of unseen data and sample generation quality. We investigate Kinetic Optimal (KO) Gaussian paths and offer the following observations: (i) We show the KE takes a simplified form on the space of Gaussian paths, where the data is incorporated only through a single, one dimensional scalar function, called the data separation function. (ii) We characterize the KO solutions with a one dimensional ODE. (iii) We approximate data-dependent KO paths by approximating the data separation function and minimizing the KE. (iv) We prove that the data separation function converges to 1 in the general case of arbitrary normalized dataset consisting of n samples in d dimension as n/drightarrow 0. A consequence of this result is that the Conditional Optimal Transport (Cond-OT) path becomes kinetic optimal as n/drightarrow 0. We further support this theory with empirical experiments on ImageNet.

Variational inference (VI) seeks to approximate a target distribution pi by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates pi by minimizing the Kullback-Leibler (KL) divergence to pi over the space of Gaussians. In this work, we develop the (Stochastic) Forward-Backward Gaussian Variational Inference (FB-GVI) algorithm to solve Gaussian VI. Our approach exploits the composite structure of the KL divergence, which can be written as the sum of a smooth term (the potential) and a non-smooth term (the entropy) over the Bures-Wasserstein (BW) space of Gaussians endowed with the Wasserstein distance. For our proposed algorithm, we obtain state-of-the-art convergence guarantees when pi is log-smooth and log-concave, as well as the first convergence guarantees to first-order stationary solutions when pi is only log-smooth.

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find invariant representations of the data. These are representations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a {\em finite sample} setting, we consider the notion of epsilon-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen SEMs? This larger collection of SEMs is generated through a parameterized family of interventions. Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds probabilistically over a family of linear SEMs without faithfulness assumptions. Our results show bounds that do not scale in ambient dimension when intervention sites are restricted to lie in a constant size subset of in-degree bounded nodes. We also show how to extend our results to a linear indirect observation model that incorporates latent variables.

Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.

Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.

Creating 4D fields of Gaussian Splatting from images or videos is a challenging task due to its under-constrained nature. While the optimization can draw photometric reference from the input videos or be regulated by generative models, directly supervising Gaussian motions remains underexplored. In this paper, we introduce a novel concept, Gaussian flow, which connects the dynamics of 3D Gaussians and pixel velocities between consecutive frames. The Gaussian flow can be efficiently obtained by splatting Gaussian dynamics into the image space. This differentiable process enables direct dynamic supervision from optical flow. Our method significantly benefits 4D dynamic content generation and 4D novel view synthesis with Gaussian Splatting, especially for contents with rich motions that are hard to be handled by existing methods. The common color drifting issue that happens in 4D generation is also resolved with improved Guassian dynamics. Superior visual quality on extensive experiments demonstrates our method's effectiveness. Quantitative and qualitative evaluations show that our method achieves state-of-the-art results on both tasks of 4D generation and 4D novel view synthesis. Project page: https://zerg-overmind.github.io/GaussianFlow.github.io/

We propose two approaches to extend the notion of knowledge distillation to Gaussian Process Regression (GPR) and Gaussian Process Classification (GPC); data-centric and distribution-centric. The data-centric approach resembles most current distillation techniques for machine learning, and refits a model on deterministic predictions from the teacher, while the distribution-centric approach, re-uses the full probabilistic posterior for the next iteration. By analyzing the properties of these approaches, we show that the data-centric approach for GPR closely relates to known results for self-distillation of kernel ridge regression and that the distribution-centric approach for GPR corresponds to ordinary GPR with a very particular choice of hyperparameters. Furthermore, we demonstrate that the distribution-centric approach for GPC approximately corresponds to data duplication and a particular scaling of the covariance and that the data-centric approach for GPC requires redefining the model from a Binomial likelihood to a continuous Bernoulli likelihood to be well-specified. To the best of our knowledge, our proposed approaches are the first to formulate knowledge distillation specifically for Gaussian Process models.

Bayesian optimization is a highly efficient approach to optimizing objective functions which are expensive to query. These objectives are typically represented by Gaussian process (GP) surrogate models which are easy to optimize and support exact inference. While standard GP surrogates have been well-established in Bayesian optimization, Bayesian neural networks (BNNs) have recently become practical function approximators, with many benefits over standard GPs such as the ability to naturally handle non-stationarity and learn representations for high-dimensional data. In this paper, we study BNNs as alternatives to standard GP surrogates for optimization. We consider a variety of approximate inference procedures for finite-width BNNs, including high-quality Hamiltonian Monte Carlo, low-cost stochastic MCMC, and heuristics such as deep ensembles. We also consider infinite-width BNNs and partially stochastic models such as deep kernel learning. We evaluate this collection of surrogate models on diverse problems with varying dimensionality, number of objectives, non-stationarity, and discrete and continuous inputs. We find: (i) the ranking of methods is highly problem dependent, suggesting the need for tailored inductive biases; (ii) HMC is the most successful approximate inference procedure for fully stochastic BNNs; (iii) full stochasticity may be unnecessary as deep kernel learning is relatively competitive; (iv) infinite-width BNNs are particularly promising, especially in high dimensions.

Generating high-quality novel view renderings of 3D Gaussian Splatting (3DGS) in scenes featuring transient objects is challenging. We propose a novel hybrid representation, termed as HybridGS, using 2D Gaussians for transient objects per image and maintaining traditional 3D Gaussians for the whole static scenes. Note that, the 3DGS itself is better suited for modeling static scenes that assume multi-view consistency, but the transient objects appear occasionally and do not adhere to the assumption, thus we model them as planar objects from a single view, represented with 2D Gaussians. Our novel representation decomposes the scene from the perspective of fundamental viewpoint consistency, making it more reasonable. Additionally, we present a novel multi-view regulated supervision method for 3DGS that leverages information from co-visible regions, further enhancing the distinctions between the transients and statics. Then, we propose a straightforward yet effective multi-stage training strategy to ensure robust training and high-quality view synthesis across various settings. Experiments on benchmark datasets show our state-of-the-art performance of novel view synthesis in both indoor and outdoor scenes, even in the presence of distracting elements.

Combining several (sample approximations of) distributions, which we term sub-posteriors, into a single distribution proportional to their product, is a common challenge. Occurring, for instance, in distributed 'big data' problems, or when working under multi-party privacy constraints. Many existing approaches resort to approximating the individual sub-posteriors for practical necessity, then find either an analytical approximation or sample approximation of the resulting (product-pooled) posterior. The quality of the posterior approximation for these approaches is poor when the sub-posteriors fall out-with a narrow range of distributional form, such as being approximately Gaussian. Recently, a Fusion approach has been proposed which finds an exact Monte Carlo approximation of the posterior, circumventing the drawbacks of approximate approaches. Unfortunately, existing Fusion approaches have a number of computational limitations, particularly when unifying a large number of sub-posteriors. In this paper, we generalise the theory underpinning existing Fusion approaches, and embed the resulting methodology within a recursive divide-and-conquer sequential Monte Carlo paradigm. This ultimately leads to a competitive Fusion approach, which is robust to increasing numbers of sub-posteriors.

Latent Gaussian process (GP) models are widely used in neuroscience to uncover hidden state evolutions from sequential observations, mainly in neural activity recordings. While latent GP models provide a principled and powerful solution in theory, the intractable posterior in non-conjugate settings necessitates approximate inference schemes, which may lack scalability. In this work, we propose cvHM, a general inference framework for latent GP models leveraging Hida-Mat\'ern kernels and conjugate computation variational inference (CVI). With cvHM, we are able to perform variational inference of latent neural trajectories with linear time complexity for arbitrary likelihoods. The reparameterization of stationary kernels using Hida-Mat\'ern GPs helps us connect the latent variable models that encode prior assumptions through dynamical systems to those that encode trajectory assumptions through GPs. In contrast to previous work, we use bidirectional information filtering, leading to a more concise implementation. Furthermore, we employ the Whittle approximate likelihood to achieve highly efficient hyperparameter learning.

Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks that lack stochastic layers) or averaged responses (e.g., trial-averaged firing rates in biological data). However, these measures of _deterministic_ representational similarity ignore the scale and geometric structure of noise, both of which play important roles in neural computation. To rectify this, we generalize previously proposed shape metrics (Williams et al. 2021) to quantify differences in _stochastic_ representations. These new distances satisfy the triangle inequality, and thus can be used as a rigorous basis for many supervised and unsupervised analyses. Leveraging this novel framework, we find that the stochastic geometries of neurobiological representations of oriented visual gratings and naturalistic scenes respectively resemble untrained and trained deep network representations. Further, we are able to more accurately predict certain network attributes (e.g. training hyperparameters) from its position in stochastic (versus deterministic) shape space.

Equivariant neural networks have shown improved performance, expressiveness and sample complexity on symmetrical domains. But for some specific symmetries, representations, and choice of coordinates, the most common point-wise activations, such as ReLU, are not equivariant, hence they cannot be employed in the design of equivariant neural networks. The theorem we present in this paper describes all possible combinations of finite-dimensional representations, choice of coordinates and point-wise activations to obtain an exactly equivariant layer, generalizing and strengthening existing characterizations. Notable cases of practical relevance are discussed as corollaries. Indeed, we prove that rotation-equivariant networks can only be invariant, as it happens for any network which is equivariant with respect to connected compact groups. Then, we discuss implications of our findings when applied to important instances of exactly equivariant networks. First, we completely characterize permutation equivariant networks such as Invariant Graph Networks with point-wise nonlinearities and their geometric counterparts, highlighting a plethora of models whose expressive power and performance are still unknown. Second, we show that feature spaces of disentangled steerable convolutional neural networks are trivial representations.

Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as identifiability. A recent breakthrough explores identifiability by leveraging the change of causal influences among latent causal variables across multiple environments liu2022identifying. However, this progress rests on the assumption that the causal relationships among latent causal variables adhere strictly to linear Gaussian models. In this paper, we extend the scope of latent causal models to involve nonlinear causal relationships, represented by polynomial models, and general noise distributions conforming to the exponential family. Additionally, we investigate the necessity of imposing changes on all causal parameters and present partial identifiability results when part of them remains unchanged. Further, we propose a novel empirical estimation method, grounded in our theoretical finding, that enables learning consistent latent causal representations. Our experimental results, obtained from both synthetic and real-world data, validate our theoretical contributions concerning identifiability and consistency.

Representation learning seeks to expose certain aspects of observed data in a learned representation that's amenable to downstream tasks like classification. For instance, a good representation for 2D images might be one that describes only global structure and discards information about detailed texture. In this paper, we present a simple but principled method to learn such global representations by combining Variational Autoencoder (VAE) with neural autoregressive models such as RNN, MADE and PixelRNN/CNN. Our proposed VAE model allows us to have control over what the global latent code can learn and , by designing the architecture accordingly, we can force the global latent code to discard irrelevant information such as texture in 2D images, and hence the VAE only "autoencodes" data in a lossy fashion. In addition, by leveraging autoregressive models as both prior distribution p(z) and decoding distribution p(x|z), we can greatly improve generative modeling performance of VAEs, achieving new state-of-the-art results on MNIST, OMNIGLOT and Caltech-101 Silhouettes density estimation tasks.

This work introduces the Efficient Transformed Gaussian Process (ETGP), a new way of creating C stochastic processes characterized by: 1) the C processes are non-stationary, 2) the C processes are dependent by construction without needing a mixing matrix, 3) training and making predictions is very efficient since the number of Gaussian Processes (GP) operations (e.g. inverting the inducing point's covariance matrix) do not depend on the number of processes. This makes the ETGP particularly suited for multi-class problems with a very large number of classes, which are the problems studied in this work. ETGPs exploit the recently proposed Transformed Gaussian Process (TGP), a stochastic process specified by transforming a Gaussian Process using an invertible transformation. However, unlike TGPs, ETGPs are constructed by transforming a single sample from a GP using C invertible transformations. We derive an efficient sparse variational inference algorithm for the proposed model and demonstrate its utility in 5 classification tasks which include low/medium/large datasets and a different number of classes, ranging from just a few to hundreds. Our results show that ETGPs, in general, outperform state-of-the-art methods for multi-class classification based on GPs, and have a lower computational cost (around one order of magnitude smaller).

Representation learning is all about discovering the hidden modular attributes that generate the data faithfully. We explore the potential of Denoising Diffusion Probabilistic Model (DM) in unsupervised learning of the modular attributes. We build a theoretical framework that connects the diffusion time-steps and the hidden attributes, which serves as an effective inductive bias for unsupervised learning. Specifically, the forward diffusion process incrementally adds Gaussian noise to samples at each time-step, which essentially collapses different samples into similar ones by losing attributes, e.g., fine-grained attributes such as texture are lost with less noise added (i.e., early time-steps), while coarse-grained ones such as shape are lost by adding more noise (i.e., late time-steps). To disentangle the modular attributes, at each time-step t, we learn a t-specific feature to compensate for the newly lost attribute, and the set of all 1,...,t-specific features, corresponding to the cumulative set of lost attributes, are trained to make up for the reconstruction error of a pre-trained DM at time-step t. On CelebA, FFHQ, and Bedroom datasets, the learned feature significantly improves attribute classification and enables faithful counterfactual generation, e.g., interpolating only one specified attribute between two images, validating the disentanglement quality. Codes are in https://github.com/yue-zhongqi/diti.