Daily Papers

Supervised ranking methods based on bi-encoder or cross-encoder architectures have shown success in multi-stage text ranking tasks, but they require large amounts of relevance judgments as training data. In this work, we propose Listwise Reranker with a Large Language Model (LRL), which achieves strong reranking effectiveness without using any task-specific training data. Different from the existing pointwise ranking methods, where documents are scored independently and ranked according to the scores, LRL directly generates a reordered list of document identifiers given the candidate documents. Experiments on three TREC web search datasets demonstrate that LRL not only outperforms zero-shot pointwise methods when reranking first-stage retrieval results, but can also act as a final-stage reranker to improve the top-ranked results of a pointwise method for improved efficiency. Additionally, we apply our approach to subsets of MIRACL, a recent multilingual retrieval dataset, with results showing its potential to generalize across different languages.

We investigate a general formulation for clustering and transductive few-shot learning, which integrates prototype-based objectives, Laplacian regularization and supervision constraints from a few labeled data points. We propose a concave-convex relaxation of the problem, and derive a computationally efficient block-coordinate bound optimizer, with convergence guarantee. At each iteration,our optimizer computes independent (parallel) updates for each point-to-cluster assignment. Therefore, it could be trivially distributed for large-scale clustering and few-shot tasks. Furthermore, we provides a thorough convergence analysis based on point-to-set maps. Were port comprehensive clustering and few-shot learning experiments over various data sets, showing that our method yields competitive performances, in term of accuracy and optimization quality, while scaling up to large problems. Using standard training on the base classes, without resorting to complex meta-learning and episodic-training strategies, our approach outperforms state-of-the-art few-shot methods by significant margins, across various models, settings and data sets. Surprisingly, we found that even standard clustering procedures (e.g., K-means), which correspond to particular, non-regularized cases of our general model, already achieve competitive performances in comparison to the state-of-the-art in few-shot learning. These surprising results point to the limitations of the current few-shot benchmarks, and question the viability of a large body of convoluted few-shot learning techniques in the recent literature.

This paper proposes a general solution to enable point cloud recognition models to handle distribution shifts at test time. Unlike prior methods, which rely heavily on training data (often inaccessible during online inference) and are limited to recognizing a fixed set of point cloud classes predefined during training, we explore a more practical and challenging scenario: adapting the model solely based on online test data to recognize both previously seen classes and novel, unseen classes at test time. To this end, we develop Point-Cache, a hierarchical cache model that captures essential clues of online test samples, particularly focusing on the global structure of point clouds and their local-part details. Point-Cache, which serves as a rich 3D knowledge base, is dynamically managed to prioritize the inclusion of high-quality samples. Designed as a plug-and-play module, our method can be flexibly integrated into large multimodal 3D models to support open-vocabulary point cloud recognition. Notably, our solution operates with efficiency comparable to zero-shot inference, as it is entirely training-free. Point-Cache demonstrates substantial gains across 8 challenging benchmarks and 4 representative large 3D models, highlighting its effectiveness. Code is available at https://github.com/auniquesun/Point-Cache.

Diffusion models generating images conditionally on text, such as Dall-E 2 and Stable Diffusion, have recently made a splash far beyond the computer vision community. Here, we tackle the related problem of generating point clouds, both unconditionally, and conditionally with images. For the latter, we introduce a novel geometrically-motivated conditioning scheme based on projecting sparse image features into the point cloud and attaching them to each individual point, at every step in the denoising process. This approach improves geometric consistency and yields greater fidelity than current methods relying on unstructured, global latent codes. Additionally, we show how to apply recent continuous-time diffusion schemes. Our method performs on par or above the state of art on conditional and unconditional experiments on synthetic data, while being faster, lighter, and delivering tractable likelihoods. We show it can also scale to diverse indoors scenes.

Bin-picking is a practical and challenging robotic manipulation task, where accurate 6D pose estimation plays a pivotal role. The workpieces in bin-picking are typically textureless and randomly stacked in a bin, which poses a significant challenge to 6D pose estimation. Existing solutions are typically learning-based methods, which require object-specific training. Their efficiency of practical deployment for novel workpieces is highly limited by data collection and model retraining. Zero-shot 6D pose estimation is a potential approach to address the issue of deployment efficiency. Nevertheless, existing zero-shot 6D pose estimation methods are designed to leverage feature matching to establish point-to-point correspondences for pose estimation, which is less effective for workpieces with textureless appearances and ambiguous local regions. In this paper, we propose ZeroBP, a zero-shot pose estimation framework designed specifically for the bin-picking task. ZeroBP learns Position-Aware Correspondence (PAC) between the scene instance and its CAD model, leveraging both local features and global positions to resolve the mismatch issue caused by ambiguous regions with similar shapes and appearances. Extensive experiments on the ROBI dataset demonstrate that ZeroBP outperforms state-of-the-art zero-shot pose estimation methods, achieving an improvement of 9.1% in average recall of correct poses.

Methods for image-to-video generation have achieved impressive, photo-realistic quality. However, adjusting specific elements in generated videos, such as object motion or camera movement, is often a tedious process of trial and error, e.g., involving re-generating videos with different random seeds. Recent techniques address this issue by fine-tuning a pre-trained model to follow conditioning signals, such as bounding boxes or point trajectories. Yet, this fine-tuning procedure can be computationally expensive, and it requires datasets with annotated object motion, which can be difficult to procure. In this work, we introduce SG-I2V, a framework for controllable image-to-video generation that is self-guidedx2013offering zero-shot control by relying solely on the knowledge present in a pre-trained image-to-video diffusion model without the need for fine-tuning or external knowledge. Our zero-shot method outperforms unsupervised baselines while being competitive with supervised models in terms of visual quality and motion fidelity.

Denoising Diffusion Probabilistic Models (DDPMs) exhibit remarkable capabilities in image generation, with studies suggesting that they can generalize by composing latent factors learned from the training data. In this work, we go further and study DDPMs trained on strictly separate subsets of the data distribution with large gaps on the support of the latent factors. We show that such a model can effectively generate images in the unexplored, intermediate regions of the distribution. For instance, when trained on clearly smiling and non-smiling faces, we demonstrate a sampling procedure which can generate slightly smiling faces without reference images (zero-shot interpolation). We replicate these findings for other attributes as well as other datasets. Our code is available at https://github.com/jdeschena/ddpm-zero-shot-interpolation.

Two-point zeroth order methods are important in many applications of zeroth-order optimization, such as robotics, wind farms, power systems, online optimization, and adversarial robustness to black-box attacks in deep neural networks, where the problem may be high-dimensional and/or time-varying. Most problems in these applications are nonconvex and contain saddle points. While existing works have shown that zeroth-order methods utilizing Omega(d) function valuations per iteration (with d denoting the problem dimension) can escape saddle points efficiently, it remains an open question if zeroth-order methods based on two-point estimators can escape saddle points. In this paper, we show that by adding an appropriate isotropic perturbation at each iteration, a zeroth-order algorithm based on 2m (for any 1 leq m leq d) function evaluations per iteration can not only find epsilon-second order stationary points polynomially fast, but do so using only Oleft(d{mepsilon^{2}psi}right) function evaluations, where psi geq Omegaleft(epsilonright) is a parameter capturing the extent to which the function of interest exhibits the strict saddle property.

Given a K-vertex simplex in a d-dimensional space, suppose we measure n points on the simplex with noise (hence, some of the observed points fall outside the simplex). Vertex hunting is the problem of estimating the K vertices of the simplex. A popular vertex hunting algorithm is successive projection algorithm (SPA). However, SPA is observed to perform unsatisfactorily under strong noise or outliers. We propose pseudo-point SPA (pp-SPA). It uses a projection step and a denoise step to generate pseudo-points and feed them into SPA for vertex hunting. We derive error bounds for pp-SPA, leveraging on extreme value theory of (possibly) high-dimensional random vectors. The results suggest that pp-SPA has faster rates and better numerical performances than SPA. Our analysis includes an improved non-asymptotic bound for the original SPA, which is of independent interest.

We present a method for generating consistent novel views from a single source image. Our approach focuses on maximizing the reuse of visible pixels from the source image. To achieve this, we use a monocular depth estimator that transfers visible pixels from the source view to the target view. Starting from a pre-trained 2D inpainting diffusion model, we train our method on the large-scale Objaverse dataset to learn 3D object priors. While training we use a novel masking mechanism based on epipolar lines to further improve the quality of our approach. This allows our framework to perform zero-shot novel view synthesis on a variety of objects. We evaluate the zero-shot abilities of our framework on three challenging datasets: Google Scanned Objects, Ray Traced Multiview, and Common Objects in 3D. See our webpage for more details: https://yashkant.github.io/invs/

We study the problem of single-image zero-shot 3D shape reconstruction. Recent works learn zero-shot shape reconstruction through generative modeling of 3D assets, but these models are computationally expensive at train and inference time. In contrast, the traditional approach to this problem is regression-based, where deterministic models are trained to directly regress the object shape. Such regression methods possess much higher computational efficiency than generative methods. This raises a natural question: is generative modeling necessary for high performance, or conversely, are regression-based approaches still competitive? To answer this, we design a strong regression-based model, called ZeroShape, based on the converging findings in this field and a novel insight. We also curate a large real-world evaluation benchmark, with objects from three different real-world 3D datasets. This evaluation benchmark is more diverse and an order of magnitude larger than what prior works use to quantitatively evaluate their models, aiming at reducing the evaluation variance in our field. We show that ZeroShape not only achieves superior performance over state-of-the-art methods, but also demonstrates significantly higher computational and data efficiency.

In this paper we address the task of finding representative subsets of points in a 3D point cloud by means of a point-wise ordering. Only a few works have tried to address this challenging vision problem, all with the help of hard to obtain point and cloud labels. Different from these works, we introduce the task of point-wise ordering in 3D point clouds through self-supervision, which we call self-ordering. We further contribute the first end-to-end trainable network that learns a point-wise ordering in a self-supervised fashion. It utilizes a novel differentiable point scoring-sorting strategy and it constructs an hierarchical contrastive scheme to obtain self-supervision signals. We extensively ablate the method and show its scalability and superior performance even compared to supervised ordering methods on multiple datasets and tasks including zero-shot ordering of point clouds from unseen categories.

Diffusion models have emerged as a powerful tool for point cloud generation. A key component that drives the impressive performance for generating high-quality samples from noise is iteratively denoise for thousands of steps. While beneficial, the complexity of learning steps has limited its applications to many 3D real-world. To address this limitation, we propose Point Straight Flow (PSF), a model that exhibits impressive performance using one step. Our idea is based on the reformulation of the standard diffusion model, which optimizes the curvy learning trajectory into a straight path. Further, we develop a distillation strategy to shorten the straight path into one step without a performance loss, enabling applications to 3D real-world with latency constraints. We perform evaluations on multiple 3D tasks and find that our PSF performs comparably to the standard diffusion model, outperforming other efficient 3D point cloud generation methods. On real-world applications such as point cloud completion and training-free text-guided generation in a low-latency setup, PSF performs favorably.

This paper focuses on the problem of constrained stochastic optimization. A zeroth order Frank-Wolfe algorithm is proposed, which in addition to the projection-free nature of the vanilla Frank-Wolfe algorithm makes it gradient free. Under convexity and smoothness assumption, we show that the proposed algorithm converges to the optimal objective function at a rate Oleft(1/T^{1/3}right), where T denotes the iteration count. In particular, the primal sub-optimality gap is shown to have a dimension dependence of Oleft(d^{1/3}right), which is the best known dimension dependence among all zeroth order optimization algorithms with one directional derivative per iteration. For non-convex functions, we obtain the Frank-Wolfe gap to be Oleft(d^{1/3}T^{-1/4}right). Experiments on black-box optimization setups demonstrate the efficacy of the proposed algorithm.

There is a growing number of tasks that work directly on point clouds. As the size of the point cloud grows, so do the computational demands of these tasks. A possible solution is to sample the point cloud first. Classic sampling approaches, such as farthest point sampling (FPS), do not consider the downstream task. A recent work showed that learning a task-specific sampling can improve results significantly. However, the proposed technique did not deal with the non-differentiability of the sampling operation and offered a workaround instead. We introduce a novel differentiable relaxation for point cloud sampling that approximates sampled points as a mixture of points in the primary input cloud. Our approximation scheme leads to consistently good results on classification and geometry reconstruction applications. We also show that the proposed sampling method can be used as a front to a point cloud registration network. This is a challenging task since sampling must be consistent across two different point clouds for a shared downstream task. In all cases, our approach outperforms existing non-learned and learned sampling alternatives. Our code is publicly available at https://github.com/itailang/SampleNet.

We show how to obtain improved active learning methods in the agnostic (adversarial noise) setting by combining marginal leverage score sampling with non-independent sampling strategies that promote spatial coverage. In particular, we propose an easily implemented method based on the pivotal sampling algorithm, which we test on problems motivated by learning-based methods for parametric PDEs and uncertainty quantification. In comparison to independent sampling, our method reduces the number of samples needed to reach a given target accuracy by up to 50%. We support our findings with two theoretical results. First, we show that any non-independent leverage score sampling method that obeys a weak one-sided ell_{infty} independence condition (which includes pivotal sampling) can actively learn d dimensional linear functions with O(dlog d) samples, matching independent sampling. This result extends recent work on matrix Chernoff bounds under ell_{infty} independence, and may be of interest for analyzing other sampling strategies beyond pivotal sampling. Second, we show that, for the important case of polynomial regression, our pivotal method obtains an improved bound of O(d) samples.

We present ZeroComp, an effective zero-shot 3D object compositing approach that does not require paired composite-scene images during training. Our method leverages ControlNet to condition from intrinsic images and combines it with a Stable Diffusion model to utilize its scene priors, together operating as an effective rendering engine. During training, ZeroComp uses intrinsic images based on geometry, albedo, and masked shading, all without the need for paired images of scenes with and without composite objects. Once trained, it seamlessly integrates virtual 3D objects into scenes, adjusting shading to create realistic composites. We developed a high-quality evaluation dataset and demonstrate that ZeroComp outperforms methods using explicit lighting estimations and generative techniques in quantitative and human perception benchmarks. Additionally, ZeroComp extends to real and outdoor image compositing, even when trained solely on synthetic indoor data, showcasing its effectiveness in image compositing.

This paper explores promptable NeRF generation (e.g., text prompt or single image prompt) for direct conditioning and fast generation of NeRF parameters for the underlying 3D scenes, thus undoing complex intermediate steps while providing full 3D generation with conditional control. Unlike previous diffusion-CLIP-based pipelines that involve tedious per-prompt optimizations, Prompt2NeRF-PIL is capable of generating a variety of 3D objects with a single forward pass, leveraging a pre-trained implicit latent space of NeRF parameters. Furthermore, in zero-shot tasks, our experiments demonstrate that the NeRFs produced by our method serve as semantically informative initializations, significantly accelerating the inference process of existing prompt-to-NeRF methods. Specifically, we will show that our approach speeds up the text-to-NeRF model DreamFusion and the 3D reconstruction speed of the image-to-NeRF method Zero-1-to-3 by 3 to 5 times.

Reconstructing accurate 3D scenes from images is a long-standing vision task. Due to the ill-posedness of the single-image reconstruction problem, most well-established methods are built upon multi-view geometry. State-of-the-art (SOTA) monocular metric depth estimation methods can only handle a single camera model and are unable to perform mixed-data training due to the metric ambiguity. Meanwhile, SOTA monocular methods trained on large mixed datasets achieve zero-shot generalization by learning affine-invariant depths, which cannot recover real-world metrics. In this work, we show that the key to a zero-shot single-view metric depth model lies in the combination of large-scale data training and resolving the metric ambiguity from various camera models. We propose a canonical camera space transformation module, which explicitly addresses the ambiguity problems and can be effortlessly plugged into existing monocular models. Equipped with our module, monocular models can be stably trained with over 8 million images with thousands of camera models, resulting in zero-shot generalization to in-the-wild images with unseen camera settings. Experiments demonstrate SOTA performance of our method on 7 zero-shot benchmarks. Notably, our method won the championship in the 2nd Monocular Depth Estimation Challenge. Our method enables the accurate recovery of metric 3D structures on randomly collected internet images, paving the way for plausible single-image metrology. The potential benefits extend to downstream tasks, which can be significantly improved by simply plugging in our model. For example, our model relieves the scale drift issues of monocular-SLAM (Fig. 1), leading to high-quality metric scale dense mapping. The code is available at https://github.com/YvanYin/Metric3D.

We present PointInfinity, an efficient family of point cloud diffusion models. Our core idea is to use a transformer-based architecture with a fixed-size, resolution-invariant latent representation. This enables efficient training with low-resolution point clouds, while allowing high-resolution point clouds to be generated during inference. More importantly, we show that scaling the test-time resolution beyond the training resolution improves the fidelity of generated point clouds and surfaces. We analyze this phenomenon and draw a link to classifier-free guidance commonly used in diffusion models, demonstrating that both allow trading off fidelity and variability during inference. Experiments on CO3D show that PointInfinity can efficiently generate high-resolution point clouds (up to 131k points, 31 times more than Point-E) with state-of-the-art quality.

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific target generative processes, where these local random variables are governed by a higher-level global random variate. The global variable helps memorize the important information from historic episodes while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our model framework, the prediction on a novel episode/task can be seen as a Bayesian inference problem. However, a main obstacle in learning with a large/infinite number of local random variables in online nature, is that one is not allowed to store the posterior distribution of the current local random variable for frequent future updates, typical in conventional variational inference. We need to be able to treat each local variable as a one-time iterate in the optimization. We propose a Normal-Inverse-Wishart model, for which we show that this one-time iterate optimization becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it is not required to maintain computational graphs for the whole gradient optimization steps per episode. Our approach is also different from existing Bayesian meta learning methods in that unlike dealing with a single random variable for the whole episodes, our approach has a hierarchical structure that allows one-time episodic optimization, desirable for principled Bayesian learning with many/infinite tasks. The code is available at https://github.com/minyoungkim21/niwmeta.

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

In recent years, particle-based variational inference (ParVI) methods such as Stein variational gradient descent (SVGD) have grown in popularity as scalable methods for Bayesian inference. Unfortunately, the properties of such methods invariably depend on hyperparameters such as the learning rate, which must be carefully tuned by the practitioner in order to ensure convergence to the target measure at a suitable rate. In this paper, we introduce a suite of new particle-based methods for scalable Bayesian inference based on coin betting, which are entirely learning-rate free. We illustrate the performance of our approach on a range of numerical examples, including several high-dimensional models and datasets, demonstrating comparable performance to other ParVI algorithms with no need to tune a learning rate.

Diffusion probabilistic models (DPMs) have demonstrated a very promising ability in high-resolution image synthesis. However, sampling from a pre-trained DPM usually requires hundreds of model evaluations, which is computationally expensive. Despite recent progress in designing high-order solvers for DPMs, there still exists room for further speedup, especially in extremely few steps (e.g., 5~10 steps). Inspired by the predictor-corrector for ODE solvers, we develop a unified corrector (UniC) that can be applied after any existing DPM sampler to increase the order of accuracy without extra model evaluations, and derive a unified predictor (UniP) that supports arbitrary order as a byproduct. Combining UniP and UniC, we propose a unified predictor-corrector framework called UniPC for the fast sampling of DPMs, which has a unified analytical form for any order and can significantly improve the sampling quality over previous methods. We evaluate our methods through extensive experiments including both unconditional and conditional sampling using pixel-space and latent-space DPMs. Our UniPC can achieve 3.87 FID on CIFAR10 (unconditional) and 7.51 FID on ImageNet 256times256 (conditional) with only 10 function evaluations. Code is available at https://github.com/wl-zhao/UniPC

Model order reduction has been extensively studied over the last two decades. Projection-based methods such as the Proper Orthogonal Decomposition and the Reduced Basis Method enjoy the important advantages of Galerkin methods in the derivation of the reduced problem, but are limited to linear data compression for which the reduced solution is sought as a linear combination of spatial modes. Nonlinear data compression must be used when the solution manifold is not embedded in a low-dimensional subspace. Early methods involve piecewise linear data compression, by constructing a dictionary of reduced-order models tailored to a partition of the solution manifold. In this work, we introduce the concept of optimal partition of the solution manifold in terms of normalized Kolmogorov widths, and prove that the optimal partitions can be found by means of a representative-based clustering algorithm using the sine dissimilarity measure on the solution manifold.

We consider a class of structured fractional minimization problems, in which the numerator part of the objective is the sum of a differentiable convex function and a convex non-smooth function, while the denominator part is a convex or concave function. This problem is difficult to solve since it is non-convex. By exploiting the structure of the problem, we propose two Coordinate Descent (CD) methods for solving this problem. The proposed methods iteratively solve a one-dimensional subproblem globally, and they are guaranteed to converge to coordinate-wise stationary points. In the case of a convex denominator, under a weak locally bounded non-convexity condition, we prove that the optimality of coordinate-wise stationary point is stronger than that of the standard critical point and directional point. Under additional suitable conditions, CD methods converge Q-linearly to coordinate-wise stationary points. In the case of a concave denominator, we show that any critical point is a global minimum, and CD methods converge to the global minimum with a sublinear convergence rate. We demonstrate the applicability of the proposed methods to some machine learning and signal processing models. Our experiments on real-world data have shown that our method significantly and consistently outperforms existing methods in terms of accuracy.

We examine a simple stochastic strategy for adapting well-known single-point acquisition functions to allow batch active learning. Unlike acquiring the top-K points from the pool set, score- or rank-based sampling takes into account that acquisition scores change as new data are acquired. This simple strategy for adapting standard single-sample acquisition strategies can even perform just as well as compute-intensive state-of-the-art batch acquisition functions, like BatchBALD or BADGE, while using orders of magnitude less compute. In addition to providing a practical option for machine learning practitioners, the surprising success of the proposed method in a wide range of experimental settings raises a difficult question for the field: when are these expensive batch acquisition methods pulling their weight?

Point-based representations have recently gained popularity in novel view synthesis, for their unique advantages, e.g., intuitive geometric representation, simple manipulation, and faster convergence. However, based on our observation, these point-based neural re-rendering methods are only expected to perform well under ideal conditions and suffer from noisy, patchy points and unbounded scenes, which are challenging to handle but defacto common in real applications. To this end, we revisit one such influential method, known as Neural Point-based Graphics (NPBG), as our baseline, and propose Robust Point-based Graphics (RPBG). We in-depth analyze the factors that prevent NPBG from achieving satisfactory renderings on generic datasets, and accordingly reform the pipeline to make it more robust to varying datasets in-the-wild. Inspired by the practices in image restoration, we greatly enhance the neural renderer to enable the attention-based correction of point visibility and the inpainting of incomplete rasterization, with only acceptable overheads. We also seek for a simple and lightweight alternative for environment modeling and an iterative method to alleviate the problem of poor geometry. By thorough evaluation on a wide range of datasets with different shooting conditions and camera trajectories, RPBG stably outperforms the baseline by a large margin, and exhibits its great robustness over state-of-the-art NeRF-based variants. Code available at https://github.com/QT-Zhu/RPBG.

We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed point solving layer into the denoising network of a diffusion model, transforming the diffusion process into a sequence of closely-related fixed point problems. Combined with a new stochastic training method, this approach significantly reduces model size, reduces memory usage, and accelerates training. Moreover, it enables the development of two new techniques to improve sampling efficiency: reallocating computation across timesteps and reusing fixed point solutions between timesteps. We conduct extensive experiments with state-of-the-art models on ImageNet, FFHQ, CelebA-HQ, and LSUN-Church, demonstrating substantial improvements in performance and efficiency. Compared to the state-of-the-art DiT model, FPDM contains 87% fewer parameters, consumes 60% less memory during training, and improves image generation quality in situations where sampling computation or time is limited. Our code and pretrained models are available at https://lukemelas.github.io/fixed-point-diffusion-models.

Diffusion probabilistic models (DPMs) have exhibited excellent performance for high-fidelity image generation while suffering from inefficient sampling. Recent works accelerate the sampling procedure by proposing fast ODE solvers that leverage the specific ODE form of DPMs. However, they highly rely on specific parameterization during inference (such as noise/data prediction), which might not be the optimal choice. In this work, we propose a novel formulation towards the optimal parameterization during sampling that minimizes the first-order discretization error of the ODE solution. Based on such formulation, we propose DPM-Solver-v3, a new fast ODE solver for DPMs by introducing several coefficients efficiently computed on the pretrained model, which we call empirical model statistics. We further incorporate multistep methods and a predictor-corrector framework, and propose some techniques for improving sample quality at small numbers of function evaluations (NFE) or large guidance scales. Experiments show that DPM-Solver-v3 achieves consistently better or comparable performance in both unconditional and conditional sampling with both pixel-space and latent-space DPMs, especially in 5sim10 NFEs. We achieve FIDs of 12.21 (5 NFE), 2.51 (10 NFE) on unconditional CIFAR10, and MSE of 0.55 (5 NFE, 7.5 guidance scale) on Stable Diffusion, bringing a speed-up of 15\%sim30\% compared to previous state-of-the-art training-free methods. Code is available at https://github.com/thu-ml/DPM-Solver-v3.

Recent advancements in generative modeling have made it possible to generate high-quality content from context information, but a key question remains: how to teach models to know when to generate content? To answer this question, this study proposes a novel event generative model that draws its statistical intuition from marked temporal point processes, and offers a clean, flexible, and computationally efficient solution for a wide range of applications involving multi-dimensional marks. We aim to capture the distribution of the point process without explicitly specifying the conditional intensity or probability density. Instead, we use a conditional generator that takes the history of events as input and generates the high-quality subsequent event that is likely to occur given the prior observations. The proposed framework offers a host of benefits, including exceptional efficiency in learning the model and generating samples, as well as considerable representational power to capture intricate dynamics in multi- or even high-dimensional event space. Our numerical results demonstrate superior performance compared to other state-of-the-art baselines.

We introduce a 3D-aware diffusion model, ZeroNVS, for single-image novel view synthesis for in-the-wild scenes. While existing methods are designed for single objects with masked backgrounds, we propose new techniques to address challenges introduced by in-the-wild multi-object scenes with complex backgrounds. Specifically, we train a generative prior on a mixture of data sources that capture object-centric, indoor, and outdoor scenes. To address issues from data mixture such as depth-scale ambiguity, we propose a novel camera conditioning parameterization and normalization scheme. Further, we observe that Score Distillation Sampling (SDS) tends to truncate the distribution of complex backgrounds during distillation of 360-degree scenes, and propose "SDS anchoring" to improve the diversity of synthesized novel views. Our model sets a new state-of-the-art result in LPIPS on the DTU dataset in the zero-shot setting, even outperforming methods specifically trained on DTU. We further adapt the challenging Mip-NeRF 360 dataset as a new benchmark for single-image novel view synthesis, and demonstrate strong performance in this setting. Our code and data are at http://kylesargent.github.io/zeronvs/

Given a factorization of an image into a sum of linear components, we present a zero-shot method to control each individual component through diffusion model sampling. For example, we can decompose an image into low and high spatial frequencies and condition these components on different text prompts. This produces hybrid images, which change appearance depending on viewing distance. By decomposing an image into three frequency subbands, we can generate hybrid images with three prompts. We also use a decomposition into grayscale and color components to produce images whose appearance changes when they are viewed in grayscale, a phenomena that naturally occurs under dim lighting. And we explore a decomposition by a motion blur kernel, which produces images that change appearance under motion blurring. Our method works by denoising with a composite noise estimate, built from the components of noise estimates conditioned on different prompts. We also show that for certain decompositions, our method recovers prior approaches to compositional generation and spatial control. Finally, we show that we can extend our approach to generate hybrid images from real images. We do this by holding one component fixed and generating the remaining components, effectively solving an inverse problem.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration complexity, and propose a generic approach that, based on optimal first-order methods, allows to obtain in a black-box fashion new zeroth-order algorithms for non-smooth convex optimization problems. Our approach not only leads to optimal oracle complexity, but also allows to obtain iteration complexity similar to first-order methods, which, in turn, allows to exploit parallel computations to accelerate the convergence of our algorithms. We also elaborate on extensions for stochastic optimization problems, saddle-point problems, and distributed optimization.

We tackle the problem of estimating a Manhattan frame, i.e. three orthogonal vanishing points, and the unknown focal length of the camera, leveraging a prior vertical direction. The direction can come from an Inertial Measurement Unit that is a standard component of recent consumer devices, e.g., smartphones. We provide an exhaustive analysis of minimal line configurations and derive two new 2-line solvers, one of which does not suffer from singularities affecting existing solvers. Additionally, we design a new non-minimal method, running on an arbitrary number of lines, to boost the performance in local optimization. Combining all solvers in a hybrid robust estimator, our method achieves increased accuracy even with a rough prior. Experiments on synthetic and real-world datasets demonstrate the superior accuracy of our method compared to the state of the art, while having comparable runtimes. We further demonstrate the applicability of our solvers for relative rotation estimation. The code is available at https://github.com/cvg/VP-Estimation-with-Prior-Gravity.

We introduce Zero-1-to-3, a framework for changing the camera viewpoint of an object given just a single RGB image. To perform novel view synthesis in this under-constrained setting, we capitalize on the geometric priors that large-scale diffusion models learn about natural images. Our conditional diffusion model uses a synthetic dataset to learn controls of the relative camera viewpoint, which allow new images to be generated of the same object under a specified camera transformation. Even though it is trained on a synthetic dataset, our model retains a strong zero-shot generalization ability to out-of-distribution datasets as well as in-the-wild images, including impressionist paintings. Our viewpoint-conditioned diffusion approach can further be used for the task of 3D reconstruction from a single image. Qualitative and quantitative experiments show that our method significantly outperforms state-of-the-art single-view 3D reconstruction and novel view synthesis models by leveraging Internet-scale pre-training.

Despite the remarkable success of diffusion models in image generation, slow sampling remains a persistent issue. To accelerate the sampling process, prior studies have reformulated diffusion sampling as an ODE/SDE and introduced higher-order numerical methods. However, these methods often produce divergence artifacts, especially with a low number of sampling steps, which limits the achievable acceleration. In this paper, we investigate the potential causes of these artifacts and suggest that the small stability regions of these methods could be the principal cause. To address this issue, we propose two novel techniques. The first technique involves the incorporation of Heavy Ball (HB) momentum, a well-known technique for improving optimization, into existing diffusion numerical methods to expand their stability regions. We also prove that the resulting methods have first-order convergence. The second technique, called Generalized Heavy Ball (GHVB), constructs a new high-order method that offers a variable trade-off between accuracy and artifact suppression. Experimental results show that our techniques are highly effective in reducing artifacts and improving image quality, surpassing state-of-the-art diffusion solvers on both pixel-based and latent-based diffusion models for low-step sampling. Our research provides novel insights into the design of numerical methods for future diffusion work.

Omnidirectional images (ODIs) are commonly used in real-world visual tasks, and high-resolution ODIs help improve the performance of related visual tasks. Most existing super-resolution methods for ODIs use end-to-end learning strategies, resulting in inferior realness of generated images and a lack of effective out-of-domain generalization capabilities in training methods. Image generation methods represented by diffusion model provide strong priors for visual tasks and have been proven to be effectively applied to image restoration tasks. Leveraging the image priors of the Stable Diffusion (SD) model, we achieve omnidirectional image super-resolution with both fidelity and realness, dubbed as OmniSSR. Firstly, we transform the equirectangular projection (ERP) images into tangent projection (TP) images, whose distribution approximates the planar image domain. Then, we use SD to iteratively sample initial high-resolution results. At each denoising iteration, we further correct and update the initial results using the proposed Octadecaplex Tangent Information Interaction (OTII) and Gradient Decomposition (GD) technique to ensure better consistency. Finally, the TP images are transformed back to obtain the final high-resolution results. Our method is zero-shot, requiring no training or fine-tuning. Experiments of our method on two benchmark datasets demonstrate the effectiveness of our proposed method.

Classifier-Free Guidance (CFG) is a widely adopted technique in diffusion/flow models to improve image fidelity and controllability. In this work, we first analytically study the effect of CFG on flow matching models trained on Gaussian mixtures where the ground-truth flow can be derived. We observe that in the early stages of training, when the flow estimation is inaccurate, CFG directs samples toward incorrect trajectories. Building on this observation, we propose CFG-Zero*, an improved CFG with two contributions: (a) optimized scale, where a scalar is optimized to correct for the inaccuracies in the estimated velocity, hence the * in the name; and (b) zero-init, which involves zeroing out the first few steps of the ODE solver. Experiments on both text-to-image (Lumina-Next, Stable Diffusion 3, and Flux) and text-to-video (Wan-2.1) generation demonstrate that CFG-Zero* consistently outperforms CFG, highlighting its effectiveness in guiding Flow Matching models. (Code is available at github.com/WeichenFan/CFG-Zero-star)

Given an unconditional diffusion model and a predictor for a target property of interest (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. Existing methods, though effective in various individual applications, often lack theoretical grounding and rigorous testing on extensive benchmarks. As a result, they could even fail on simple tasks, and applying them to a new problem becomes unavoidably difficult. This paper introduces a novel algorithmic framework encompassing existing methods as special cases, unifying the study of training-free guidance into the analysis of an algorithm-agnostic design space. Via theoretical and empirical investigation, we propose an efficient and effective hyper-parameter searching strategy that can be readily applied to any downstream task. We systematically benchmark across 7 diffusion models on 16 tasks with 40 targets, and improve performance by 8.5% on average. Our framework and benchmark offer a solid foundation for conditional generation in a training-free manner.

We consider the problem of estimating the optimal transport map between two probability distributions, P and Q in mathbb R^d, on the basis of i.i.d. samples. All existing statistical analyses of this problem require the assumption that the transport map is Lipschitz, a strong requirement that, in particular, excludes any examples where the transport map is discontinuous. As a first step towards developing estimation procedures for discontinuous maps, we consider the important special case where the data distribution Q is a discrete measure supported on a finite number of points in mathbb R^d. We study a computationally efficient estimator initially proposed by Pooladian and Niles-Weed (2021), based on entropic optimal transport, and show in the semi-discrete setting that it converges at the minimax-optimal rate n^{-1/2}, independent of dimension. Other standard map estimation techniques both lack finite-sample guarantees in this setting and provably suffer from the curse of dimensionality. We confirm these results in numerical experiments, and provide experiments for other settings, not covered by our theory, which indicate that the entropic estimator is a promising methodology for other discontinuous transport map estimation problems.

Audio-visual zero-shot learning aims to classify samples consisting of a pair of corresponding audio and video sequences from classes that are not present during training. An analysis of the audio-visual data reveals a large degree of hyperbolicity, indicating the potential benefit of using a hyperbolic transformation to achieve curvature-aware geometric learning, with the aim of exploring more complex hierarchical data structures for this task. The proposed approach employs a novel loss function that incorporates cross-modality alignment between video and audio features in the hyperbolic space. Additionally, we explore the use of multiple adaptive curvatures for hyperbolic projections. The experimental results on this very challenging task demonstrate that our proposed hyperbolic approach for zero-shot learning outperforms the SOTA method on three datasets: VGGSound-GZSL, UCF-GZSL, and ActivityNet-GZSL achieving a harmonic mean (HM) improvement of around 3.0%, 7.0%, and 5.3%, respectively.

We present a Non-parametric Network for 3D point cloud analysis, Point-NN, which consists of purely non-learnable components: farthest point sampling (FPS), k-nearest neighbors (k-NN), and pooling operations, with trigonometric functions. Surprisingly, it performs well on various 3D tasks, requiring no parameters or training, and even surpasses existing fully trained models. Starting from this basic non-parametric model, we propose two extensions. First, Point-NN can serve as a base architectural framework to construct Parametric Networks by simply inserting linear layers on top. Given the superior non-parametric foundation, the derived Point-PN exhibits a high performance-efficiency trade-off with only a few learnable parameters. Second, Point-NN can be regarded as a plug-and-play module for the already trained 3D models during inference. Point-NN captures the complementary geometric knowledge and enhances existing methods for different 3D benchmarks without re-training. We hope our work may cast a light on the community for understanding 3D point clouds with non-parametric methods. Code is available at https://github.com/ZrrSkywalker/Point-NN.

We study the problem of posterior sampling in discrete-state spaces using discrete diffusion models. While posterior sampling methods for continuous diffusion models have achieved remarkable progress, analogous methods for discrete diffusion models remain challenging. In this work, we introduce a principled plug-and-play discrete diffusion posterior sampling algorithm based on split Gibbs sampling, which we call SG-DPS. Our algorithm enables reward-guided generation and solving inverse problems in discrete-state spaces. We demonstrate that SG-DPS converges to the true posterior distribution on synthetic benchmarks, and enjoys state-of-the-art posterior sampling performance on a range of benchmarks for discrete data, achieving up to 2x improved performance compared to existing baselines.

Recently, using diffusion models for zero-shot image restoration (IR) has become a new hot paradigm. This type of method only needs to use the pre-trained off-the-shelf diffusion models, without any finetuning, and can directly handle various IR tasks. The upper limit of the restoration performance depends on the pre-trained diffusion models, which are in rapid evolution. However, current methods only discuss how to deal with fixed-size images, but dealing with images of arbitrary sizes is very important for practical applications. This paper focuses on how to use those diffusion-based zero-shot IR methods to deal with any size while maintaining the excellent characteristics of zero-shot. A simple way to solve arbitrary size is to divide it into fixed-size patches and solve each patch independently. But this may yield significant artifacts since it neither considers the global semantics of all patches nor the local information of adjacent patches. Inspired by the Range-Null space Decomposition, we propose the Mask-Shift Restoration to address local incoherence and propose the Hierarchical Restoration to alleviate out-of-domain issues. Our simple, parameter-free approaches can be used not only for image restoration but also for image generation of unlimited sizes, with the potential to be a general tool for diffusion models. Code: https://github.com/wyhuai/DDNM/tree/main/hq_demo

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.

Temporal Point Processes (TPP) are probabilistic generative frameworks. They model discrete event sequences localized in continuous time. Generally, real-life events reveal descriptive information, known as marks. Marked TPPs model time and marks of the event together for practical relevance. Conditioned on past events, marked TPPs aim to learn the joint distribution of the time and the mark of the next event. For simplicity, conditionally independent TPP models assume time and marks are independent given event history. They factorize the conditional joint distribution of time and mark into the product of individual conditional distributions. This structural limitation in the design of TPP models hurt the predictive performance on entangled time and mark interactions. In this work, we model the conditional inter-dependence of time and mark to overcome the limitations of conditionally independent models. We construct a multivariate TPP conditioning the time distribution on the current event mark in addition to past events. Besides the conventional intensity-based models for conditional joint distribution, we also draw on flexible intensity-free TPP models from the literature. The proposed TPP models outperform conditionally independent and dependent models in standard prediction tasks. Our experimentation on various datasets with multiple evaluation metrics highlights the merit of the proposed approach.

Practitioners frequently aim to infer an unobserved population trajectory using sample snapshots at multiple time points. For instance, in single-cell sequencing, scientists would like to learn how gene expression evolves over time. But sequencing any cell destroys that cell. So we cannot access any cell's full trajectory, but we can access snapshot samples from many cells. Stochastic differential equations are commonly used to analyze systems with full individual-trajectory access; since here we have only sample snapshots, these methods are inapplicable. The deep learning community has recently explored using Schr\"odinger bridges (SBs) and their extensions to estimate these dynamics. However, these methods either (1) interpolate between just two time points or (2) require a single fixed reference dynamic within the SB, which is often just set to be Brownian motion. But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model class for the reference dynamic but not the exact values of the parameters within it. So we propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a class of reference dynamics, not a single fixed one. In particular, we suggest an iterative projection method inspired by Schr\"odinger bridges; we alternate between learning a piecewise SB on the unobserved trajectories and using the learned SB to refine our best guess for the dynamics within the reference class. We demonstrate the advantages of our method via a well-known simulated parametric model from ecology, simulated and real data from systems biology, and real motion-capture data.

We advance the study of incentivized bandit exploration, in which arm choices are viewed as recommendations and are required to be Bayesian incentive compatible. Recent work has shown under certain independence assumptions that after collecting enough initial samples, the popular Thompson sampling algorithm becomes incentive compatible. We give an analog of this result for linear bandits, where the independence of the prior is replaced by a natural convexity condition. This opens up the possibility of efficient and regret-optimal incentivized exploration in high-dimensional action spaces. In the semibandit model, we also improve the sample complexity for the pre-Thompson sampling phase of initial data collection.

Incorporating a temporal dimension into pretrained image diffusion models for video generation is a prevalent approach. However, this method is computationally demanding and necessitates large-scale video datasets. More critically, the heterogeneity between image and video datasets often results in catastrophic forgetting of the image expertise. Recent attempts to directly extract video snippets from image diffusion models have somewhat mitigated these problems. Nevertheless, these methods can only generate brief video clips with simple movements and fail to capture fine-grained motion or non-grid deformation. In this paper, we propose a novel Zero-Shot video Sampling algorithm, denoted as ZS^2, capable of directly sampling high-quality video clips from existing image synthesis methods, such as Stable Diffusion, without any training or optimization. Specifically, ZS^2 utilizes the dependency noise model and temporal momentum attention to ensure content consistency and animation coherence, respectively. This ability enables it to excel in related tasks, such as conditional and context-specialized video generation and instruction-guided video editing. Experimental results demonstrate that ZS^2 achieves state-of-the-art performance in zero-shot video generation, occasionally outperforming recent supervised methods. Homepage: https://densechen.github.io/zss/.

We introduce PointOdyssey, a large-scale synthetic dataset, and data generation framework, for the training and evaluation of long-term fine-grained tracking algorithms. Our goal is to advance the state-of-the-art by placing emphasis on long videos with naturalistic motion. Toward the goal of naturalism, we animate deformable characters using real-world motion capture data, we build 3D scenes to match the motion capture environments, and we render camera viewpoints using trajectories mined via structure-from-motion on real videos. We create combinatorial diversity by randomizing character appearance, motion profiles, materials, lighting, 3D assets, and atmospheric effects. Our dataset currently includes 104 videos, averaging 2,000 frames long, with orders of magnitude more correspondence annotations than prior work. We show that existing methods can be trained from scratch in our dataset and outperform the published variants. Finally, we introduce modifications to the PIPs point tracking method, greatly widening its temporal receptive field, which improves its performance on PointOdyssey as well as on two real-world benchmarks. Our data and code are publicly available at: https://pointodyssey.com

Processing large point clouds is a challenging task. Therefore, the data is often sampled to a size that can be processed more easily. The question is how to sample the data? A popular sampling technique is Farthest Point Sampling (FPS). However, FPS is agnostic to a downstream application (classification, retrieval, etc.). The underlying assumption seems to be that minimizing the farthest point distance, as done by FPS, is a good proxy to other objective functions. We show that it is better to learn how to sample. To do that, we propose a deep network to simplify 3D point clouds. The network, termed S-NET, takes a point cloud and produces a smaller point cloud that is optimized for a particular task. The simplified point cloud is not guaranteed to be a subset of the original point cloud. Therefore, we match it to a subset of the original points in a post-processing step. We contrast our approach with FPS by experimenting on two standard data sets and show significantly better results for a variety of applications. Our code is publicly available at: https://github.com/orendv/learning_to_sample

In the stochastic multi-armed bandit problem, a randomized probability matching policy called Thompson sampling (TS) has shown excellent performance in various reward models. In addition to the empirical performance, TS has been shown to achieve asymptotic problem-dependent lower bounds in several models. However, its optimality has been mainly addressed under light-tailed or one-parameter models that belong to exponential families. In this paper, we consider the optimality of TS for the Pareto model that has a heavy tail and is parameterized by two unknown parameters. Specifically, we discuss the optimality of TS with probability matching priors that include the Jeffreys prior and the reference priors. We first prove that TS with certain probability matching priors can achieve the optimal regret bound. Then, we show the suboptimality of TS with other priors, including the Jeffreys and the reference priors. Nevertheless, we find that TS with the Jeffreys and reference priors can achieve the asymptotic lower bound if one uses a truncation procedure. These results suggest carefully choosing noninformative priors to avoid suboptimality and show the effectiveness of truncation procedures in TS-based policies.

We address the task of estimating camera parameters from a set of images depicting a scene. Popular feature-based structure-from-motion (SfM) tools solve this task by incremental reconstruction: they repeat triangulation of sparse 3D points and registration of more camera views to the sparse point cloud. We re-interpret incremental structure-from-motion as an iterated application and refinement of a visual relocalizer, that is, of a method that registers new views to the current state of the reconstruction. This perspective allows us to investigate alternative visual relocalizers that are not rooted in local feature matching. We show that scene coordinate regression, a learning-based relocalization approach, allows us to build implicit, neural scene representations from unposed images. Different from other learning-based reconstruction methods, we do not require pose priors nor sequential inputs, and we optimize efficiently over thousands of images. Our method, ACE0 (ACE Zero), estimates camera poses to an accuracy comparable to feature-based SfM, as demonstrated by novel view synthesis. Project page: https://nianticlabs.github.io/acezero/

Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To address these limitations, variants of the OT problem, including unbalanced OT, Optimal partial transport (OPT), and Hellinger Kantorovich (HK), have been proposed. In this paper, we propose the Linear optimal partial transport (LOPT) embedding, which extends the (local) linearization technique on OT and HK to the OPT problem. The proposed embedding allows for faster computation of OPT distance between pairs of positive measures. Besides our theoretical contributions, we demonstrate the LOPT embedding technique in point-cloud interpolation and PCA analysis.

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to optimal control, to PDE-constrained optimization. We develop an adaptive inexact Newton method for this problem class. In each iteration, we solve the Lagrangian Newton system inexactly via a randomized iterative sketching solver, and select a suitable stepsize by performing line search on an exact augmented Lagrangian merit function. The randomized solvers have advantages over deterministic linear system solvers by significantly reducing per-iteration flops complexity and storage cost, when equipped with suitable sketching matrices. Our method adaptively controls the accuracy of the randomized solver and the penalty parameters of the exact augmented Lagrangian, to ensure that the inexact Newton direction is a descent direction of the exact augmented Lagrangian. This allows us to establish a global almost sure convergence. We also show that a unit stepsize is admissible locally, so that our method exhibits a local linear convergence. Furthermore, we prove that the linear convergence can be strengthened to superlinear convergence if we gradually sharpen the adaptive accuracy condition on the randomized solver. We demonstrate the superior performance of our method on benchmark nonlinear problems in CUTEst test set, constrained logistic regression with data from LIBSVM, and a PDE-constrained problem.

In this paper, we present PointmapDiffusion, a novel framework for single-image novel view synthesis (NVS) that utilizes pre-trained 2D diffusion models. Our method is the first to leverage pointmaps (i.e. rasterized 3D scene coordinates) as a conditioning signal, capturing geometric prior from the reference images to guide the diffusion process. By embedding reference attention blocks and a ControlNet for pointmap features, our model balances between generative capability and geometric consistency, enabling accurate view synthesis across varying viewpoints. Extensive experiments on diverse real-world datasets demonstrate that PointmapDiffusion achieves high-quality, multi-view consistent results with significantly fewer trainable parameters compared to other baselines for single-image NVS tasks.

Learned optimizers (LOs) can significantly reduce the wall-clock training time of neural networks, substantially reducing training costs. However, they often suffer from poor meta-generalization, especially when training networks larger than those seen during meta-training. To address this, we use the recently proposed Maximal Update Parametrization (muP), which allows zero-shot generalization of optimizer hyperparameters from smaller to larger models. We extend muP theory to learned optimizers, treating the meta-training problem as finding the learned optimizer under muP. Our evaluation shows that LOs meta-trained with muP substantially improve meta-generalization as compared to LOs trained under standard parametrization (SP). Notably, when applied to large-width models, our best muLO, trained for 103 GPU-hours, matches or exceeds the performance of VeLO, the largest publicly available learned optimizer, meta-trained with 4000 TPU-months of compute. Moreover, muLOs demonstrate better generalization than their SP counterparts to deeper networks and to much longer training horizons (25 times longer) than those seen during meta-training.

Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Few prior works study deep learning on point sets. PointNet by Qi et al. is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to recognize fine-grained patterns and generalizability to complex scenes. In this work, we introduce a hierarchical neural network that applies PointNet recursively on a nested partitioning of the input point set. By exploiting metric space distances, our network is able to learn local features with increasing contextual scales. With further observation that point sets are usually sampled with varying densities, which results in greatly decreased performance for networks trained on uniform densities, we propose novel set learning layers to adaptively combine features from multiple scales. Experiments show that our network called PointNet++ is able to learn deep point set features efficiently and robustly. In particular, results significantly better than state-of-the-art have been obtained on challenging benchmarks of 3D point clouds.

Multi-view stereo reconstruction (MVS) in the wild requires to first estimate the camera parameters e.g. intrinsic and extrinsic parameters. These are usually tedious and cumbersome to obtain, yet they are mandatory to triangulate corresponding pixels in 3D space, which is the core of all best performing MVS algorithms. In this work, we take an opposite stance and introduce DUSt3R, a radically novel paradigm for Dense and Unconstrained Stereo 3D Reconstruction of arbitrary image collections, i.e. operating without prior information about camera calibration nor viewpoint poses. We cast the pairwise reconstruction problem as a regression of pointmaps, relaxing the hard constraints of usual projective camera models. We show that this formulation smoothly unifies the monocular and binocular reconstruction cases. In the case where more than two images are provided, we further propose a simple yet effective global alignment strategy that expresses all pairwise pointmaps in a common reference frame. We base our network architecture on standard Transformer encoders and decoders, allowing us to leverage powerful pretrained models. Our formulation directly provides a 3D model of the scene as well as depth information, but interestingly, we can seamlessly recover from it, pixel matches, relative and absolute camera. Exhaustive experiments on all these tasks showcase that the proposed DUSt3R can unify various 3D vision tasks and set new SoTAs on monocular/multi-view depth estimation as well as relative pose estimation. In summary, DUSt3R makes many geometric 3D vision tasks easy.

Guided sampling is a vital approach for applying diffusion models in real-world tasks that embeds human-defined guidance during the sampling procedure. This paper considers a general setting where the guidance is defined by an (unnormalized) energy function. The main challenge for this setting is that the intermediate guidance during the diffusion sampling procedure, which is jointly defined by the sampling distribution and the energy function, is unknown and is hard to estimate. To address this challenge, we propose an exact formulation of the intermediate guidance as well as a novel training objective named contrastive energy prediction (CEP) to learn the exact guidance. Our method is guaranteed to converge to the exact guidance under unlimited model capacity and data samples, while previous methods can not. We demonstrate the effectiveness of our method by applying it to offline reinforcement learning (RL). Extensive experiments on D4RL benchmarks demonstrate that our method outperforms existing state-of-the-art algorithms. We also provide some examples of applying CEP for image synthesis to demonstrate the scalability of CEP on high-dimensional data.

Generating high-quality stereo videos that mimic human binocular vision requires maintaining consistent depth perception and temporal coherence across frames. While diffusion models have advanced image and video synthesis, generating high-quality stereo videos remains challenging due to the difficulty of maintaining consistent temporal and spatial coherence between left and right views. We introduce StereoCrafter-Zero, a novel framework for zero-shot stereo video generation that leverages video diffusion priors without the need for paired training data. Key innovations include a noisy restart strategy to initialize stereo-aware latents and an iterative refinement process that progressively harmonizes the latent space, addressing issues like temporal flickering and view inconsistencies. Comprehensive evaluations, including quantitative metrics and user studies, demonstrate that StereoCrafter-Zero produces high-quality stereo videos with improved depth consistency and temporal smoothness, even when depth estimations are imperfect. Our framework is robust and adaptable across various diffusion models, setting a new benchmark for zero-shot stereo video generation and enabling more immersive visual experiences. Our code can be found in~https://github.com/shijianjian/StereoCrafter-Zero.

This work presents AnyDoor, a diffusion-based image generator with the power to teleport target objects to new scenes at user-specified locations in a harmonious way. Instead of tuning parameters for each object, our model is trained only once and effortlessly generalizes to diverse object-scene combinations at the inference stage. Such a challenging zero-shot setting requires an adequate characterization of a certain object. To this end, we complement the commonly used identity feature with detail features, which are carefully designed to maintain texture details yet allow versatile local variations (e.g., lighting, orientation, posture, etc.), supporting the object in favorably blending with different surroundings. We further propose to borrow knowledge from video datasets, where we can observe various forms (i.e., along the time axis) of a single object, leading to stronger model generalizability and robustness. Extensive experiments demonstrate the superiority of our approach over existing alternatives as well as its great potential in real-world applications, such as virtual try-on and object moving. Project page is https://damo-vilab.github.io/AnyDoor-Page/.

Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting finite-sum structure, which generically arises in empirical variants of learning problems in these contexts. Further, methods with computable approximation errors are highly desirable, as they provide verifiable exit criteria. Motivated by these applications, we study finite-sum monotone inclusion problems, which model broad classes of equilibrium problems. Our main contributions are variants of the classical Halpern iteration that employ variance reduction to obtain improved complexity guarantees in which n component operators in the finite sum are ``on average'' either cocoercive or Lipschitz continuous and monotone, with parameter L. The resulting oracle complexity of our methods, which provide guarantees for the last iterate and for a (computable) operator norm residual, is mathcal{O}( n + nLvarepsilon^{-1}), which improves upon existing methods by a factor up to n. This constitutes the first variance reduction-type result for general finite-sum monotone inclusions and for more specific problems such as convex-concave optimization when operator norm residual is the optimality measure. We further argue that, up to poly-logarithmic factors, this complexity is unimprovable in the monotone Lipschitz setting; i.e., the provided result is near-optimal.

Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of DPMs is guided sampling, which usually needs a large guidance scale to obtain the best sample quality. The commonly-used fast sampler for guided sampling is DDIM, a first-order diffusion ODE solver that generally needs 100 to 250 steps for high-quality samples. Although recent works propose dedicated high-order solvers and achieve a further speedup for sampling without guidance, their effectiveness for guided sampling has not been well-tested before. In this work, we demonstrate that previous high-order fast samplers suffer from instability issues, and they even become slower than DDIM when the guidance scale grows large. To further speed up guided sampling, we propose DPM-Solver++, a high-order solver for the guided sampling of DPMs. DPM-Solver++ solves the diffusion ODE with the data prediction model and adopts thresholding methods to keep the solution matches training data distribution. We further propose a multistep variant of DPM-Solver++ to address the instability issue by reducing the effective step size. Experiments show that DPM-Solver++ can generate high-quality samples within only 15 to 20 steps for guided sampling by pixel-space and latent-space DPMs.

Monocular depth estimation is fundamental for 3D scene understanding and downstream applications. However, even under the supervised setup, it is still challenging and ill-posed due to the lack of full geometric constraints. Although a scene can consist of millions of pixels, there are fewer high-level patterns. We propose iDisc to learn those patterns with internal discretized representations. The method implicitly partitions the scene into a set of high-level patterns. In particular, our new module, Internal Discretization (ID), implements a continuous-discrete-continuous bottleneck to learn those concepts without supervision. In contrast to state-of-the-art methods, the proposed model does not enforce any explicit constraints or priors on the depth output. The whole network with the ID module can be trained end-to-end, thanks to the bottleneck module based on attention. Our method sets the new state of the art with significant improvements on NYU-Depth v2 and KITTI, outperforming all published methods on the official KITTI benchmark. iDisc can also achieve state-of-the-art results on surface normal estimation. Further, we explore the model generalization capability via zero-shot testing. We observe the compelling need to promote diversification in the outdoor scenario. Hence, we introduce splits of two autonomous driving datasets, DDAD and Argoverse. Code is available at http://vis.xyz/pub/idisc .

We present a probabilistic model for point cloud generation, which is fundamental for various 3D vision tasks such as shape completion, upsampling, synthesis and data augmentation. Inspired by the diffusion process in non-equilibrium thermodynamics, we view points in point clouds as particles in a thermodynamic system in contact with a heat bath, which diffuse from the original distribution to a noise distribution. Point cloud generation thus amounts to learning the reverse diffusion process that transforms the noise distribution to the distribution of a desired shape. Specifically, we propose to model the reverse diffusion process for point clouds as a Markov chain conditioned on certain shape latent. We derive the variational bound in closed form for training and provide implementations of the model. Experimental results demonstrate that our model achieves competitive performance in point cloud generation and auto-encoding. The code is available at https://github.com/luost26/diffusion-point-cloud.

We study the behavior of deterministic methods for solving inverse problems in imaging. These methods are commonly designed to achieve two goals: (1) attaining high perceptual quality, and (2) generating reconstructions that are consistent with the measurements. We provide a rigorous proof that the better a predictor satisfies these two requirements, the larger its Lipschitz constant must be, regardless of the nature of the degradation involved. In particular, to approach perfect perceptual quality and perfect consistency, the Lipschitz constant of the model must grow to infinity. This implies that such methods are necessarily more susceptible to adversarial attacks. We demonstrate our theory on single image super-resolution algorithms, addressing both noisy and noiseless settings. We also show how this undesired behavior can be leveraged to explore the posterior distribution, thereby allowing the deterministic model to imitate stochastic methods.

Stylizing a dynamic scene based on an exemplar image is critical for various real-world applications, including gaming, filmmaking, and augmented and virtual reality. However, achieving consistent stylization across both spatial and temporal dimensions remains a significant challenge. Most existing methods are designed for static scenes and often require an optimization process for each style image, limiting their adaptability. We introduce ZDySS, a zero-shot stylization framework for dynamic scenes, allowing our model to generalize to previously unseen style images at inference. Our approach employs Gaussian splatting for scene representation, linking each Gaussian to a learned feature vector that renders a feature map for any given view and timestamp. By applying style transfer on the learned feature vectors instead of the rendered feature map, we enhance spatio-temporal consistency across frames. Our method demonstrates superior performance and coherence over state-of-the-art baselines in tests on real-world dynamic scenes, making it a robust solution for practical applications.

3D meshes are widely used in computer vision and graphics for their efficiency in animation and minimal memory use, playing a crucial role in movies, games, AR, and VR. However, creating temporally consistent and realistic textures for mesh sequences remains labor-intensive for professional artists. On the other hand, while video diffusion models excel at text-driven video generation, they often lack 3D geometry awareness and struggle with achieving multi-view consistent texturing for 3D meshes. In this work, we present Tex4D, a zero-shot approach that integrates inherent 3D geometry knowledge from mesh sequences with the expressiveness of video diffusion models to produce multi-view and temporally consistent 4D textures. Given an untextured mesh sequence and a text prompt as inputs, our method enhances multi-view consistency by synchronizing the diffusion process across different views through latent aggregation in the UV space. To ensure temporal consistency, we leverage prior knowledge from a conditional video generation model for texture synthesis. However, straightforwardly combining the video diffusion model and the UV texture aggregation leads to blurry results. We analyze the underlying causes and propose a simple yet effective modification to the DDIM sampling process to address this issue. Additionally, we introduce a reference latent texture to strengthen the correlation between frames during the denoising process. To the best of our knowledge, Tex4D is the first method specifically designed for 4D scene texturing. Extensive experiments demonstrate its superiority in producing multi-view and multi-frame consistent videos based on untextured mesh sequences.

Overparametrization often helps improve the generalization performance. This paper proposes a dual view of overparametrization suggesting that downsampling may also help generalize. Motivated by this dual view, we characterize two out-of-sample prediction risks of the sketched ridgeless least square estimator in the proportional regime masymp n asymp p, where m is the sketching size, n the sample size, and p the feature dimensionality. Our results reveal the statistical role of downsampling. Specifically, downsampling does not always hurt the generalization performance, and may actually help improve it in some cases. We identify the optimal sketching sizes that minimize the out-of-sample prediction risks, and find that the optimally sketched estimator has stabler risk curves that eliminates the peaks of those for the full-sample estimator. We then propose a practical procedure to empirically identify the optimal sketching size. Finally, we extend our results to cover central limit theorems and misspecified models. Numerical studies strongly support our theory.

Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems consist of two nested sub-problems, called the outer and inner problems, respectively. In practice, often at least one of these sub-problems is overparameterized. In this case, there are many ways to choose among optima that achieve equivalent objective values. Inspired by recent studies of the implicit bias induced by optimization algorithms in single-level optimization, we investigate the implicit bias of gradient-based algorithms for bilevel optimization. We delineate two standard BLO methods -- cold-start and warm-start -- and show that the converged solution or long-run behavior depends to a large degree on these and other algorithmic choices, such as the hypergradient approximation. We also show that the inner solutions obtained by warm-start BLO can encode a surprising amount of information about the outer objective, even when the outer parameters are low-dimensional. We believe that implicit bias deserves as central a role in the study of bilevel optimization as it has attained in the study of single-level neural net optimization.

Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is known to be far from trivial. In this work we introduce a methodology for zero-shot inference of Markov jump processes (MJPs), on bounded state spaces, from noisy and sparse observations, which consists of two components. First, a broad probability distribution over families of MJPs, as well as over possible observation times and noise mechanisms, with which we simulate a synthetic dataset of hidden MJPs and their noisy observation process. Second, a neural network model that processes subsets of the simulated observations, and that is trained to output the initial condition and rate matrix of the target MJP in a supervised way. We empirically demonstrate that one and the same (pretrained) model can infer, in a zero-shot fashion, hidden MJPs evolving in state spaces of different dimensionalities. Specifically, we infer MJPs which describe (i) discrete flashing ratchet systems, which are a type of Brownian motors, and the conformational dynamics in (ii) molecular simulations, (iii) experimental ion channel data and (iv) simple protein folding models. What is more, we show that our model performs on par with state-of-the-art models which are finetuned to the target datasets.

In this paper we provide a novel analytical perspective on the theoretical understanding of gradient-based learning algorithms by interpreting consensus-based optimization (CBO), a recently proposed multi-particle derivative-free optimization method, as a stochastic relaxation of gradient descent. Remarkably, we observe that through communication of the particles, CBO exhibits a stochastic gradient descent (SGD)-like behavior despite solely relying on evaluations of the objective function. The fundamental value of such link between CBO and SGD lies in the fact that CBO is provably globally convergent to global minimizers for ample classes of nonsmooth and nonconvex objective functions, hence, on the one side, offering a novel explanation for the success of stochastic relaxations of gradient descent. On the other side, contrary to the conventional wisdom for which zero-order methods ought to be inefficient or not to possess generalization abilities, our results unveil an intrinsic gradient descent nature of such heuristics. This viewpoint furthermore complements previous insights into the working principles of CBO, which describe the dynamics in the mean-field limit through a nonlinear nonlocal partial differential equation that allows to alleviate complexities of the nonconvex function landscape. Our proofs leverage a completely nonsmooth analysis, which combines a novel quantitative version of the Laplace principle (log-sum-exp trick) and the minimizing movement scheme (proximal iteration). In doing so, we furnish useful and precise insights that explain how stochastic perturbations of gradient descent overcome energy barriers and reach deep levels of nonconvex functions. Instructive numerical illustrations support the provided theoretical insights.

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.

We consider the stochastic linear contextual bandit problem with high-dimensional features. We analyze the Thompson sampling algorithm using special classes of sparsity-inducing priors (e.g., spike-and-slab) to model the unknown parameter and provide a nearly optimal upper bound on the expected cumulative regret. To the best of our knowledge, this is the first work that provides theoretical guarantees of Thompson sampling in high-dimensional and sparse contextual bandits. For faster computation, we use variational inference instead of Markov Chain Monte Carlo (MCMC) to approximate the posterior distribution. Extensive simulations demonstrate the improved performance of our proposed algorithm over existing ones.

We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function. We show that under reasonable conditions on approximation quality and regularity of the models, any such algorithm drives a natural stationarity measure to zero at the rate O(k^{-1/4}). As a consequence, we obtain the first complexity guarantees for the stochastic proximal point, proximal subgradient, and regularized Gauss-Newton methods for minimizing compositions of convex functions with smooth maps. The guiding principle, underlying the complexity guarantees, is that all algorithms under consideration can be interpreted as approximate descent methods on an implicit smoothing of the problem, given by the Moreau envelope. Specializing to classical circumstances, we obtain the long-sought convergence rate of the stochastic projected gradient method, without batching, for minimizing a smooth function on a closed convex set.

Text-to-3D generation has recently garnered significant attention, fueled by 2D diffusion models trained on billions of image-text pairs. Existing methods primarily rely on score distillation to leverage the 2D diffusion priors to supervise the generation of 3D models, e.g., NeRF. However, score distillation is prone to suffer the view inconsistency problem, and implicit NeRF modeling can also lead to an arbitrary shape, thus leading to less realistic and uncontrollable 3D generation. In this work, we propose a flexible framework of Points-to-3D to bridge the gap between sparse yet freely available 3D points and realistic shape-controllable 3D generation by distilling the knowledge from both 2D and 3D diffusion models. The core idea of Points-to-3D is to introduce controllable sparse 3D points to guide the text-to-3D generation. Specifically, we use the sparse point cloud generated from the 3D diffusion model, Point-E, as the geometric prior, conditioned on a single reference image. To better utilize the sparse 3D points, we propose an efficient point cloud guidance loss to adaptively drive the NeRF's geometry to align with the shape of the sparse 3D points. In addition to controlling the geometry, we propose to optimize the NeRF for a more view-consistent appearance. To be specific, we perform score distillation to the publicly available 2D image diffusion model ControlNet, conditioned on text as well as depth map of the learned compact geometry. Qualitative and quantitative comparisons demonstrate that Points-to-3D improves view consistency and achieves good shape controllability for text-to-3D generation. Points-to-3D provides users with a new way to improve and control text-to-3D generation.

The irregularity and permutation invariance of point cloud data pose challenges for effective learning. Conventional methods for addressing this issue involve converting raw point clouds to intermediate representations such as 3D voxel grids or range images. While such intermediate representations solve the problem of permutation invariance, they can result in significant loss of information. Approaches that do learn on raw point clouds either have trouble in resolving neighborhood relationships between points or are too complicated in their formulation. In this paper, we propose a novel approach to representing point clouds as a locality preserving 1D ordering induced by the Hilbert space-filling curve. We also introduce Point2Point, a neural architecture that can effectively learn on Hilbert-sorted point clouds. We show that Point2Point shows competitive performance on point cloud segmentation and generation tasks. Finally, we show the performance of Point2Point on Spatio-temporal Occupancy prediction from Point clouds.

A key step in any scanning-based asset creation workflow is to convert unordered point clouds to a surface. Classical methods (e.g., Poisson reconstruction) start to degrade in the presence of noisy and partial scans. Hence, deep learning based methods have recently been proposed to produce complete surfaces, even from partial scans. However, such data-driven methods struggle to generalize to new shapes with large geometric and topological variations. We present Points2Surf, a novel patch-based learning framework that produces accurate surfaces directly from raw scans without normals. Learning a prior over a combination of detailed local patches and coarse global information improves generalization performance and reconstruction accuracy. Our extensive comparison on both synthetic and real data demonstrates a clear advantage of our method over state-of-the-art alternatives on previously unseen classes (on average, Points2Surf brings down reconstruction error by 30\% over SPR and by 270\%+ over deep learning based SotA methods) at the cost of longer computation times and a slight increase in small-scale topological noise in some cases. Our source code, pre-trained model, and dataset are available on: https://github.com/ErlerPhilipp/points2surf

Diffusion probabilistic models (DPMs) have shown remarkable performance in visual synthesis but are computationally expensive due to the need for multiple evaluations during the sampling. Recent predictor-corrector diffusion samplers have significantly reduced the required number of function evaluations (NFE), but inherently suffer from a misalignment issue caused by the extra corrector step, especially with a large classifier-free guidance scale (CFG). In this paper, we introduce a new fast DPM sampler called DC-Solver, which leverages dynamic compensation (DC) to mitigate the misalignment of the predictor-corrector samplers. The dynamic compensation is controlled by compensation ratios that are adaptive to the sampling steps and can be optimized on only 10 datapoints by pushing the sampling trajectory toward a ground truth trajectory. We further propose a cascade polynomial regression (CPR) which can instantly predict the compensation ratios on unseen sampling configurations. Additionally, we find that the proposed dynamic compensation can also serve as a plug-and-play module to boost the performance of predictor-only samplers. Extensive experiments on both unconditional sampling and conditional sampling demonstrate that our DC-Solver can consistently improve the sampling quality over previous methods on different DPMs with a wide range of resolutions up to 1024times1024. Notably, we achieve 10.38 FID (NFE=5) on unconditional FFHQ and 0.394 MSE (NFE=5, CFG=7.5) on Stable-Diffusion-2.1. Code is available at https://github.com/wl-zhao/DC-Solver

Recently, several point-based image editing methods (e.g., DragDiffusion, FreeDrag, DragNoise) have emerged, yielding precise and high-quality results based on user instructions. However, these methods often make insufficient use of semantic information, leading to less desirable results. In this paper, we proposed a novel mask-free point-based image editing method, AdaptiveDrag, which provides a more flexible editing approach and generates images that better align with user intent. Specifically, we design an auto mask generation module using super-pixel division for user-friendliness. Next, we leverage a pre-trained diffusion model to optimize the latent, enabling the dragging of features from handle points to target points. To ensure a comprehensive connection between the input image and the drag process, we have developed a semantic-driven optimization. We design adaptive steps that are supervised by the positions of the points and the semantic regions derived from super-pixel segmentation. This refined optimization process also leads to more realistic and accurate drag results. Furthermore, to address the limitations in the generative consistency of the diffusion model, we introduce an innovative corresponding loss during the sampling process. Building on these effective designs, our method delivers superior generation results using only the single input image and the handle-target point pairs. Extensive experiments have been conducted and demonstrate that the proposed method outperforms others in handling various drag instructions (e.g., resize, movement, extension) across different domains (e.g., animals, human face, land space, clothing).

We consider stochastic unconstrained bilevel optimization problems when only the first-order gradient oracles are available. While numerous optimization methods have been proposed for tackling bilevel problems, existing methods either tend to require possibly expensive calculations regarding Hessians of lower-level objectives, or lack rigorous finite-time performance guarantees. In this work, we propose a Fully First-order Stochastic Approximation (F2SA) method, and study its non-asymptotic convergence properties. Specifically, we show that F2SA converges to an epsilon-stationary solution of the bilevel problem after epsilon^{-7/2}, epsilon^{-5/2}, and epsilon^{-3/2} iterations (each iteration using O(1) samples) when stochastic noises are in both level objectives, only in the upper-level objective, and not present (deterministic settings), respectively. We further show that if we employ momentum-assisted gradient estimators, the iteration complexities can be improved to epsilon^{-5/2}, epsilon^{-4/2}, and epsilon^{-3/2}, respectively. We demonstrate even superior practical performance of the proposed method over existing second-order based approaches on MNIST data-hypercleaning experiments.

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting. The algorithmic insight obtained from our analysis extends to more general settings often considered in practice. Experimentally, we outperform previously proposed posterior sampling algorithms in a wide variety of problems including random inpainting, block inpainting, denoising, deblurring, destriping, and super-resolution.

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo methods can be costly to do so. We propose here a new procedure based on importance sampling and control variates for estimating more efficiently multiple expectations with the same sample. We first show that there exists a family of optimal estimators combining both importance sampling and control variates, which however cannot be used in practice because they require the knowledge of the values of the expectations to estimate. Motivated by the form of these optimal estimators and some interesting properties, we therefore propose an adaptive algorithm. The general idea is to adaptively update the parameters of the estimators for approaching the optimal ones. We suggest then a quantitative stopping criterion that exploits the trade-off between approaching these optimal parameters and having a sufficient budget left. This left budget is then used to draw a new independent sample from the final sampling distribution, allowing to get unbiased estimators of the expectations. We show how to apply our procedure to sensitivity analysis, by estimating Sobol' indices and quantifying the impact of the input distributions. Finally, realistic test cases show the practical interest of the proposed algorithm, and its significant improvement over estimating the expectations separately.

Non-linear state-space models, also known as general hidden Markov models, are ubiquitous in statistical machine learning, being the most classical generative models for serial data and sequences in general. The particle-based, rapid incremental smoother PaRIS is a sequential Monte Carlo (SMC) technique allowing for efficient online approximation of expectations of additive functionals under the smoothing distribution in these models. Such expectations appear naturally in several learning contexts, such as likelihood estimation (MLE) and Markov score climbing (MSC). PARIS has linear computational complexity, limited memory requirements and comes with non-asymptotic bounds, convergence results and stability guarantees. Still, being based on self-normalised importance sampling, the PaRIS estimator is biased. Our first contribution is to design a novel additive smoothing algorithm, the Parisian particle Gibbs PPG sampler, which can be viewed as a PaRIS algorithm driven by conditional SMC moves, resulting in bias-reduced estimates of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. Our second contribution is to apply PPG in a learning framework, covering MLE and MSC as special examples. In this context, we establish, under standard assumptions, non-asymptotic bounds highlighting the value of bias reduction and the implicit Rao--Blackwellization of PPG. These are the first non-asymptotic results of this kind in this setting. We illustrate our theoretical results with numerical experiments supporting our claims.

We propose a new method for solving imaging inverse problems using text-to-image latent diffusion models as general priors. Existing methods using latent diffusion models for inverse problems typically rely on simple null text prompts, which can lead to suboptimal performance. To address this limitation, we introduce a method for prompt tuning, which jointly optimizes the text embedding on-the-fly while running the reverse diffusion process. This allows us to generate images that are more faithful to the diffusion prior. In addition, we propose a method to keep the evolution of latent variables within the range space of the encoder, by projection. This helps to reduce image artifacts, a major problem when using latent diffusion models instead of pixel-based diffusion models. Our combined method, called P2L, outperforms both image- and latent-diffusion model-based inverse problem solvers on a variety of tasks, such as super-resolution, deblurring, and inpainting.

Point clouds are naturally sparse, while image pixels are dense. The inconsistency limits feature fusion from both modalities for point-wise scene flow estimation. Previous methods rarely predict scene flow from the entire point clouds of the scene with one-time inference due to the memory inefficiency and heavy overhead from distance calculation and sorting involved in commonly used farthest point sampling, KNN, and ball query algorithms for local feature aggregation. To mitigate these issues in scene flow learning, we regularize raw points to a dense format by storing 3D coordinates in 2D grids. Unlike the sampling operation commonly used in existing works, the dense 2D representation 1) preserves most points in the given scene, 2) brings in a significant boost of efficiency, and 3) eliminates the density gap between points and pixels, allowing us to perform effective feature fusion. We also present a novel warping projection technique to alleviate the information loss problem resulting from the fact that multiple points could be mapped into one grid during projection when computing cost volume. Sufficient experiments demonstrate the efficiency and effectiveness of our method, outperforming the prior-arts on the FlyingThings3D and KITTI dataset.

Point-based interactive colorization techniques allow users to effortlessly colorize grayscale images using user-provided color hints. However, point-based methods often face challenges when different colors are given to semantically similar areas, leading to color intermingling and unsatisfactory results-an issue we refer to as color collapse. The fundamental cause of color collapse is the inadequacy of points for defining the boundaries for each color. To mitigate color collapse, we introduce a lasso tool that can control the scope of each color hint. Additionally, we design a framework that leverages the user-provided lassos to localize the attention masks. The experimental results show that using a single lasso is as effective as applying 4.18 individual color hints and can achieve the desired outcomes in 30% less time than using points alone.

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.

Denoising Diffusion Probabilistic Models (DDPMs) can generate high-quality samples such as image and audio samples. However, DDPMs require hundreds to thousands of iterations to produce final samples. Several prior works have successfully accelerated DDPMs through adjusting the variance schedule (e.g., Improved Denoising Diffusion Probabilistic Models) or the denoising equation (e.g., Denoising Diffusion Implicit Models (DDIMs)). However, these acceleration methods cannot maintain the quality of samples and even introduce new noise at a high speedup rate, which limit their practicability. To accelerate the inference process while keeping the sample quality, we provide a fresh perspective that DDPMs should be treated as solving differential equations on manifolds. Under such a perspective, we propose pseudo numerical methods for diffusion models (PNDMs). Specifically, we figure out how to solve differential equations on manifolds and show that DDIMs are simple cases of pseudo numerical methods. We change several classical numerical methods to corresponding pseudo numerical methods and find that the pseudo linear multi-step method is the best in most situations. According to our experiments, by directly using pre-trained models on Cifar10, CelebA and LSUN, PNDMs can generate higher quality synthetic images with only 50 steps compared with 1000-step DDIMs (20x speedup), significantly outperform DDIMs with 250 steps (by around 0.4 in FID) and have good generalization on different variance schedules. Our implementation is available at https://github.com/luping-liu/PNDM.

In this paper, we study the problem of principal component analysis with generative modeling assumptions, adopting a general model for the observed matrix that encompasses notable special cases, including spiked matrix recovery and phase retrieval. The key assumption is that the underlying signal lies near the range of an L-Lipschitz continuous generative model with bounded k-dimensional inputs. We propose a quadratic estimator, and show that it enjoys a statistical rate of order frac{klog L{m}}, where m is the number of samples. We also provide a near-matching algorithm-independent lower bound. Moreover, we provide a variant of the classic power method, which projects the calculated data onto the range of the generative model during each iteration. We show that under suitable conditions, this method converges exponentially fast to a point achieving the above-mentioned statistical rate. We perform experiments on various image datasets for spiked matrix and phase retrieval models, and illustrate performance gains of our method to the classic power method and the truncated power method devised for sparse principal component analysis.

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

Monocular depth estimation is scale-ambiguous, and thus requires scale supervision to produce metric predictions. Even so, the resulting models will be geometry-specific, with learned scales that cannot be directly transferred across domains. Because of that, recent works focus instead on relative depth, eschewing scale in favor of improved up-to-scale zero-shot transfer. In this work we introduce ZeroDepth, a novel monocular depth estimation framework capable of predicting metric scale for arbitrary test images from different domains and camera parameters. This is achieved by (i) the use of input-level geometric embeddings that enable the network to learn a scale prior over objects; and (ii) decoupling the encoder and decoder stages, via a variational latent representation that is conditioned on single frame information. We evaluated ZeroDepth targeting both outdoor (KITTI, DDAD, nuScenes) and indoor (NYUv2) benchmarks, and achieved a new state-of-the-art in both settings using the same pre-trained model, outperforming methods that train on in-domain data and require test-time scaling to produce metric estimates.

Diffusion models, which employ stochastic differential equations to sample images through integrals, have emerged as a dominant class of generative models. However, the rationality of the diffusion process itself receives limited attention, leaving the question of whether the problem is well-posed and well-conditioned. In this paper, we uncover a vexing propensity of diffusion models: they frequently exhibit the infinite Lipschitz near the zero point of timesteps. This poses a threat to the stability and accuracy of the diffusion process, which relies on integral operations. We provide a comprehensive evaluation of the issue from both theoretical and empirical perspectives. To address this challenge, we propose a novel approach, dubbed E-TSDM, which eliminates the Lipschitz singularity of the diffusion model near zero. Remarkably, our technique yields a substantial improvement in performance, e.g., on the high-resolution FFHQ dataset (256times256). Moreover, as a byproduct of our method, we manage to achieve a dramatic reduction in the Frechet Inception Distance of other acceleration methods relying on network Lipschitz, including DDIM and DPM-Solver, by over 33%. We conduct extensive experiments on diverse datasets to validate our theory and method. Our work not only advances the understanding of the general diffusion process, but also provides insights for the design of diffusion models.

We introduce a gradient-based approach for the problem of Bayesian optimal experimental design to learn causal models in a batch setting -- a critical component for causal discovery from finite data where interventions can be costly or risky. Existing methods rely on greedy approximations to construct a batch of experiments while using black-box methods to optimize over a single target-state pair to intervene with. In this work, we completely dispose of the black-box optimization techniques and greedy heuristics and instead propose a conceptually simple end-to-end gradient-based optimization procedure to acquire a set of optimal intervention target-state pairs. Such a procedure enables parameterization of the design space to efficiently optimize over a batch of multi-target-state interventions, a setting which has hitherto not been explored due to its complexity. We demonstrate that our proposed method outperforms baselines and existing acquisition strategies in both single-target and multi-target settings across a number of synthetic datasets.

The primary axes of interest in image-generating diffusion models are image quality, the amount of variation in the results, and how well the results align with a given condition, e.g., a class label or a text prompt. The popular classifier-free guidance approach uses an unconditional model to guide a conditional model, leading to simultaneously better prompt alignment and higher-quality images at the cost of reduced variation. These effects seem inherently entangled, and thus hard to control. We make the surprising observation that it is possible to obtain disentangled control over image quality without compromising the amount of variation by guiding generation using a smaller, less-trained version of the model itself rather than an unconditional model. This leads to significant improvements in ImageNet generation, setting record FIDs of 1.01 for 64x64 and 1.25 for 512x512, using publicly available networks. Furthermore, the method is also applicable to unconditional diffusion models, drastically improving their quality.

Nonconvex optimization is central in solving many machine learning problems, in which block-wise structure is commonly encountered. In this work, we propose cyclic block coordinate methods for nonconvex optimization problems with non-asymptotic gradient norm guarantees. Our convergence analysis is based on a gradient Lipschitz condition with respect to a Mahalanobis norm, inspired by a recent progress on cyclic block coordinate methods. In deterministic settings, our convergence guarantee matches the guarantee of (full-gradient) gradient descent, but with the gradient Lipschitz constant being defined w.r.t.~a Mahalanobis norm. In stochastic settings, we use recursive variance reduction to decrease the per-iteration cost and match the arithmetic operation complexity of current optimal stochastic full-gradient methods, with a unified analysis for both finite-sum and infinite-sum cases. We prove a faster linear convergence result when a Polyak-{\L}ojasiewicz (P{\L}) condition holds. To our knowledge, this work is the first to provide non-asymptotic convergence guarantees -- variance-reduced or not -- for a cyclic block coordinate method in general composite (smooth + nonsmooth) nonconvex settings. Our experimental results demonstrate the efficacy of the proposed cyclic scheme in training deep neural nets.

Accurate monocular metric depth estimation (MMDE) is crucial to solving downstream tasks in 3D perception and modeling. However, the remarkable accuracy of recent MMDE methods is confined to their training domains. These methods fail to generalize to unseen domains even in the presence of moderate domain gaps, which hinders their practical applicability. We propose a new model, UniDepth, capable of reconstructing metric 3D scenes from solely single images across domains. Departing from the existing MMDE methods, UniDepth directly predicts metric 3D points from the input image at inference time without any additional information, striving for a universal and flexible MMDE solution. In particular, UniDepth implements a self-promptable camera module predicting dense camera representation to condition depth features. Our model exploits a pseudo-spherical output representation, which disentangles camera and depth representations. In addition, we propose a geometric invariance loss that promotes the invariance of camera-prompted depth features. Thorough evaluations on ten datasets in a zero-shot regime consistently demonstrate the superior performance of UniDepth, even when compared with methods directly trained on the testing domains. Code and models are available at: https://github.com/lpiccinelli-eth/unidepth

Diffusion models have achieved remarkable success in text-to-image synthesis, largely attributed to the use of classifier-free guidance (CFG), which enables high-quality, condition-aligned image generation. CFG combines the conditional score (e.g., text-conditioned) with the unconditional score to control the output. However, the unconditional score is in charge of estimating the transition between manifolds of adjacent timesteps from x_t to x_{t-1}, which may inadvertently interfere with the trajectory toward the specific condition. In this work, we introduce a novel approach that leverages a geometric perspective on the unconditional score to enhance CFG performance when conditional scores are available. Specifically, we propose a method that filters the singular vectors of both conditional and unconditional scores using singular value decomposition. This filtering process aligns the unconditional score with the conditional score, thereby refining the sampling trajectory to stay closer to the manifold. Our approach improves image quality with negligible additional computation. We provide deeper insights into the score function behavior in diffusion models and present a practical technique for achieving more accurate and contextually coherent image synthesis.

Latest methods represent shapes with open surfaces using unsigned distance functions (UDFs). They train neural networks to learn UDFs and reconstruct surfaces with the gradients around the zero level set of the UDF. However, the differential networks struggle from learning the zero level set where the UDF is not differentiable, which leads to large errors on unsigned distances and gradients around the zero level set, resulting in highly fragmented and discontinuous surfaces. To resolve this problem, we propose to learn a more continuous zero level set in UDFs with level set projections. Our insight is to guide the learning of zero level set using the rest non-zero level sets via a projection procedure. Our idea is inspired from the observations that the non-zero level sets are much smoother and more continuous than the zero level set. We pull the non-zero level sets onto the zero level set with gradient constraints which align gradients over different level sets and correct unsigned distance errors on the zero level set, leading to a smoother and more continuous unsigned distance field. We conduct comprehensive experiments in surface reconstruction for point clouds, real scans or depth maps, and further explore the performance in unsupervised point cloud upsampling and unsupervised point normal estimation with the learned UDF, which demonstrate our non-trivial improvements over the state-of-the-art methods. Code is available at https://github.com/junshengzhou/LevelSetUDF .

In the absence of parallax cues, a learning-based single image depth estimation (SIDE) model relies heavily on shading and contextual cues in the image. While this simplicity is attractive, it is necessary to train such models on large and varied datasets, which are difficult to capture. It has been shown that using embeddings from pre-trained foundational models, such as CLIP, improves zero shot transfer in several applications. Taking inspiration from this, in our paper we explore the use of global image priors generated from a pre-trained ViT model to provide more detailed contextual information. We argue that the embedding vector from a ViT model, pre-trained on a large dataset, captures greater relevant information for SIDE than the usual route of generating pseudo image captions, followed by CLIP based text embeddings. Based on this idea, we propose a new SIDE model using a diffusion backbone which is conditioned on ViT embeddings. Our proposed design establishes a new state-of-the-art (SOTA) for SIDE on NYUv2 dataset, achieving Abs Rel error of 0.059 (14% improvement) compared to 0.069 by the current SOTA (VPD). And on KITTI dataset, achieving Sq Rel error of 0.139 (2% improvement) compared to 0.142 by the current SOTA (GEDepth). For zero-shot transfer with a model trained on NYUv2, we report mean relative improvement of (20%, 23%, 81%, 25%) over NeWCRFs on (Sun-RGBD, iBims1, DIODE, HyperSim) datasets, compared to (16%, 18%, 45%, 9%) by ZoeDepth. The project page is available at https://ecodepth-iitd.github.io

Bayesian Optimization (BO) is typically used to optimize an unknown function f that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Even if provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open problem, often tackled by assuming an additive structure for f. By doing so, BO algorithms typically introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. This paper contains two main contributions: (i) we relax the restrictive assumptions on the additive structure of f without weakening the maximization guarantees of the acquisition function, and (ii) we address the over-exploration problem for decentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms, especially when the additive structure of f comprises high-dimensional factors.

We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching parameters. Our results hold for a broad class of asymptotically free sketches under very mild data assumptions. For squared prediction risk, we provide a decomposition into an unsketched equivalent implicit ridge bias and a sketching-based variance, and prove that the risk can be globally optimized by only tuning sketch size in infinite ensembles. For general subquadratic prediction risk functionals, we extend GCV to construct consistent risk estimators, and thereby obtain distributional convergence of the GCV-corrected predictions in Wasserstein-2 metric. This in particular allows construction of prediction intervals with asymptotically correct coverage conditional on the training data. We also propose an "ensemble trick" whereby the risk for unsketched ridge regression can be efficiently estimated via GCV using small sketched ridge ensembles. We empirically validate our theoretical results using both synthetic and real large-scale datasets with practical sketches including CountSketch and subsampled randomized discrete cosine transforms.

Conditional generative models typically demand large annotated training sets to achieve high-quality synthesis. As a result, there has been significant interest in designing models that perform plug-and-play generation, i.e., to use a predefined or pretrained model, which is not explicitly trained on the generative task, to guide the generative process (e.g., using language). However, such guidance is typically useful only towards synthesizing high-level semantics rather than editing fine-grained details as in image-to-image translation tasks. To this end, and capitalizing on the powerful fine-grained generative control offered by the recent diffusion-based generative models, we introduce Steered Diffusion, a generalized framework for photorealistic zero-shot conditional image generation using a diffusion model trained for unconditional generation. The key idea is to steer the image generation of the diffusion model at inference time via designing a loss using a pre-trained inverse model that characterizes the conditional task. This loss modulates the sampling trajectory of the diffusion process. Our framework allows for easy incorporation of multiple conditions during inference. We present experiments using steered diffusion on several tasks including inpainting, colorization, text-guided semantic editing, and image super-resolution. Our results demonstrate clear qualitative and quantitative improvements over state-of-the-art diffusion-based plug-and-play models while adding negligible additional computational cost.

Existing fully-supervised point cloud segmentation methods suffer in the dynamic testing environment with emerging new classes. Few-shot point cloud segmentation algorithms address this problem by learning to adapt to new classes at the sacrifice of segmentation accuracy for the base classes, which severely impedes its practicality. This largely motivates us to present the first attempt at a more practical paradigm of generalized few-shot point cloud segmentation, which requires the model to generalize to new categories with only a few support point clouds and simultaneously retain the capability to segment base classes. We propose the geometric words to represent geometric components shared between the base and novel classes, and incorporate them into a novel geometric-aware semantic representation to facilitate better generalization to the new classes without forgetting the old ones. Moreover, we introduce geometric prototypes to guide the segmentation with geometric prior knowledge. Extensive experiments on S3DIS and ScanNet consistently illustrate the superior performance of our method over baseline methods. Our code is available at: https://github.com/Pixie8888/GFS-3DSeg_GWs.

This paper proposes a new method to infer keypoints from arbitrary object categories in practical scenarios where point cloud data (PCD) are noisy, down-sampled and arbitrarily rotated. Our proposed model adheres to the following principles: i) keypoints inference is fully unsupervised (no annotation given), ii) keypoints position error should be low and resilient to PCD perturbations (robustness), iii) keypoints should not change their indexes for the intra-class objects (semantic coherence), iv) keypoints should be close to or proximal to PCD surface (compactness). We achieve these desiderata by proposing a new self-supervised training strategy for keypoints estimation that does not assume any a priori knowledge of the object class, and a model architecture with coupled auxiliary losses that promotes the desired keypoints properties. We compare the keypoints estimated by the proposed approach with those of the state-of-the-art unsupervised approaches. The experiments show that our approach outperforms by estimating keypoints with improved coverage (+9.41%) while being semantically consistent (+4.66%) that best characterizes the object's 3D shape for downstream tasks. Code and data are available at: https://github.com/IITPAVIS/SC3K

Recent advances in 2D image generation have achieved remarkable quality,largely driven by the capacity of diffusion models and the availability of large-scale datasets. However, direct 3D generation is still constrained by the scarcity and lower fidelity of 3D datasets. In this paper, we introduce Zero-1-to-G, a novel approach that addresses this problem by enabling direct single-view generation on Gaussian splats using pretrained 2D diffusion models. Our key insight is that Gaussian splats, a 3D representation, can be decomposed into multi-view images encoding different attributes. This reframes the challenging task of direct 3D generation within a 2D diffusion framework, allowing us to leverage the rich priors of pretrained 2D diffusion models. To incorporate 3D awareness, we introduce cross-view and cross-attribute attention layers, which capture complex correlations and enforce 3D consistency across generated splats. This makes Zero-1-to-G the first direct image-to-3D generative model to effectively utilize pretrained 2D diffusion priors, enabling efficient training and improved generalization to unseen objects. Extensive experiments on both synthetic and in-the-wild datasets demonstrate superior performance in 3D object generation, offering a new approach to high-quality 3D generation.

Point management is a critical component in optimizing 3D Gaussian Splatting (3DGS) models, as the point initiation (e.g., via structure from motion) is distributionally inappropriate. Typically, the Adaptive Density Control (ADC) algorithm is applied, leveraging view-averaged gradient magnitude thresholding for point densification, opacity thresholding for pruning, and regular all-points opacity reset. However, we reveal that this strategy is limited in tackling intricate/special image regions (e.g., transparent) as it is unable to identify all the 3D zones that require point densification, and lacking an appropriate mechanism to handle the ill-conditioned points with negative impacts (occlusion due to false high opacity). To address these limitations, we propose a Localized Point Management (LPM) strategy, capable of identifying those error-contributing zones in the highest demand for both point addition and geometry calibration. Zone identification is achieved by leveraging the underlying multiview geometry constraints, with the guidance of image rendering errors. We apply point densification in the identified zone, whilst resetting the opacity of those points residing in front of these regions so that a new opportunity is created to correct ill-conditioned points. Serving as a versatile plugin, LPM can be seamlessly integrated into existing 3D Gaussian Splatting models. Experimental evaluation across both static 3D and dynamic 4D scenes validate the efficacy of our LPM strategy in boosting a variety of existing 3DGS models both quantitatively and qualitatively. Notably, LPM improves both vanilla 3DGS and SpaceTimeGS to achieve state-of-the-art rendering quality while retaining real-time speeds, outperforming on challenging datasets such as Tanks & Temples and the Neural 3D Video Dataset.

We investigate the problem of stochastic, combinatorial multi-armed bandits where the learner only has access to bandit feedback and the reward function can be non-linear. We provide a general framework for adapting discrete offline approximation algorithms into sublinear alpha-regret methods that only require bandit feedback, achieving Oleft(T^2{3}log(T)^1{3}right) expected cumulative alpha-regret dependence on the horizon T. The framework only requires the offline algorithms to be robust to small errors in function evaluation. The adaptation procedure does not even require explicit knowledge of the offline approximation algorithm -- the offline algorithm can be used as black box subroutine. To demonstrate the utility of the proposed framework, the proposed framework is applied to multiple problems in submodular maximization, adapting approximation algorithms for cardinality and for knapsack constraints. The new CMAB algorithms for knapsack constraints outperform a full-bandit method developed for the adversarial setting in experiments with real-world data.

Recent developments in the field of diffusion models have demonstrated an exceptional capacity to generate high-quality prompt-conditioned image edits. Nevertheless, previous approaches have primarily relied on textual prompts for image editing, which tend to be less effective when making precise edits to specific objects or fine-grained regions within a scene containing single/multiple objects. We introduce a novel framework for zero-shot localized multi-object editing through a multi-diffusion process to overcome this challenge. This framework empowers users to perform various operations on objects within an image, such as adding, replacing, or editing many objects in a complex scene in one pass. Our approach leverages foreground masks and corresponding simple text prompts that exert localized influences on the target regions resulting in high-fidelity image editing. A combination of cross-attention and background preservation losses within the latent space ensures that the characteristics of the object being edited are preserved while simultaneously achieving a high-quality, seamless reconstruction of the background with fewer artifacts compared to the current methods. We also curate and release a dataset dedicated to multi-object editing, named LoMOE-Bench. Our experiments against existing state-of-the-art methods demonstrate the improved effectiveness of our approach in terms of both image editing quality and inference speed.

Existing video frame interpolation (VFI) methods blindly predict where each object is at a specific timestep t ("time indexing"), which struggles to predict precise object movements. Given two images of a baseball, there are infinitely many possible trajectories: accelerating or decelerating, straight or curved. This often results in blurry frames as the method averages out these possibilities. Instead of forcing the network to learn this complicated time-to-location mapping implicitly together with predicting the frames, we provide the network with an explicit hint on how far the object has traveled between start and end frames, a novel approach termed "distance indexing". This method offers a clearer learning goal for models, reducing the uncertainty tied to object speeds. We further observed that, even with this extra guidance, objects can still be blurry especially when they are equally far from both input frames (i.e., halfway in-between), due to the directional ambiguity in long-range motion. To solve this, we propose an iterative reference-based estimation strategy that breaks down a long-range prediction into several short-range steps. When integrating our plug-and-play strategies into state-of-the-art learning-based models, they exhibit markedly sharper outputs and superior perceptual quality in arbitrary time interpolations, using a uniform distance indexing map in the same format as time indexing. Additionally, distance indexing can be specified pixel-wise, which enables temporal manipulation of each object independently, offering a novel tool for video editing tasks like re-timing.

Monte Carlo (MC) integration has been employed as the standard approximation method for the Sliced Wasserstein (SW) distance, whose analytical expression involves an intractable expectation. However, MC integration is not optimal in terms of absolute approximation error. To provide a better class of empirical SW, we propose quasi-sliced Wasserstein (QSW) approximations that rely on Quasi-Monte Carlo (QMC) methods. For a comprehensive investigation of QMC for SW, we focus on the 3D setting, specifically computing the SW between probability measures in three dimensions. In greater detail, we empirically evaluate various methods to construct QMC point sets on the 3D unit-hypersphere, including the Gaussian-based and equal area mappings, generalized spiral points, and optimizing discrepancy energies. Furthermore, to obtain an unbiased estimator for stochastic optimization, we extend QSW to Randomized Quasi-Sliced Wasserstein (RQSW) by introducing randomness in the discussed point sets. Theoretically, we prove the asymptotic convergence of QSW and the unbiasedness of RQSW. Finally, we conduct experiments on various 3D tasks, such as point-cloud comparison, point-cloud interpolation, image style transfer, and training deep point-cloud autoencoders, to demonstrate the favorable performance of the proposed QSW and RQSW variants.

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness requirements. These requirements can be imposed (with generalization guarantees) by formulating constrained learning problems that can then be tackled by dual ascent algorithms. Yet, though these algorithms converge in objective value, even in non-convex settings, they cannot guarantee that their outcome is feasible. Doing so requires randomizing over all iterates, which is impractical in virtually any modern applications. Still, final iterates have been observed to perform well in practice. In this work, we address this gap between theory and practice by characterizing the constraint violation of Lagrangian minimizers associated with optimal dual variables, despite lack of convexity. To do this, we leverage the fact that non-convex, finite-dimensional constrained learning problems can be seen as parametrizations of convex, functional problems. Our results show that rich parametrizations effectively mitigate the issue of feasibility in dual methods, shedding light on prior empirical successes of dual learning. We illustrate our findings in fair learning tasks.

Combinatorial optimization (CO) is naturally discrete, making machine learning based on differentiable optimization inapplicable. Karalias & Loukas (2020) adapted the probabilistic method to incorporate CO into differentiable optimization. Their work ignited the research on unsupervised learning for CO, composed of two main components: probabilistic objectives and derandomization. However, each component confronts unique challenges. First, deriving objectives under various conditions (e.g., cardinality constraints and minimum) is nontrivial. Second, the derandomization process is underexplored, and the existing derandomization methods are either random sampling or naive rounding. In this work, we aim to tackle prevalent (i.e., commonly involved) conditions in unsupervised CO. First, we concretize the targets for objective construction and derandomization with theoretical justification. Then, for various conditions commonly involved in different CO problems, we derive nontrivial objectives and derandomization to meet the targets. Finally, we apply the derivations to various CO problems. Via extensive experiments on synthetic and real-world graphs, we validate the correctness of our derivations and show our empirical superiority w.r.t. both optimization quality and speed.

In recent years, huge progress has been made on learning neural implicit representations from multi-view images for 3D reconstruction. As an additional input complementing coordinates, using sinusoidal functions as positional encodings plays a key role in revealing high frequency details with coordinate-based neural networks. However, high frequency positional encodings make the optimization unstable, which results in noisy reconstructions and artifacts in empty space. To resolve this issue in a general sense, we introduce to learn neural implicit representations with quantized coordinates, which reduces the uncertainty and ambiguity in the field during optimization. Instead of continuous coordinates, we discretize continuous coordinates into discrete coordinates using nearest interpolation among quantized coordinates which are obtained by discretizing the field in an extremely high resolution. We use discrete coordinates and their positional encodings to learn implicit functions through volume rendering. This significantly reduces the variations in the sample space, and triggers more multi-view consistency constraints on intersections of rays from different views, which enables to infer implicit function in a more effective way. Our quantized coordinates do not bring any computational burden, and can seamlessly work upon the latest methods. Our evaluations under the widely used benchmarks show our superiority over the state-of-the-art. Our code is available at https://github.com/MachinePerceptionLab/CQ-NIR.

Recently, the impressive empirical success of policy gradient (PG) methods has catalyzed the development of their theoretical foundations. Despite the huge efforts directed at the design of efficient stochastic PG-type algorithms, the understanding of their convergence to a globally optimal policy is still limited. In this work, we develop improved global convergence guarantees for a general class of Fisher-non-degenerate parameterized policies which allows to address the case of continuous state action spaces. First, we propose a Normalized Policy Gradient method with Implicit Gradient Transport (N-PG-IGT) and derive a mathcal{O}(varepsilon^{-2.5}) sample complexity of this method for finding a global varepsilon-optimal policy. Improving over the previously known mathcal{O}(varepsilon^{-3}) complexity, this algorithm does not require the use of importance sampling or second-order information and samples only one trajectory per iteration. Second, we further improve this complexity to mathcal{mathcal{O} }(varepsilon^{-2}) by considering a Hessian-Aided Recursive Policy Gradient ((N)-HARPG) algorithm enhanced with a correction based on a Hessian-vector product. Interestingly, both algorithms are (i) simple and easy to implement: single-loop, do not require large batches of trajectories and sample at most two trajectories per iteration; (ii) computationally and memory efficient: they do not require expensive subroutines at each iteration and can be implemented with memory linear in the dimension of parameters.

We investigate the extent to which offline demonstration data can improve online learning. It is natural to expect some improvement, but the question is how, and by how much? We show that the degree of improvement must depend on the quality of the demonstration data. To generate portable insights, we focus on Thompson sampling (TS) applied to a multi-armed bandit as a prototypical online learning algorithm and model. The demonstration data is generated by an expert with a given competence level, a notion we introduce. We propose an informed TS algorithm that utilizes the demonstration data in a coherent way through Bayes' rule and derive a prior-dependent Bayesian regret bound. This offers insight into how pretraining can greatly improve online performance and how the degree of improvement increases with the expert's competence level. We also develop a practical, approximate informed TS algorithm through Bayesian bootstrapping and show substantial empirical regret reduction through experiments.

Recent AI-based video editing has enabled users to edit videos through simple text prompts, significantly simplifying the editing process. However, recent zero-shot video editing techniques primarily focus on global or single-object edits, which can lead to unintended changes in other parts of the video. When multiple objects require localized edits, existing methods face challenges, such as unfaithful editing, editing leakage, and lack of suitable evaluation datasets and metrics. To overcome these limitations, we propose a zero-shot Multi-Instance Video Editing framework, called MIVE. MIVE is a general-purpose mask-based framework, not dedicated to specific objects (e.g., people). MIVE introduces two key modules: (i) Disentangled Multi-instance Sampling (DMS) to prevent editing leakage and (ii) Instance-centric Probability Redistribution (IPR) to ensure precise localization and faithful editing. Additionally, we present our new MIVE Dataset featuring diverse video scenarios and introduce the Cross-Instance Accuracy (CIA) Score to evaluate editing leakage in multi-instance video editing tasks. Our extensive qualitative, quantitative, and user study evaluations demonstrate that MIVE significantly outperforms recent state-of-the-art methods in terms of editing faithfulness, accuracy, and leakage prevention, setting a new benchmark for multi-instance video editing. The project page is available at https://kaist-viclab.github.io/mive-site/

This paper introduces a method for zero-shot video restoration using pre-trained image restoration diffusion models. Traditional video restoration methods often need retraining for different settings and struggle with limited generalization across various degradation types and datasets. Our approach uses a hierarchical token merging strategy for keyframes and local frames, combined with a hybrid correspondence mechanism that blends optical flow and feature-based nearest neighbor matching (latent merging). We show that our method not only achieves top performance in zero-shot video restoration but also significantly surpasses trained models in generalization across diverse datasets and extreme degradations (8times super-resolution and high-standard deviation video denoising). We present evidence through quantitative metrics and visual comparisons on various challenging datasets. Additionally, our technique works with any 2D restoration diffusion model, offering a versatile and powerful tool for video enhancement tasks without extensive retraining. This research leads to more efficient and widely applicable video restoration technologies, supporting advancements in fields that require high-quality video output. See our project page for video results at https://jimmycv07.github.io/DiffIR2VR_web/.

Two different approaches exist to handle missing values for prediction: either imputation, prior to fitting any predictive algorithms, or dedicated methods able to natively incorporate missing values. While imputation is widely (and easily) use, it is unfortunately biased when low-capacity predictors (such as linear models) are applied afterward. However, in practice, naive imputation exhibits good predictive performance. In this paper, we study the impact of imputation in a high-dimensional linear model with MCAR missing data. We prove that zero imputation performs an implicit regularization closely related to the ridge method, often used in high-dimensional problems. Leveraging on this connection, we establish that the imputation bias is controlled by a ridge bias, which vanishes in high dimension. As a predictor, we argue in favor of the averaged SGD strategy, applied to zero-imputed data. We establish an upper bound on its generalization error, highlighting that imputation is benign in the d sqrt n regime. Experiments illustrate our findings.

Exploiting partial first-order information in a cyclic way is arguably the most natural strategy to obtain scalable first-order methods. However, despite their wide use in practice, cyclic schemes are far less understood from a theoretical perspective than their randomized counterparts. Motivated by a recent success in analyzing an extrapolated cyclic scheme for generalized variational inequalities, we propose an Accelerated Cyclic Coordinate Dual Averaging with Extrapolation (A-CODER) method for composite convex optimization, where the objective function can be expressed as the sum of a smooth convex function accessible via a gradient oracle and a convex, possibly nonsmooth, function accessible via a proximal oracle. We show that A-CODER attains the optimal convergence rate with improved dependence on the number of blocks compared to prior work. Furthermore, for the setting where the smooth component of the objective function is expressible in a finite sum form, we introduce a variance-reduced variant of A-CODER, VR-A-CODER, with state-of-the-art complexity guarantees. Finally, we demonstrate the effectiveness of our algorithms through numerical experiments.

Scene flow estimation is the task of describing the 3D motion field between temporally successive point clouds. State-of-the-art methods use strong priors and test-time optimization techniques, but require on the order of tens of seconds to process full-size point clouds, making them unusable as computer vision primitives for real-time applications such as open world object detection. Feedforward methods are considerably faster, running on the order of tens to hundreds of milliseconds for full-size point clouds, but require expensive human supervision. To address both limitations, we propose Scene Flow via Distillation, a simple, scalable distillation framework that uses a label-free optimization method to produce pseudo-labels to supervise a feedforward model. Our instantiation of this framework, ZeroFlow, achieves state-of-the-art performance on the Argoverse 2 Self-Supervised Scene Flow Challenge while using zero human labels by simply training on large-scale, diverse unlabeled data. At test-time, ZeroFlow is over 1000x faster than label-free state-of-the-art optimization-based methods on full-size point clouds (34 FPS vs 0.028 FPS) and over 1000x cheaper to train on unlabeled data compared to the cost of human annotation (\394 vs ~750,000). To facilitate further research, we will release our code, trained model weights, and high quality pseudo-labels for the Argoverse 2 and Waymo Open datasets.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm -- using only the number of iterations as feedback -- can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a (delta,epsilon)-stationary point from O(epsilon^{-4}delta^{-1}) stochastic gradient queries to O(epsilon^{-3}delta^{-1}), which we also show to be optimal. Our primary technique is a reduction from non-smooth non-convex optimization to online learning, after which our results follow from standard regret bounds in online learning. For deterministic and second-order smooth objectives, applying more advanced optimistic online learning techniques enables a new complexity of O(epsilon^{-1.5}delta^{-0.5}). Our techniques also recover all optimal or best-known results for finding epsilon stationary points of smooth or second-order smooth objectives in both stochastic and deterministic settings.

We study the problem of convergence to a stationary point in zero-sum games. We propose competitive gradient optimization (CGO ), a gradient-based method that incorporates the interactions between the two players in zero-sum games for optimization updates. We provide continuous-time analysis of CGO and its convergence properties while showing that in the continuous limit, CGO predecessors degenerate to their gradient descent ascent (GDA) variants. We provide a rate of convergence to stationary points and further propose a generalized class of alpha-coherent function for which we provide convergence analysis. We show that for strictly alpha-coherent functions, our algorithm convergences to a saddle point. Moreover, we propose optimistic CGO (OCGO), an optimistic variant, for which we show convergence rate to saddle points in alpha-coherent class of functions.

We consider the optimization problem of the form min_{x in R^d} f(x) triangleq E_{xi} [F(x; xi)], where the component F(x;xi) is L-mean-squared Lipschitz but possibly nonconvex and nonsmooth. The recently proposed gradient-free method requires at most O( L^4 d^{3/2} epsilon^{-4} + Delta L^3 d^{3/2} delta^{-1} epsilon^{-4}) stochastic zeroth-order oracle complexity to find a (delta,epsilon)-Goldstein stationary point of objective function, where Delta = f(x_0) - inf_{x in R^d} f(x) and x_0 is the initial point of the algorithm. This paper proposes a more efficient algorithm using stochastic recursive gradient estimators, which improves the complexity to O(L^3 d^{3/2} epsilon^{-3}+ Delta L^2 d^{3/2} delta^{-1} epsilon^{-3}).

The quality of point clouds is often limited by noise introduced during their capture process. Consequently, a fundamental 3D vision task is the removal of noise, known as point cloud filtering or denoising. State-of-the-art learning based methods focus on training neural networks to infer filtered displacements and directly shift noisy points onto the underlying clean surfaces. In high noise conditions, they iterate the filtering process. However, this iterative filtering is only done at test time and is less effective at ensuring points converge quickly onto the clean surfaces. We propose IterativePFN (iterative point cloud filtering network), which consists of multiple IterationModules that model the true iterative filtering process internally, within a single network. We train our IterativePFN network using a novel loss function that utilizes an adaptive ground truth target at each iteration to capture the relationship between intermediate filtering results during training. This ensures that the filtered results converge faster to the clean surfaces. Our method is able to obtain better performance compared to state-of-the-art methods. The source code can be found at: https://github.com/ddsediri/IterativePFN.

We present a novel video generation framework that integrates 3-dimensional geometry and dynamic awareness. To achieve this, we augment 2D videos with 3D point trajectories and align them in pixel space. The resulting 3D-aware video dataset, PointVid, is then used to fine-tune a latent diffusion model, enabling it to track 2D objects with 3D Cartesian coordinates. Building on this, we regularize the shape and motion of objects in the video to eliminate undesired artifacts, \eg, nonphysical deformation. Consequently, we enhance the quality of generated RGB videos and alleviate common issues like object morphing, which are prevalent in current video models due to a lack of shape awareness. With our 3D augmentation and regularization, our model is capable of handling contact-rich scenarios such as task-oriented videos. These videos involve complex interactions of solids, where 3D information is essential for perceiving deformation and contact. Furthermore, our model improves the overall quality of video generation by promoting the 3D consistency of moving objects and reducing abrupt changes in shape and motion.

Off-policy learning from multistep returns is crucial for sample-efficient reinforcement learning, but counteracting off-policy bias without exacerbating variance is challenging. Classically, off-policy bias is corrected in a per-decision manner: past temporal-difference errors are re-weighted by the instantaneous Importance Sampling (IS) ratio after each action via eligibility traces. Many off-policy algorithms rely on this mechanism, along with differing protocols for cutting the IS ratios to combat the variance of the IS estimator. Unfortunately, once a trace has been fully cut, the effect cannot be reversed. This has led to the development of credit-assignment strategies that account for multiple past experiences at a time. These trajectory-aware methods have not been extensively analyzed, and their theoretical justification remains uncertain. In this paper, we propose a multistep operator that can express both per-decision and trajectory-aware methods. We prove convergence conditions for our operator in the tabular setting, establishing the first guarantees for several existing methods as well as many new ones. Finally, we introduce Recency-Bounded Importance Sampling (RBIS), which leverages trajectory awareness to perform robustly across lambda-values in an off-policy control task.

High-fidelity human 3D models can now be learned directly from videos, typically by combining a template-based surface model with neural representations. However, obtaining a template surface requires expensive multi-view capture systems, laser scans, or strictly controlled conditions. Previous methods avoid using a template but rely on a costly or ill-posed mapping from observation to canonical space. We propose a hybrid point-based representation for reconstructing animatable characters that does not require an explicit surface model, while being generalizable to novel poses. For a given video, our method automatically produces an explicit set of 3D points representing approximate canonical geometry, and learns an articulated deformation model that produces pose-dependent point transformations. The points serve both as a scaffold for high-frequency neural features and an anchor for efficiently mapping between observation and canonical space. We demonstrate on established benchmarks that our representation overcomes limitations of prior work operating in either canonical or in observation space. Moreover, our automatic point extraction approach enables learning models of human and animal characters alike, matching the performance of the methods using rigged surface templates despite being more general. Project website: https://lemonatsu.github.io/npc/

We address the problem of generating videos from unposed internet photos. A handful of input images serve as keyframes, and our model interpolates between them to simulate a path moving between the cameras. Given random images, a model's ability to capture underlying geometry, recognize scene identity, and relate frames in terms of camera position and orientation reflects a fundamental understanding of 3D structure and scene layout. However, existing video models such as Luma Dream Machine fail at this task. We design a self-supervised method that takes advantage of the consistency of videos and variability of multiview internet photos to train a scalable, 3D-aware video model without any 3D annotations such as camera parameters. We validate that our method outperforms all baselines in terms of geometric and appearance consistency. We also show our model benefits applications that enable camera control, such as 3D Gaussian Splatting. Our results suggest that we can scale up scene-level 3D learning using only 2D data such as videos and multiview internet photos.

Point cloud sampling is a less explored research topic for this data representation. The most commonly used sampling methods are still classical random sampling and farthest point sampling. With the development of neural networks, various methods have been proposed to sample point clouds in a task-based learning manner. However, these methods are mostly generative-based, rather than selecting points directly using mathematical statistics. Inspired by the Canny edge detection algorithm for images and with the help of the attention mechanism, this paper proposes a non-generative Attention-based Point cloud Edge Sampling method (APES), which captures salient points in the point cloud outline. Both qualitative and quantitative experimental results show the superior performance of our sampling method on common benchmark tasks.

This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural optimization and stochastic optimization. Our presentation of black-box optimization, strongly influenced by Nesterov's seminal book and Nemirovski's lecture notes, includes the analysis of cutting plane methods, as well as (accelerated) gradient descent schemes. We also pay special attention to non-Euclidean settings (relevant algorithms include Frank-Wolfe, mirror descent, and dual averaging) and discuss their relevance in machine learning. We provide a gentle introduction to structural optimization with FISTA (to optimize a sum of a smooth and a simple non-smooth term), saddle-point mirror prox (Nemirovski's alternative to Nesterov's smoothing), and a concise description of interior point methods. In stochastic optimization we discuss stochastic gradient descent, mini-batches, random coordinate descent, and sublinear algorithms. We also briefly touch upon convex relaxation of combinatorial problems and the use of randomness to round solutions, as well as random walks based methods.

The entropic fictitious play (EFP) is a recently proposed algorithm that minimizes the sum of a convex functional and entropy in the space of measures -- such an objective naturally arises in the optimization of a two-layer neural network in the mean-field regime. In this work, we provide a concise primal-dual analysis of EFP in the setting where the learning problem exhibits a finite-sum structure. We establish quantitative global convergence guarantees for both the continuous-time and discrete-time dynamics based on properties of a proximal Gibbs measure introduced in Nitanda et al. (2022). Furthermore, our primal-dual framework entails a memory-efficient particle-based implementation of the EFP update, and also suggests a connection to gradient boosting methods. We illustrate the efficiency of our novel implementation in experiments including neural network optimization and image synthesis.

We propose SharpDepth, a novel approach to monocular metric depth estimation that combines the metric accuracy of discriminative depth estimation methods (e.g., Metric3D, UniDepth) with the fine-grained boundary sharpness typically achieved by generative methods (e.g., Marigold, Lotus). Traditional discriminative models trained on real-world data with sparse ground-truth depth can accurately predict metric depth but often produce over-smoothed or low-detail depth maps. Generative models, in contrast, are trained on synthetic data with dense ground truth, generating depth maps with sharp boundaries yet only providing relative depth with low accuracy. Our approach bridges these limitations by integrating metric accuracy with detailed boundary preservation, resulting in depth predictions that are both metrically precise and visually sharp. Our extensive zero-shot evaluations on standard depth estimation benchmarks confirm SharpDepth effectiveness, showing its ability to achieve both high depth accuracy and detailed representation, making it well-suited for applications requiring high-quality depth perception across diverse, real-world environments.

Large-scale text-to-image diffusion models achieve unprecedented success in image generation and editing. However, how to extend such success to video editing is unclear. Recent initial attempts at video editing require significant text-to-video data and computation resources for training, which is often not accessible. In this work, we propose vid2vid-zero, a simple yet effective method for zero-shot video editing. Our vid2vid-zero leverages off-the-shelf image diffusion models, and doesn't require training on any video. At the core of our method is a null-text inversion module for text-to-video alignment, a cross-frame modeling module for temporal consistency, and a spatial regularization module for fidelity to the original video. Without any training, we leverage the dynamic nature of the attention mechanism to enable bi-directional temporal modeling at test time. Experiments and analyses show promising results in editing attributes, subjects, places, etc., in real-world videos. Code is made available at https://github.com/baaivision/vid2vid-zero.

We present a unified framework capable of solving a broad range of 3D tasks. Our approach features a stateful recurrent model that continuously updates its state representation with each new observation. Given a stream of images, this evolving state can be used to generate metric-scale pointmaps (per-pixel 3D points) for each new input in an online fashion. These pointmaps reside within a common coordinate system, and can be accumulated into a coherent, dense scene reconstruction that updates as new images arrive. Our model, called CUT3R (Continuous Updating Transformer for 3D Reconstruction), captures rich priors of real-world scenes: not only can it predict accurate pointmaps from image observations, but it can also infer unseen regions of the scene by probing at virtual, unobserved views. Our method is simple yet highly flexible, naturally accepting varying lengths of images that may be either video streams or unordered photo collections, containing both static and dynamic content. We evaluate our method on various 3D/4D tasks and demonstrate competitive or state-of-the-art performance in each. Project Page: https://cut3r.github.io/

Diffusion models have demonstrated impressive generative capabilities, but their exposure bias problem, described as the input mismatch between training and sampling, lacks in-depth exploration. In this paper, we systematically investigate the exposure bias problem in diffusion models by first analytically modelling the sampling distribution, based on which we then attribute the prediction error at each sampling step as the root cause of the exposure bias issue. Furthermore, we discuss potential solutions to this issue and propose an intuitive metric for it. Along with the elucidation of exposure bias, we propose a simple, yet effective, training-free method called Epsilon Scaling to alleviate the exposure bias. We show that Epsilon Scaling explicitly moves the sampling trajectory closer to the vector field learned in the training phase by scaling down the network output (Epsilon), mitigating the input mismatch between training and sampling. Experiments on various diffusion frameworks (ADM, DDPM/DDIM, EDM, LDM), unconditional and conditional settings, and deterministic vs. stochastic sampling verify the effectiveness of our method. Remarkably, our ADM-ES, as a SOTA stochastic sampler, obtains 2.17 FID on CIFAR-10 under 100-step unconditional generation. The code is available at https://github.com/forever208/ADM-ES and https://github.com/forever208/EDM-ES.

Masked point modeling has become a promising scheme of self-supervised pre-training for point clouds. Existing methods reconstruct either the original points or related features as the objective of pre-training. However, considering the diversity of downstream tasks, it is necessary for the model to have both low- and high-level representation modeling capabilities to capture geometric details and semantic contexts during pre-training. To this end, M^3CS is proposed to enable the model with the above abilities. Specifically, with masked point cloud as input, M^3CS introduces two decoders to predict masked representations and the original points simultaneously. While an extra decoder doubles parameters for the decoding process and may lead to overfitting, we propose siamese decoders to keep the amount of learnable parameters unchanged. Further, we propose an online codebook projecting continuous tokens into discrete ones before reconstructing masked points. In such way, we can enforce the decoder to take effect through the combinations of tokens rather than remembering each token. Comprehensive experiments show that M^3CS achieves superior performance at both classification and segmentation tasks, outperforming existing methods.

We present an approach to estimating camera rotation in crowded, real-world scenes from handheld monocular video. While camera rotation estimation is a well-studied problem, no previous methods exhibit both high accuracy and acceptable speed in this setting. Because the setting is not addressed well by other datasets, we provide a new dataset and benchmark, with high-accuracy, rigorously verified ground truth, on 17 video sequences. Methods developed for wide baseline stereo (e.g., 5-point methods) perform poorly on monocular video. On the other hand, methods used in autonomous driving (e.g., SLAM) leverage specific sensor setups, specific motion models, or local optimization strategies (lagging batch processing) and do not generalize well to handheld video. Finally, for dynamic scenes, commonly used robustification techniques like RANSAC require large numbers of iterations, and become prohibitively slow. We introduce a novel generalization of the Hough transform on SO(3) to efficiently and robustly find the camera rotation most compatible with optical flow. Among comparably fast methods, ours reduces error by almost 50\% over the next best, and is more accurate than any method, irrespective of speed. This represents a strong new performance point for crowded scenes, an important setting for computer vision. The code and the dataset are available at https://fabiendelattre.com/robust-rotation-estimation.

Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how they differ from meta-learning is lacking. In this paper, we propose a framework to analyze such learning-based acceleration approaches, where one can immediately identify a departure from classical meta-learning. We show that this departure may lead to arbitrary deterioration of model performance. Based on our analysis, we introduce a novel training method for learning-based acceleration of iterative methods. Furthermore, we theoretically prove that the proposed method improves upon the existing methods, and demonstrate its significant advantage and versatility through various numerical applications.

In this paper, we present DM-Calib, a diffusion-based approach for estimating pinhole camera intrinsic parameters from a single input image. Monocular camera calibration is essential for many 3D vision tasks. However, most existing methods depend on handcrafted assumptions or are constrained by limited training data, resulting in poor generalization across diverse real-world images. Recent advancements in stable diffusion models, trained on massive data, have shown the ability to generate high-quality images with varied characteristics. Emerging evidence indicates that these models implicitly capture the relationship between camera focal length and image content. Building on this insight, we explore how to leverage the powerful priors of diffusion models for monocular pinhole camera calibration. Specifically, we introduce a new image-based representation, termed Camera Image, which losslessly encodes the numerical camera intrinsics and integrates seamlessly with the diffusion framework. Using this representation, we reformulate the problem of estimating camera intrinsics as the generation of a dense Camera Image conditioned on an input image. By fine-tuning a stable diffusion model to generate a Camera Image from a single RGB input, we can extract camera intrinsics via a RANSAC operation. We further demonstrate that our monocular calibration method enhances performance across various 3D tasks, including zero-shot metric depth estimation, 3D metrology, pose estimation and sparse-view reconstruction. Extensive experiments on multiple public datasets show that our approach significantly outperforms baselines and provides broad benefits to 3D vision tasks. Code is available at https://github.com/JunyuanDeng/DM-Calib.

We introduce pix2gestalt, a framework for zero-shot amodal segmentation, which learns to estimate the shape and appearance of whole objects that are only partially visible behind occlusions. By capitalizing on large-scale diffusion models and transferring their representations to this task, we learn a conditional diffusion model for reconstructing whole objects in challenging zero-shot cases, including examples that break natural and physical priors, such as art. As training data, we use a synthetically curated dataset containing occluded objects paired with their whole counterparts. Experiments show that our approach outperforms supervised baselines on established benchmarks. Our model can furthermore be used to significantly improve the performance of existing object recognition and 3D reconstruction methods in the presence of occlusions.

Few-shot learning is valuable in many real-world applications, but learning a generalizable model without overfitting to the few labeled datapoints is challenging. In this work, we focus on Few-shot Learning with Auxiliary Data (FLAD), a training paradigm that assumes access to auxiliary data during few-shot learning in hopes of improving generalization. Previous works have proposed automated methods for mixing auxiliary and target data, but these methods typically scale linearly (or worse) with the number of auxiliary datasets, limiting their practicality. In this work we relate FLAD to the explore-exploit dilemma that is central to the multi-armed bandit setting and derive algorithms whose computational complexity is independent of the number of auxiliary datasets, allowing us to scale to 100x more auxiliary datasets than prior methods. We propose two algorithms -- EXP3-FLAD and UCB1-FLAD -- and compare them with prior FLAD methods that either explore or exploit, finding that the combination of exploration and exploitation is crucial. Through extensive experimentation we find that our methods outperform all pre-existing FLAD methods by 4% and lead to the first 3 billion parameter language models that outperform the 175 billion parameter GPT-3. Overall, our work suggests that the discovery of better, more efficient mixing strategies for FLAD may provide a viable path towards substantially improving generalization in few-shot learning.

Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as powerful priors. These attempts have paved the way for using diffusion models in a wide range of inverse problems. However, the existing methods entail computationally demanding iterative sampling procedures and optimize a separate solution for each measurement, which leads to limited scalability and lack of generalization capability across unseen samples. To address these limitations, we propose a novel approach, Diffusion prior-based Amortized Variational Inference (DAVI) that solves inverse problems with a diffusion prior from an amortized variational inference perspective. Specifically, instead of separate measurement-wise optimization, our amortized inference learns a function that directly maps measurements to the implicit posterior distributions of corresponding clean data, enabling a single-step posterior sampling even for unseen measurements. Extensive experiments on image restoration tasks, e.g., Gaussian deblur, 4times super-resolution, and box inpainting with two benchmark datasets, demonstrate our approach's superior performance over strong baselines. Code is available at https://github.com/mlvlab/DAVI.

We introduce a new family of particle evolution samplers suitable for constrained domains and non-Euclidean geometries. Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent minimize the Kullback-Leibler (KL) divergence to constrained target distributions by evolving particles in a dual space defined by a mirror map. Stein Variational Natural Gradient exploits non-Euclidean geometry to more efficiently minimize the KL divergence to unconstrained targets. We derive these samplers from a new class of mirrored Stein operators and adaptive kernels developed in this work. We demonstrate that these new samplers yield accurate approximations to distributions on the simplex, deliver valid confidence intervals in post-selection inference, and converge more rapidly than prior methods in large-scale unconstrained posterior inference. Finally, we establish the convergence of our new procedures under verifiable conditions on the target distribution.

Video generation models have demonstrated great capabilities of producing impressive monocular videos, however, the generation of 3D stereoscopic video remains under-explored. We propose a pose-free and training-free approach for generating 3D stereoscopic videos using an off-the-shelf monocular video generation model. Our method warps a generated monocular video into camera views on stereoscopic baseline using estimated video depth, and employs a novel frame matrix video inpainting framework. The framework leverages the video generation model to inpaint frames observed from different timestamps and views. This effective approach generates consistent and semantically coherent stereoscopic videos without scene optimization or model fine-tuning. Moreover, we develop a disocclusion boundary re-injection scheme that further improves the quality of video inpainting by alleviating the negative effects propagated from disoccluded areas in the latent space. We validate the efficacy of our proposed method by conducting experiments on videos from various generative models, including Sora [4 ], Lumiere [2], WALT [8 ], and Zeroscope [ 42]. The experiments demonstrate that our method has a significant improvement over previous methods. The code will be released at https://daipengwa.github.io/SVG_ProjectPage.

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.

In this work, we tackle the task of point cloud denoising through a novel framework that adapts Diffusion Schr\"odinger bridges to points clouds. Unlike previous approaches that predict point-wise displacements from point features or learned noise distributions, our method learns an optimal transport plan between paired point clouds. Experiments on object datasets like PU-Net and real-world datasets such as ScanNet++ and ARKitScenes show that P2P-Bridge achieves significant improvements over existing methods. While our approach demonstrates strong results using only point coordinates, we also show that incorporating additional features, such as color information or point-wise DINOv2 features, further enhances the performance. Code and pretrained models are available at https://p2p-bridge.github.io.

Video editing is a challenging task that requires manipulating videos on both the spatial and temporal dimensions. Existing methods for video editing mainly focus on changing the appearance or style of the objects in the video, while keeping their structures unchanged. However, there is no existing method that allows users to interactively ``drag'' any points of instances on the first frame to precisely reach the target points with other frames consistently deformed. In this paper, we propose a new diffusion-based method for interactive point-based video manipulation, called Drag-A-Video. Our method allows users to click pairs of handle points and target points as well as masks on the first frame of an input video. Then, our method transforms the inputs into point sets and propagates these sets across frames. To precisely modify the contents of the video, we employ a new video-level motion supervision to update the features of the video and introduce the latent offsets to achieve this update at multiple denoising timesteps. We propose a temporal-consistent point tracking module to coordinate the movement of the points in the handle point sets. We demonstrate the effectiveness and flexibility of our method on various videos. The website of our work is available here: https://drag-a-video.github.io/.

We consider learning in an adversarial Markov Decision Process (MDP) where the loss functions can change arbitrarily over K episodes and the state space can be arbitrarily large. We assume that the Q-function of any policy is linear in some known features, that is, a linear function approximation exists. The best existing regret upper bound for this setting (Luo et al., 2021) is of order mathcal O(K^{2/3}) (omitting all other dependencies), given access to a simulator. This paper provides two algorithms that improve the regret to mathcal O(sqrt K) in the same setting. Our first algorithm makes use of a refined analysis of the Follow-the-Regularized-Leader (FTRL) algorithm with the log-barrier regularizer. This analysis allows the loss estimators to be arbitrarily negative and might be of independent interest. Our second algorithm develops a magnitude-reduced loss estimator, further removing the polynomial dependency on the number of actions in the first algorithm and leading to the optimal regret bound (up to logarithmic terms and dependency on the horizon). Moreover, we also extend the first algorithm to simulator-free linear MDPs, which achieves mathcal O(K^{8/9}) regret and greatly improves over the best existing bound mathcal O(K^{14/15}). This algorithm relies on a better alternative to the Matrix Geometric Resampling procedure by Neu & Olkhovskaya (2020), which could again be of independent interest.

There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to scientific data. The latter require restrictive assumptions such as log-concavity to escape the curse of dimensionality. We partially bridge this gap by introducing conditionally strongly log-concave (CSLC) models, which factorize the data distribution into a product of conditional probability distributions that are strongly log-concave. This factorization is obtained with orthogonal projectors adapted to the data distribution. It leads to efficient parameter estimation and sampling algorithms, with theoretical guarantees, although the data distribution is not globally log-concave. We show that several challenging multiscale processes are conditionally log-concave using wavelet packet orthogonal projectors. Numerical results are shown for physical fields such as the varphi^4 model and weak lensing convergence maps with higher resolution than in previous works.

Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards speeding up diffusion generative modeling in practice, theoretical underpinnings for acceleration techniques remain severely limited. In this paper, we design novel training-free algorithms to accelerate popular deterministic (i.e., DDIM) and stochastic (i.e., DDPM) samplers. Our accelerated deterministic sampler converges at a rate O(1/{T}^2) with T the number of steps, improving upon the O(1/T) rate for the DDIM sampler; and our accelerated stochastic sampler converges at a rate O(1/T), outperforming the rate O(1/T) for the DDPM sampler. The design of our algorithms leverages insights from higher-order approximation, and shares similar intuitions as popular high-order ODE solvers like the DPM-Solver-2. Our theory accommodates ell_2-accurate score estimates, and does not require log-concavity or smoothness on the target distribution.

We introduce ORIGEN, the first zero-shot method for 3D orientation grounding in text-to-image generation across multiple objects and diverse categories. While previous work on spatial grounding in image generation has mainly focused on 2D positioning, it lacks control over 3D orientation. To address this, we propose a reward-guided sampling approach using a pretrained discriminative model for 3D orientation estimation and a one-step text-to-image generative flow model. While gradient-ascent-based optimization is a natural choice for reward-based guidance, it struggles to maintain image realism. Instead, we adopt a sampling-based approach using Langevin dynamics, which extends gradient ascent by simply injecting random noise--requiring just a single additional line of code. Additionally, we introduce adaptive time rescaling based on the reward function to accelerate convergence. Our experiments show that ORIGEN outperforms both training-based and test-time guidance methods across quantitative metrics and user studies.

Implicit neural networks have emerged as a crucial technology in 3D surface reconstruction. To reconstruct continuous surfaces from discrete point clouds, encoding the input points into regular grid features (plane or volume) has been commonly employed in existing approaches. However, these methods typically use the grid as an index for uniformly scattering point features. Compared with the irregular point features, the regular grid features may sacrifice some reconstruction details but improve efficiency. To take full advantage of these two types of features, we introduce a novel and high-efficiency attention mechanism between the grid and point features named Point-Grid Transformer (GridFormer). This mechanism treats the grid as a transfer point connecting the space and point cloud. Our method maximizes the spatial expressiveness of grid features and maintains computational efficiency. Furthermore, optimizing predictions over the entire space could potentially result in blurred boundaries. To address this issue, we further propose a boundary optimization strategy incorporating margin binary cross-entropy loss and boundary sampling. This approach enables us to achieve a more precise representation of the object structure. Our experiments validate that our method is effective and outperforms the state-of-the-art approaches under widely used benchmarks by producing more precise geometry reconstructions. The code is available at https://github.com/list17/GridFormer.

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at https://github.com/GFNOrg/gfn-diffusion as a base for future work on diffusion models for amortized inference.

In this paper, we consider the problem of Iterative Machine Teaching (IMT), where the teacher provides examples to the learner iteratively such that the learner can achieve fast convergence to a target model. However, existing IMT algorithms are solely based on parameterized families of target models. They mainly focus on convergence in the parameter space, resulting in difficulty when the target models are defined to be functions without dependency on parameters. To address such a limitation, we study a more general task -- Nonparametric Iterative Machine Teaching (NIMT), which aims to teach nonparametric target models to learners in an iterative fashion. Unlike parametric IMT that merely operates in the parameter space, we cast NIMT as a functional optimization problem in the function space. To solve it, we propose both random and greedy functional teaching algorithms. We obtain the iterative teaching dimension (ITD) of the random teaching algorithm under proper assumptions, which serves as a uniform upper bound of ITD in NIMT. Further, the greedy teaching algorithm has a significantly lower ITD, which reaches a tighter upper bound of ITD in NIMT. Finally, we verify the correctness of our theoretical findings with extensive experiments in nonparametric scenarios.

Recent years have witnessed the rapid progress and broad application of diffusion probabilistic models (DPMs). Sampling from DPMs can be viewed as solving an ordinary differential equation (ODE). Despite the promising performance, the generation of DPMs usually consumes much time due to the large number of function evaluations (NFE). Though recent works have accelerated the sampling to around 20 steps with high-order solvers, the sample quality with less than 10 NFE can still be improved. In this paper, we propose a unified sampling framework (USF) to study the optional strategies for solver. Under this framework, we further reveal that taking different solving strategies at different timesteps may help further decrease the truncation error, and a carefully designed solver schedule has the potential to improve the sample quality by a large margin. Therefore, we propose a new sampling framework based on the exponential integral formulation that allows free choices of solver strategy at each step and design specific decisions for the framework. Moreover, we propose S^3, a predictor-based search method that automatically optimizes the solver schedule to get a better time-quality trade-off of sampling. We demonstrate that S^3 can find outstanding solver schedules which outperform the state-of-the-art sampling methods on CIFAR-10, CelebA, ImageNet, and LSUN-Bedroom datasets. Specifically, we achieve 2.69 FID with 10 NFE and 6.86 FID with 5 NFE on CIFAR-10 dataset, outperforming the SOTA method significantly. We further apply S^3 to Stable-Diffusion model and get an acceleration ratio of 2times, showing the feasibility of sampling in very few steps without retraining the neural network.

Reconstructing meshes from point clouds is an important task in fields such as robotics, autonomous systems, and medical imaging. This survey examines state-of-the-art learning-based approaches to mesh reconstruction, categorizing them into five paradigms: PointNet family, autoencoder architectures, deformation-based methods, point-move techniques, and primitive-based approaches. Each paradigm is explored in depth, detailing the primary approaches and their underlying methodologies. By comparing these techniques, our study serves as a comprehensive guide, and equips researchers and practitioners with the knowledge to navigate the landscape of learning-based mesh reconstruction techniques. The findings underscore the transformative potential of these methods, which often surpass traditional techniques in allowing detailed and efficient reconstructions.

Classifier-Free Guidance (CFG) has been a default technique in various visual generative models, yet it requires inference from both conditional and unconditional models during sampling. We propose to build visual models that are free from guided sampling. The resulting algorithm, Guidance-Free Training (GFT), matches the performance of CFG while reducing sampling to a single model, halving the computational cost. Unlike previous distillation-based approaches that rely on pretrained CFG networks, GFT enables training directly from scratch. GFT is simple to implement. It retains the same maximum likelihood objective as CFG and differs mainly in the parameterization of conditional models. Implementing GFT requires only minimal modifications to existing codebases, as most design choices and hyperparameters are directly inherited from CFG. Our extensive experiments across five distinct visual models demonstrate the effectiveness and versatility of GFT. Across domains of diffusion, autoregressive, and masked-prediction modeling, GFT consistently achieves comparable or even lower FID scores, with similar diversity-fidelity trade-offs compared with CFG baselines, all while being guidance-free. Code will be available at https://github.com/thu-ml/GFT.

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.

We propose a method that achieves near-optimal rates for smooth stochastic convex optimization and requires essentially no prior knowledge of problem parameters. This improves on prior work which requires knowing at least the initial distance to optimality d0. Our method, U-DoG, combines UniXGrad (Kavis et al., 2019) and DoG (Ivgi et al., 2023) with novel iterate stabilization techniques. It requires only loose bounds on d0 and the noise magnitude, provides high probability guarantees under sub-Gaussian noise, and is also near-optimal in the non-smooth case. Our experiments show consistent, strong performance on convex problems and mixed results on neural network training.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

This paper proposes a new type of generative model that is able to quickly learn a latent representation without an encoder. This is achieved using empirical Bayes to calculate the expectation of the posterior, which is implemented by initialising a latent vector with zeros, then using the gradient of the log-likelihood of the data with respect to this zero vector as new latent points. The approach has similar characteristics to autoencoders, but with a simpler architecture, and is demonstrated in a variational autoencoder equivalent that permits sampling. This also allows implicit representation networks to learn a space of implicit functions without requiring a hypernetwork, retaining their representation advantages across datasets. The experiments show that the proposed method converges faster, with significantly lower reconstruction error than autoencoders, while requiring half the parameters.

Classifier-free guidance is a key component for enhancing the performance of conditional generative models across diverse tasks. While it has previously demonstrated remarkable improvements for the sample quality, it has only been exclusively employed for diffusion models. In this paper, we integrate classifier-free guidance into Flow Matching (FM) models, an alternative simulation-free approach that trains Continuous Normalizing Flows (CNFs) based on regressing vector fields. We explore the usage of Guided Flows for a variety of downstream applications. We show that Guided Flows significantly improves the sample quality in conditional image generation and zero-shot text-to-speech synthesis, boasting state-of-the-art performance. Notably, we are the first to apply flow models for plan generation in the offline reinforcement learning setting, showcasing a 10x speedup in computation compared to diffusion models while maintaining comparable performance.

Despite the success of physics-informed neural networks (PINNs) in approximating partial differential equations (PDEs), PINNs can sometimes fail to converge to the correct solution in problems involving complicated PDEs. This is reflected in several recent studies on characterizing the "failure modes" of PINNs, although a thorough understanding of the connection between PINN failure modes and sampling strategies is missing. In this paper, we provide a novel perspective of failure modes of PINNs by hypothesizing that training PINNs relies on successful "propagation" of solution from initial and/or boundary condition points to interior points. We show that PINNs with poor sampling strategies can get stuck at trivial solutions if there are propagation failures, characterized by highly imbalanced PDE residual fields. To mitigate propagation failures, we propose a novel Retain-Resample-Release sampling (R3) algorithm that can incrementally accumulate collocation points in regions of high PDE residuals with little to no computational overhead. We provide an extension of R3 sampling to respect the principle of causality while solving time-dependent PDEs. We theoretically analyze the behavior of R3 sampling and empirically demonstrate its efficacy and efficiency in comparison with baselines on a variety of PDE problems.

Point-based radiance field rendering has demonstrated impressive results for novel view synthesis, offering a compelling blend of rendering quality and computational efficiency. However, also latest approaches in this domain are not without their shortcomings. 3D Gaussian Splatting [Kerbl and Kopanas et al. 2023] struggles when tasked with rendering highly detailed scenes, due to blurring and cloudy artifacts. On the other hand, ADOP [R\"uckert et al. 2022] can accommodate crisper images, but the neural reconstruction network decreases performance, it grapples with temporal instability and it is unable to effectively address large gaps in the point cloud. In this paper, we present TRIPS (Trilinear Point Splatting), an approach that combines ideas from both Gaussian Splatting and ADOP. The fundamental concept behind our novel technique involves rasterizing points into a screen-space image pyramid, with the selection of the pyramid layer determined by the projected point size. This approach allows rendering arbitrarily large points using a single trilinear write. A lightweight neural network is then used to reconstruct a hole-free image including detail beyond splat resolution. Importantly, our render pipeline is entirely differentiable, allowing for automatic optimization of both point sizes and positions. Our evaluation demonstrate that TRIPS surpasses existing state-of-the-art methods in terms of rendering quality while maintaining a real-time frame rate of 60 frames per second on readily available hardware. This performance extends to challenging scenarios, such as scenes featuring intricate geometry, expansive landscapes, and auto-exposed footage.

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior, hyperparameters, and inducing points, making accurate learning challenging. Here, we present a method to keep all such errors in check using the recently proposed dual sparse variational GP. Our method enables accurate inference for generic likelihoods and improves learning by actively building and updating a memory of past data. We demonstrate its effectiveness in several applications involving Bayesian optimization, active learning, and continual learning.

Diffusion-based image restoration (IR) methods aim to use diffusion models to recover high-quality (HQ) images from degraded images and achieve promising performance. Due to the inherent property of diffusion models, most of these methods need long serial sampling chains to restore HQ images step-by-step. As a result, it leads to expensive sampling time and high computation costs. Moreover, such long sampling chains hinder understanding the relationship between the restoration results and the inputs since it is hard to compute the gradients in the whole chains. In this work, we aim to rethink the diffusion-based IR models through a different perspective, i.e., a deep equilibrium (DEQ) fixed point system. Specifically, we derive an analytical solution by modeling the entire sampling chain in diffusion-based IR models as a joint multivariate fixed point system. With the help of the analytical solution, we are able to conduct single-image sampling in a parallel way and restore HQ images without training. Furthermore, we compute fast gradients in DEQ and found that initialization optimization can boost performance and control the generation direction. Extensive experiments on benchmarks demonstrate the effectiveness of our proposed method on typical IR tasks and real-world settings. The code and models will be made publicly available.

We develop a variant of the stochastic prox-linear method for minimizing the Conditional Value-at-Risk (CVaR) objective. CVaR is a risk measure focused on minimizing worst-case performance, defined as the average of the top quantile of the losses. In machine learning, such a risk measure is useful to train more robust models. Although the stochastic subgradient method (SGM) is a natural choice for minimizing the CVaR objective, we show that our stochastic prox-linear (SPL+) algorithm can better exploit the structure of the objective, while still providing a convenient closed form update. Our SPL+ method also adapts to the scaling of the loss function, which allows for easier tuning. We then specialize a general convergence theorem for SPL+ to our setting, and show that it allows for a wider selection of step sizes compared to SGM. We support this theoretical finding experimentally.

Many state-of-the-art hyperparameter optimization (HPO) algorithms rely on model-based optimizers that learn surrogate models of the target function to guide the search. Gaussian processes are the de facto surrogate model due to their ability to capture uncertainty but they make strong assumptions about the observation noise, which might not be warranted in practice. In this work, we propose to leverage conformalized quantile regression which makes minimal assumptions about the observation noise and, as a result, models the target function in a more realistic and robust fashion which translates to quicker HPO convergence on empirical benchmarks. To apply our method in a multi-fidelity setting, we propose a simple, yet effective, technique that aggregates observed results across different resource levels and outperforms conventional methods across many empirical tasks.

Graph convolutional neural networks have recently shown great potential for the task of zero-shot learning. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, multi-layer architectures, which are required to propagate knowledge to distant nodes in the graph, dilute the knowledge by performing extensive Laplacian smoothing at each layer and thereby consequently decrease performance. In order to still enjoy the benefit brought by the graph structure while preventing dilution of knowledge from distant nodes, we propose a Dense Graph Propagation (DGP) module with carefully designed direct links among distant nodes. DGP allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants. A weighting scheme is further used to weigh their contribution depending on the distance to the node to improve information propagation in the graph. Combined with finetuning of the representations in a two-stage training approach our method outperforms state-of-the-art zero-shot learning approaches.

2D-to-3D reconstruction is an ill-posed problem, yet humans are good at solving this problem due to their prior knowledge of the 3D world developed over years. Driven by this observation, we propose NeRDi, a single-view NeRF synthesis framework with general image priors from 2D diffusion models. Formulating single-view reconstruction as an image-conditioned 3D generation problem, we optimize the NeRF representations by minimizing a diffusion loss on its arbitrary view renderings with a pretrained image diffusion model under the input-view constraint. We leverage off-the-shelf vision-language models and introduce a two-section language guidance as conditioning inputs to the diffusion model. This is essentially helpful for improving multiview content coherence as it narrows down the general image prior conditioned on the semantic and visual features of the single-view input image. Additionally, we introduce a geometric loss based on estimated depth maps to regularize the underlying 3D geometry of the NeRF. Experimental results on the DTU MVS dataset show that our method can synthesize novel views with higher quality even compared to existing methods trained on this dataset. We also demonstrate our generalizability in zero-shot NeRF synthesis for in-the-wild images.

We propose the convergent graph solver (CGS), a deep learning method that learns iterative mappings to predict the properties of a graph system at its stationary state (fixed point) with guaranteed convergence. CGS systematically computes the fixed points of a target graph system and decodes them to estimate the stationary properties of the system without the prior knowledge of existing solvers or intermediate solutions. The forward propagation of CGS proceeds in three steps: (1) constructing the input dependent linear contracting iterative maps, (2) computing the fixed-points of the linear maps, and (3) decoding the fixed-points to estimate the properties. The contractivity of the constructed linear maps guarantees the existence and uniqueness of the fixed points following the Banach fixed point theorem. To train CGS efficiently, we also derive a tractable analytical expression for its gradient by leveraging the implicit function theorem. We evaluate the performance of CGS by applying it to various network-analytic and graph benchmark problems. The results indicate that CGS has competitive capabilities for predicting the stationary properties of graph systems, irrespective of whether the target systems are linear or non-linear. CGS also shows high performance for graph classification problems where the existence or the meaning of a fixed point is hard to be clearly defined, which highlights the potential of CGS as a general graph neural network architecture.

This paper advocates the use of implicit surface representation in autoencoder-based self-supervised 3D representation learning. The most popular and accessible 3D representation, i.e., point clouds, involves discrete samples of the underlying continuous 3D surface. This discretization process introduces sampling variations on the 3D shape, making it challenging to develop transferable knowledge of the true 3D geometry. In the standard autoencoding paradigm, the encoder is compelled to encode not only the 3D geometry but also information on the specific discrete sampling of the 3D shape into the latent code. This is because the point cloud reconstructed by the decoder is considered unacceptable unless there is a perfect mapping between the original and the reconstructed point clouds. This paper introduces the Implicit AutoEncoder (IAE), a simple yet effective method that addresses the sampling variation issue by replacing the commonly-used point-cloud decoder with an implicit decoder. The implicit decoder reconstructs a continuous representation of the 3D shape, independent of the imperfections in the discrete samples. Extensive experiments demonstrate that the proposed IAE achieves state-of-the-art performance across various self-supervised learning benchmarks.

We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold. The estimator fuses samples from a hierarchy of data sources of differing fidelities and costs for variance reduction while guaranteeing definiteness, in contrast with previous approaches. The new estimator makes covariance estimation tractable in applications where simulation or data collection is expensive; to that end, we develop an optimal sample allocation scheme that minimizes the mean-squared error of the estimator given a fixed budget. Guaranteed definiteness is crucial to metric learning, data assimilation, and other downstream tasks. Evaluations of our approach using data from physical applications (heat conduction, fluid dynamics) demonstrate more accurate metric learning and speedups of more than one order of magnitude compared to benchmarks.

Generalizing metric monocular depth estimation presents a significant challenge due to its ill-posed nature, while the entanglement between camera parameters and depth amplifies issues further, hindering multi-dataset training and zero-shot accuracy. This challenge is particularly evident in autonomous vehicles and mobile robotics, where data is collected with fixed camera setups, limiting the geometric diversity. Yet, this context also presents an opportunity: the fixed relationship between the camera and the ground plane imposes additional perspective geometry constraints, enabling depth regression via vertical image positions of objects. However, this cue is highly susceptible to overfitting, thus we propose a novel canonical representation that maintains consistency across varied camera setups, effectively disentangling depth from specific parameters and enhancing generalization across datasets. We also propose a novel architecture that adaptively and probabilistically fuses depths estimated via object size and vertical image position cues. A comprehensive evaluation demonstrates the effectiveness of the proposed approach on five autonomous driving datasets, achieving accurate metric depth estimation for varying resolutions, aspect ratios and camera setups. Notably, we achieve comparable accuracy to existing zero-shot methods, despite training on a single dataset with a single-camera setup.

Large-scale pre-trained models have shown promising open-world performance for both vision and language tasks. However, their transferred capacity on 3D point clouds is still limited and only constrained to the classification task. In this paper, we first collaborate CLIP and GPT to be a unified 3D open-world learner, named as PointCLIP V2, which fully unleashes their potential for zero-shot 3D classification, segmentation, and detection. To better align 3D data with the pre-trained language knowledge, PointCLIP V2 contains two key designs. For the visual end, we prompt CLIP via a shape projection module to generate more realistic depth maps, narrowing the domain gap between projected point clouds with natural images. For the textual end, we prompt the GPT model to generate 3D-specific text as the input of CLIP's textual encoder. Without any training in 3D domains, our approach significantly surpasses PointCLIP by +42.90%, +40.44%, and +28.75% accuracy on three datasets for zero-shot 3D classification. On top of that, V2 can be extended to few-shot 3D classification, zero-shot 3D part segmentation, and 3D object detection in a simple manner, demonstrating our generalization ability for unified 3D open-world learning.

Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We first show that the marginal coverage guarantee of conformal prediction holds on imputed data for any missingness distribution and almost all imputation functions. However, we emphasize that the average coverage varies depending on the pattern of missing values: conformal methods tend to construct prediction intervals that under-cover the response conditionally to some missing patterns. This motivates our novel generalized conformalized quantile regression framework, missing data augmentation, which yields prediction intervals that are valid conditionally to the patterns of missing values, despite their exponential number. We then show that a universally consistent quantile regression algorithm trained on the imputed data is Bayes optimal for the pinball risk, thus achieving valid coverage conditionally to any given data point. Moreover, we examine the case of a linear model, which demonstrates the importance of our proposal in overcoming the heteroskedasticity induced by missing values. Using synthetic and data from critical care, we corroborate our theory and report improved performance of our methods.

The success of image generative models has enabled us to build methods that can edit images based on text or other user input. However, these methods are bespoke, imprecise, require additional information, or are limited to only 2D image edits. We present GeoDiffuser, a zero-shot optimization-based method that unifies common 2D and 3D image-based object editing capabilities into a single method. Our key insight is to view image editing operations as geometric transformations. We show that these transformations can be directly incorporated into the attention layers in diffusion models to implicitly perform editing operations. Our training-free optimization method uses an objective function that seeks to preserve object style but generate plausible images, for instance with accurate lighting and shadows. It also inpaints disoccluded parts of the image where the object was originally located. Given a natural image and user input, we segment the foreground object using SAM and estimate a corresponding transform which is used by our optimization approach for editing. GeoDiffuser can perform common 2D and 3D edits like object translation, 3D rotation, and removal. We present quantitative results, including a perceptual study, that shows how our approach is better than existing methods. Visit https://ivl.cs.brown.edu/research/geodiffuser.html for more information.

While methods for monocular depth estimation have made significant strides on standard benchmarks, zero-shot metric depth estimation remains unsolved. Challenges include the joint modeling of indoor and outdoor scenes, which often exhibit significantly different distributions of RGB and depth, and the depth-scale ambiguity due to unknown camera intrinsics. Recent work has proposed specialized multi-head architectures for jointly modeling indoor and outdoor scenes. In contrast, we advocate a generic, task-agnostic diffusion model, with several advancements such as log-scale depth parameterization to enable joint modeling of indoor and outdoor scenes, conditioning on the field-of-view (FOV) to handle scale ambiguity and synthetically augmenting FOV during training to generalize beyond the limited camera intrinsics in training datasets. Furthermore, by employing a more diverse training mixture than is common, and an efficient diffusion parameterization, our method, DMD (Diffusion for Metric Depth) achieves a 25\% reduction in relative error (REL) on zero-shot indoor and 33\% reduction on zero-shot outdoor datasets over the current SOTA using only a small number of denoising steps. For an overview see https://diffusion-vision.github.io/dmd

We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a general framework for first-order optimization of these processes, that performs jointly, in a single loop, optimization and sampling steps. This approach is inspired by recent advances in bilevel optimization and automatic implicit differentiation, leveraging the point of view of sampling as optimization over the space of probability distributions. We provide theoretical guarantees on the performance of our method, as well as experimental results demonstrating its effectiveness in real-world settings.

Single camera 3D pose estimation is an ill-defined problem due to inherent ambiguities from depth, occlusion or keypoint noise. Multi-hypothesis pose estimation accounts for this uncertainty by providing multiple 3D poses consistent with the 2D measurements. Current research has predominantly concentrated on generating multiple hypotheses for single frame static pose estimation. In this study we focus on the new task of multi-hypothesis motion estimation. Motion estimation is not simply pose estimation applied to multiple frames, which would ignore temporal correlation across frames. Instead, it requires distributions which are capable of generating temporally consistent samples, which is significantly more challenging. To this end, we introduce Platypose, a framework that uses a diffusion model pretrained on 3D human motion sequences for zero-shot 3D pose sequence estimation. Platypose outperforms baseline methods on multiple hypotheses for motion estimation. Additionally, Platypose also achieves state-of-the-art calibration and competitive joint error when tested on static poses from Human3.6M, MPI-INF-3DHP and 3DPW. Finally, because it is zero-shot, our method generalizes flexibly to different settings such as multi-camera inference.

This paper presents Dual Lagrangian Learning (DLL), a principled learning methodology for dual conic optimization proxies. DLL leverages conic duality and the representation power of ML models to provide high-duality, dual-feasible solutions, and therefore valid Lagrangian dual bounds, for linear and nonlinear conic optimization problems. The paper introduces a systematic dual completion procedure, differentiable conic projection layers, and a self-supervised learning framework based on Lagrangian duality. It also provides closed-form dual completion formulae for broad classes of conic problems, which eliminate the need for costly implicit layers. The effectiveness of DLL is demonstrated on linear and nonlinear conic optimization problems. The proposed methodology significantly outperforms a state-of-the-art learning-based method, and achieves 1000x speedups over commercial interior-point solvers with optimality gaps under 0.5\% on average.

Learning implicit representations has been a widely used solution for surface reconstruction from 3D point clouds. The latest methods infer a distance or occupancy field by overfitting a neural network on a single point cloud. However, these methods suffer from a slow inference due to the slow convergence of neural networks and the extensive calculation of distances to surface points, which limits them to small scale points. To resolve the scalability issue in surface reconstruction, we propose GridPull to improve the efficiency of learning implicit representations from large scale point clouds. Our novelty lies in the fast inference of a discrete distance field defined on grids without using any neural components. To remedy the lack of continuousness brought by neural networks, we introduce a loss function to encourage continuous distances and consistent gradients in the field during pulling queries onto the surface in grids near to the surface. We use uniform grids for a fast grid search to localize sampled queries, and organize surface points in a tree structure to speed up the calculation of distances to the surface. We do not rely on learning priors or normal supervision during optimization, and achieve superiority over the latest methods in terms of complexity and accuracy. We evaluate our method on shape and scene benchmarks, and report numerical and visual comparisons with the latest methods to justify our effectiveness and superiority. The code is available at https://github.com/chenchao15/GridPull.

Given a (machine learning) classifier and a collection of unlabeled data, how can we efficiently identify misclassification patterns presented in this dataset? To address this problem, we propose a human-machine collaborative framework that consists of a team of human annotators and a sequential recommendation algorithm. The recommendation algorithm is conceptualized as a stochastic sampler that, in each round, queries the annotators a subset of samples for their true labels and obtains the feedback information on whether the samples are misclassified. The sampling mechanism needs to balance between discovering new patterns of misclassification (exploration) and confirming the potential patterns of classification (exploitation). We construct a determinantal point process, whose intensity balances the exploration-exploitation trade-off through the weighted update of the posterior at each round to form the generator of the stochastic sampler. The numerical results empirically demonstrate the competitive performance of our framework on multiple datasets at various signal-to-noise ratios.

Zero-shot novel view synthesis (NVS) from a single image is an essential problem in 3D object understanding. While recent approaches that leverage pre-trained generative models can synthesize high-quality novel views from in-the-wild inputs, they still struggle to maintain 3D consistency across different views. In this paper, we present Consistent-1-to-3, which is a generative framework that significantly mitigate this issue. Specifically, we decompose the NVS task into two stages: (i) transforming observed regions to a novel view, and (ii) hallucinating unseen regions. We design a scene representation transformer and view-conditioned diffusion model for performing these two stages respectively. Inside the models, to enforce 3D consistency, we propose to employ epipolor-guided attention to incorporate geometry constraints, and multi-view attention to better aggregate multi-view information. Finally, we design a hierarchy generation paradigm to generate long sequences of consistent views, allowing a full 360 observation of the provided object image. Qualitative and quantitative evaluation over multiple datasets demonstrate the effectiveness of the proposed mechanisms against state-of-the-art approaches. Our project page is at https://jianglongye.com/consistent123/

This paper presents a novel preconditioning strategy for the classic 8-point algorithm (8-PA) for estimating an essential matrix from 360-FoV images (i.e., equirectangular images) in spherical projection. To alleviate the effect of uneven key-feature distributions and outlier correspondences, which can potentially decrease the accuracy of an essential matrix, our method optimizes a non-rigid transformation to deform a spherical camera into a new spatial domain, defining a new constraint and a more robust and accurate solution for an essential matrix. Through several experiments using random synthetic points, 360-FoV, and fish-eye images, we demonstrate that our normalization can increase the camera pose accuracy by about 20% without significantly overhead the computation time. In addition, we present further benefits of our method through both a constant weighted least-square optimization that improves further the well known Gold Standard Method (GSM) (i.e., the non-linear optimization by using epipolar errors); and a relaxation of the number of RANSAC iterations, both showing that our normalization outcomes a more reliable, robust, and accurate solution.

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.

Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly when considering exponential or non-parametric kernels. Although non-parametric kernels are an option, such models require large datasets. While exponential kernels are more data efficient and relevant for specific applications where events immediately trigger more events, they are ill-suited for applications where latencies need to be estimated, such as in neuroscience. This work aims to offer an efficient solution to TPP inference using general parametric kernels with finite support. The developed solution consists of a fast ell_2 gradient-based solver leveraging a discretized version of the events. After theoretically supporting the use of discretization, the statistical and computational efficiency of the novel approach is demonstrated through various numerical experiments. Finally, the method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG). Given the use of general parametric kernels, results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.

Recently, implicit neural representations have gained popularity for learning-based 3D reconstruction. While demonstrating promising results, most implicit approaches are limited to comparably simple geometry of single objects and do not scale to more complicated or large-scale scenes. The key limiting factor of implicit methods is their simple fully-connected network architecture which does not allow for integrating local information in the observations or incorporating inductive biases such as translational equivariance. In this paper, we propose Convolutional Occupancy Networks, a more flexible implicit representation for detailed reconstruction of objects and 3D scenes. By combining convolutional encoders with implicit occupancy decoders, our model incorporates inductive biases, enabling structured reasoning in 3D space. We investigate the effectiveness of the proposed representation by reconstructing complex geometry from noisy point clouds and low-resolution voxel representations. We empirically find that our method enables the fine-grained implicit 3D reconstruction of single objects, scales to large indoor scenes, and generalizes well from synthetic to real data.

Single point-supervised object detection is gaining attention due to its cost-effectiveness. However, existing approaches focus on generating horizontal bounding boxes (HBBs) while ignoring oriented bounding boxes (OBBs) commonly used for objects in aerial images. This paper proposes PointOBB, the first single Point-based OBB generation method, for oriented object detection. PointOBB operates through the collaborative utilization of three distinctive views: an original view, a resized view, and a rotated/flipped (rot/flp) view. Upon the original view, we leverage the resized and rot/flp views to build a scale augmentation module and an angle acquisition module, respectively. In the former module, a Scale-Sensitive Consistency (SSC) loss is designed to enhance the deep network's ability to perceive the object scale. For accurate object angle predictions, the latter module incorporates self-supervised learning to predict angles, which is associated with a scale-guided Dense-to-Sparse (DS) matching strategy for aggregating dense angles corresponding to sparse objects. The resized and rot/flp views are switched using a progressive multi-view switching strategy during training to achieve coupled optimization of scale and angle. Experimental results on the DIOR-R and DOTA-v1.0 datasets demonstrate that PointOBB achieves promising performance, and significantly outperforms potential point-supervised baselines.

This paper presents the evaluation methodology, datasets, and results of the BOP Challenge 2020, the third in a series of public competitions organized with the goal to capture the status quo in the field of 6D object pose estimation from an RGB-D image. In 2020, to reduce the domain gap between synthetic training and real test RGB images, the participants were provided 350K photorealistic training images generated by BlenderProc4BOP, a new open-source and light-weight physically-based renderer (PBR) and procedural data generator. Methods based on deep neural networks have finally caught up with methods based on point pair features, which were dominating previous editions of the challenge. Although the top-performing methods rely on RGB-D image channels, strong results were achieved when only RGB channels were used at both training and test time - out of the 26 evaluated methods, the third method was trained on RGB channels of PBR and real images, while the fifth on RGB channels of PBR images only. Strong data augmentation was identified as a key component of the top-performing CosyPose method, and the photorealism of PBR images was demonstrated effective despite the augmentation. The online evaluation system stays open and is available on the project website: bop.felk.cvut.cz.

We present InterHandGen, a novel framework that learns the generative prior of two-hand interaction. Sampling from our model yields plausible and diverse two-hand shapes in close interaction with or without an object. Our prior can be incorporated into any optimization or learning methods to reduce ambiguity in an ill-posed setup. Our key observation is that directly modeling the joint distribution of multiple instances imposes high learning complexity due to its combinatorial nature. Thus, we propose to decompose the modeling of joint distribution into the modeling of factored unconditional and conditional single instance distribution. In particular, we introduce a diffusion model that learns the single-hand distribution unconditional and conditional to another hand via conditioning dropout. For sampling, we combine anti-penetration and classifier-free guidance to enable plausible generation. Furthermore, we establish the rigorous evaluation protocol of two-hand synthesis, where our method significantly outperforms baseline generative models in terms of plausibility and diversity. We also demonstrate that our diffusion prior can boost the performance of two-hand reconstruction from monocular in-the-wild images, achieving new state-of-the-art accuracy.

We investigate the theoretical foundations of classifier-free guidance (CFG). CFG is the dominant method of conditional sampling for text-to-image diffusion models, yet unlike other aspects of diffusion, it remains on shaky theoretical footing. In this paper, we disprove common misconceptions, by showing that CFG interacts differently with DDPM (Ho et al., 2020) and DDIM (Song et al., 2021), and neither sampler with CFG generates the gamma-powered distribution p(x|c)^gamma p(x)^{1-gamma}. Then, we clarify the behavior of CFG by showing that it is a kind of predictor-corrector method (Song et al., 2020) that alternates between denoising and sharpening, which we call predictor-corrector guidance (PCG). We prove that in the SDE limit, CFG is actually equivalent to combining a DDIM predictor for the conditional distribution together with a Langevin dynamics corrector for a gamma-powered distribution (with a carefully chosen gamma). Our work thus provides a lens to theoretically understand CFG by embedding it in a broader design space of principled sampling methods.

We propose a novel point cloud U-Net diffusion architecture for 3D generative modeling capable of generating high-quality and diverse 3D shapes while maintaining fast generation times. Our network employs a dual-branch architecture, combining the high-resolution representations of points with the computational efficiency of sparse voxels. Our fastest variant outperforms all non-diffusion generative approaches on unconditional shape generation, the most popular benchmark for evaluating point cloud generative models, while our largest model achieves state-of-the-art results among diffusion methods, with a runtime approximately 70% of the previously state-of-the-art PVD. Beyond unconditional generation, we perform extensive evaluations, including conditional generation on all categories of ShapeNet, demonstrating the scalability of our model to larger datasets, and implicit generation which allows our network to produce high quality point clouds on fewer timesteps, further decreasing the generation time. Finally, we evaluate the architecture's performance in point cloud completion and super-resolution. Our model excels in all tasks, establishing it as a state-of-the-art diffusion U-Net for point cloud generative modeling. The code is publicly available at https://github.com/JohnRomanelis/SPVD.git.

We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. This MMD, which is also known as energy distance, has several advantageous properties like efficient computation via slicing and sorting. We approximate the joint distribution of the ground truth and the observations using discrete Wasserstein gradient flows and establish an error bound for the posterior distributions. Further, we prove that our particle flow is indeed a Wasserstein gradient flow of an appropriate functional. The power of our method is demonstrated by numerical examples including conditional image generation and inverse problems like superresolution, inpainting and computed tomography in low-dose and limited-angle settings.

We introduce a theoretical framework for sampling from unnormalized densities based on a smoothing scheme that uses an isotropic Gaussian kernel with a single fixed noise scale. We prove one can decompose sampling from a density (minimal assumptions made on the density) into a sequence of sampling from log-concave conditional densities via accumulation of noisy measurements with equal noise levels. Our construction is unique in that it keeps track of a history of samples, making it non-Markovian as a whole, but it is lightweight algorithmically as the history only shows up in the form of a running empirical mean of samples. Our sampling algorithm generalizes walk-jump sampling (Saremi & Hyv\"arinen, 2019). The "walk" phase becomes a (non-Markovian) chain of (log-concave) Markov chains. The "jump" from the accumulated measurements is obtained by empirical Bayes. We study our sampling algorithm quantitatively using the 2-Wasserstein metric and compare it with various Langevin MCMC algorithms. We also report a remarkable capacity of our algorithm to "tunnel" between modes of a distribution.