| # DDIM反转 | |
| 在此篇笔记我们会来探索**反转**，看看它是如何影响取样的，并把它应用到扩散模型的编辑图像功能中去。 | |
| ## 你将会学到什么 | |
| - DDIM采样是怎么工作的 | |
| - 确定性vs随机性取样器 | |
| - DDIM反转的理论支撑 | |
| - 使用反转来编辑图像 | |
| 我们开始吧！ | |
| ## 设置 | |
| ```python | |
| # !pip install -q transformers diffusers accelerate | |
| ``` | |
| ```python | |
| import torch | |
| import requests | |
| import torch.nn as nn | |
| import torch.nn.functional as F | |
| from PIL import Image | |
| from io import BytesIO | |
| from tqdm.auto import tqdm | |
| from matplotlib import pyplot as plt | |
| from torchvision import transforms as tfms | |
| from diffusers import StableDiffusionPipeline, DDIMScheduler | |
| # Useful function for later | |
| def load_image(url, size=None): | |
| response = requests.get(url,timeout=0.2) | |
| img = Image.open(BytesIO(response.content)).convert('RGB') | |
| if size is not None: | |
| img = img.resize(size) | |
| return img | |
| ``` | |
| ```python | |
| device = torch.device("cuda" if torch.cuda.is_available() else "cpu") | |
| ``` | |
| ## 加载一个已训练的pipeline | |
| ```python | |
| # Load a pipeline | |
| pipe = StableDiffusionPipeline.from_pretrained("runwayml/stable-diffusion-v1-5").to(device) | |
| ``` | |
| ```python | |
| # Set up a DDIM scheduler: | |
| pipe.scheduler = DDIMScheduler.from_config(pipe.scheduler.config) | |
| ``` | |
| ```python | |
| # Sample an image to make sure it is all working | |
| prompt = 'Beautiful DSLR Photograph of a penguin on the beach, golden hour' | |
| negative_prompt = 'blurry, ugly, stock photo' | |
| im = pipe(prompt, negative_prompt=negative_prompt).images[0] | |
| im.resize((256, 256)) # resize for convenient viewing | |
| ``` | |
| ## DDIM取样过程 | |
| 在给定时间 $t$, 带噪图像 $x_t$ 是原始图像（$x_0$）与一些噪声 ($\epsilon$)的叠加。这是在DDIM论文中$x_t$的定义式，我们把它引用到此节里： | |
| $$ x_t = \sqrt{\alpha_t}x_0 + \sqrt{1-\alpha_t}\epsilon $$ | |
| $\epsilon$ 是一些归一方差的高斯噪声 | |
| $\alpha_t$ ('alpha')在DDPM论文中也被叫做$\bar{\alpha}$ ('alpha_bar')，被用来定义噪声调度器（scheduler）。在扩散模型中，alpha调度器是被计算出来并排序存储在`scheduler.alphas_cumprod`中。这令人费解，我理解！我们把这些值画出来，然后在下文中我们会使用DDIM的标注方式。 | |
| ```python | |
| # Plot 'alpha' (alpha_bar in DDPM language, alphas_cumprod in diffusers for clarity) | |
| timesteps = pipe.scheduler.timesteps.cpu() | |
| alphas = pipe.scheduler.alphas_cumprod[timesteps] | |
| plt.plot(timesteps, alphas, label='alpha_t'); | |
| plt.legend(); | |
| ``` | |
| 最初（timestep 0 ，图中左侧）是从一个无噪的干净图像开始，$\alpha_t = 1$。当我们到达更高的timesteps，我们得到一个几乎全是噪声的图像，$\alpha_t$也几乎下降到0。 | |
| 在采样过程，我们从timestep1000的纯噪声开始，慢慢地向timestep0前进。为了计算采样轨迹中的下一时刻($x_{t-1}$因为我们是从后向前移动)的值，我们预测噪声($\epsilon_\theta(x_t)$，这就是我们模型的输出），用它来预测出无噪的图片$x_0$。在这之后我们用这个预测结果朝着'$x_t$的方向'方向移动一小步。最终，我们可以加一些带$\sigma_t$系数的额外噪声。这是论文中与上述操作相关的章节内容： | |
|  | |
| 好，我们有了在可控量度噪声下，从$x_t$ 移动到 $x_{t-1}$的公式。今天我们所说案例是不需要再额外添加噪声的 - 即完全确定的DDIM采样。我们来看看这些是如何用代码表达的。 | |
| ```python | |
| # Sample function (regular DDIM) | |
| @torch.no_grad() | |
| def sample(prompt, start_step=0, start_latents=None, | |
| guidance_scale=3.5, num_inference_steps=30, | |
| num_images_per_prompt=1, do_classifier_free_guidance=True, | |
| negative_prompt='', device=device): | |
| # Encode prompt | |
| text_embeddings = pipe._encode_prompt( | |
| prompt, device, num_images_per_prompt, do_classifier_free_guidance, negative_prompt | |
| ) | |
| # Set num inference steps | |
| pipe.scheduler.set_timesteps(num_inference_steps, device=device) | |
| # Create a random starting point if we don't have one already | |
| if start_latents is None: | |
| start_latents = torch.randn(1, 4, 64, 64, device=device) | |
| start_latents *= pipe.scheduler.init_noise_sigma | |
| latents = start_latents.clone() | |
| for i in tqdm(range(start_step, num_inference_steps)): | |
| t = pipe.scheduler.timesteps[i] | |
| # expand the latents if we are doing classifier free guidance | |
| latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents | |
| latent_model_input = pipe.scheduler.scale_model_input(latent_model_input, t) | |
| # predict the noise residual | |
| noise_pred = pipe.unet(latent_model_input, t, encoder_hidden_states=text_embeddings).sample | |
| # perform guidance | |
| if do_classifier_free_guidance: | |
| noise_pred_uncond, noise_pred_text = noise_pred.chunk(2) | |
| noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond) | |
| # Normally we'd rely on the scheduler to handle the update step: | |
| # latents = pipe.scheduler.step(noise_pred, t, latents).prev_sample | |
| # Instead, let's do it ourselves: | |
| prev_t = max(1, t.item() - (1000//num_inference_steps)) # t-1 | |
| alpha_t = pipe.scheduler.alphas_cumprod[t.item()] | |
| alpha_t_prev = pipe.scheduler.alphas_cumprod[prev_t] | |
| predicted_x0 = (latents - (1-alpha_t).sqrt()*noise_pred) / alpha_t.sqrt() | |
| direction_pointing_to_xt = (1-alpha_t_prev).sqrt()*noise_pred | |
| latents = alpha_t_prev.sqrt()*predicted_x0 + direction_pointing_to_xt | |
| # Post-processing | |
| images = pipe.decode_latents(latents) | |
| images = pipe.numpy_to_pil(images) | |
| return images | |
| ``` | |
| ```python | |
| # Test our sampling function by generating an image | |
| sample('Watercolor painting of a beach sunset', negative_prompt=negative_prompt, num_inference_steps=50)[0].resize((256, 256)) | |
| ``` | |
| 看看你是否能把这些代码和论文中的公式对应起来。注意$\sigma$=0是因为我们只注意 无-额外-噪声 的场景，所以我们略去了公式中的那部分。 | |
| ## 反转 | |
| 反转的目标就是'颠倒'取样的过程。我们想最终得到一个带噪的隐式（latent），如果把它作为我们正常取样过程的起始点，结果将生成一副原图像。 | |
| 这里我们先加载一个原始图像，当然你也可以生成一副图像来代替。 | |
| ```python | |
| # https://www.pexels.com/photo/a-beagle-on-green-grass-field-8306128/ | |
| input_image = load_image('https://images.pexels.com/photos/8306128/pexels-photo-8306128.jpeg', size=(512, 512)) | |
| input_image | |
| ``` | |
| 我们可以用包含随意分类指引（classifier-free-guidance）的prompt来做反转操作，输入一个图片的描述： | |
| ```python | |
| input_image_prompt = "Photograph of a puppy on the grass" | |
| ``` | |
| 接下来我们来把这个PIL图像变成一些列隐式，它们会被用来当作反转的起点： | |
| ```python | |
| # encode with VAE | |
| with torch.no_grad(): latent = pipe.vae.encode(tfms.functional.to_tensor(input_image).unsqueeze(0).to(device)*2-1) | |
| l = 0.18215 * latent.latent_dist.sample() | |
| ``` | |
| 好了，到有趣的部分了。这个函数看起来和上面的取样函数很像，但我们在timesteps上是在向相反的方向移动，从t=0开始，向越来越多的噪声前进。代替更新隐式时噪声会越来越少，我们估计所预测出的噪声，用它来撤回一步更新操作，把它们从t移动到t+1。 | |
| ```python | |
| ## Inversion | |
| @torch.no_grad() | |
| def invert(start_latents, prompt, guidance_scale=3.5, num_inference_steps=80, | |
| num_images_per_prompt=1, do_classifier_free_guidance=True, | |
| negative_prompt='', device=device): | |
| # Encode prompt | |
| text_embeddings = pipe._encode_prompt( | |
| prompt, device, num_images_per_prompt, do_classifier_free_guidance, negative_prompt | |
| ) | |
| # latents are now the specified start latents | |
| latents = start_latents.clone() | |
| # We'll keep a list of the inverted latents as the process goes on | |
| intermediate_latents = [] | |
| # Set num inference steps | |
| pipe.scheduler.set_timesteps(num_inference_steps, device=device) | |
| # Reversed timesteps <<<<<<<<<<<<<<<<<<<< | |
| timesteps = reversed(pipe.scheduler.timesteps) | |
| for i in tqdm(range(1, num_inference_steps), total=num_inference_steps-1): | |
| # We'll skip the final iteration | |
| if i >= num_inference_steps - 1: continue | |
| t = timesteps[i] | |
| # expand the latents if we are doing classifier free guidance | |
| latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents | |
| latent_model_input = pipe.scheduler.scale_model_input(latent_model_input, t) | |
| # predict the noise residual | |
| noise_pred = pipe.unet(latent_model_input, t, encoder_hidden_states=text_embeddings).sample | |
| # perform guidance | |
| if do_classifier_free_guidance: | |
| noise_pred_uncond, noise_pred_text = noise_pred.chunk(2) | |
| noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond) | |
| current_t = max(0, t.item() - (1000//num_inference_steps))#t | |
| next_t = t # min(999, t.item() + (1000//num_inference_steps)) # t+1 | |
| alpha_t = pipe.scheduler.alphas_cumprod[current_t] | |
| alpha_t_next = pipe.scheduler.alphas_cumprod[next_t] | |
| # Inverted update step (re-arranging the update step to get x(t) (new latents) as a function of x(t-1) (current latents) | |
| latents = (latents - (1-alpha_t).sqrt()*noise_pred)*(alpha_t_next.sqrt()/alpha_t.sqrt()) + (1-alpha_t_next).sqrt()*noise_pred | |
| # Store | |
| intermediate_latents.append(latents) | |
| return torch.cat(intermediate_latents) | |
| ``` | |
| 把它在小狗图片的隐式表达上运行，我们可以在反转的中间过程得到一系列的隐式： | |
| ```python | |
| inverted_latents = invert(l, input_image_prompt,num_inference_steps=50) | |
| inverted_latents.shape | |
| ``` | |
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| torch.Size([48, 4, 64, 64]) | |
| 我们可以来看一下最终的隐式 - 希望这可以作为我们尝试新的取样过程的起点噪声： | |
| ```python | |
| # Decode the final inverted latents: | |
| with torch.no_grad(): | |
| im = pipe.decode_latents(inverted_latents[-1].unsqueeze(0)) | |
| pipe.numpy_to_pil(im)[0] | |
| ``` | |
|  | |
| 你可以把这个反转隐式通过正常的 __call__ 方法来传递给pipeline。 | |
| ```python | |
| pipe(input_image_prompt, latents=inverted_latents[-1][None], num_inference_steps=50, guidance_scale=3.5).images[0] | |
| ``` | |
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|  | |
| 但这里我们遇见了第一个问题：这 **并不是我们一开始的那张图片**！这是因为DDIM的反转依赖一个重要的假设，在t时刻预测的噪声与t+1时刻会是相同的 - 这在我们只反转50或100步时是不陈立的。我们可以寄希望于更多的timesteps开得到一个更准确的反转，但我们也可以'作弊'一下，就是说直接从做对应反转过程中的第20/50步的隐式开始： | |
| ```python | |
| # The reason we want to be able to specify start step | |
| start_step=20 | |
| sample(input_image_prompt, start_latents=inverted_latents[-(start_step+1)][None], | |
| start_step=start_step, num_inference_steps=50)[0] | |
| ``` | |
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|  | |
| 距离我们的输入图像已经很接近了！我们为什么要这么做？嗯，这是因为如果我们现在若要用一个新的prompt来生成图像，我们会得到一个匹配于源图像，除了，与新prompt相关的内容。例如，把'小狗'替换为'猫'，我们能看到一只猫在几乎一样草地背景上： | |
| ```python | |
| # Sampling with a new prompt | |
| start_step=10 | |
| new_prompt = input_image_prompt.replace('puppy', 'cat') | |
| sample(new_prompt, start_latents=inverted_latents[-(start_step+1)][None], | |
| start_step=start_step, num_inference_steps=50)[0] | |
| ``` | |
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|  | |
| ### 为什么不直接用 img2img？ | |
| 为什么要做反转，不是多此一举吗？为什么不直接对输入图片加入噪声，然后用新的promt直接来去噪呢？我们可以这么做，但这会带来一个到处都被改变得夸张得多的照片（如果我们加入了很多噪声），或哪也没怎么变的图像（如果加了太少的噪声）。来自己试试： | |
| ```python | |
| start_step = 10 | |
| num_inference_steps=50 | |
| pipe.scheduler.set_timesteps(num_inference_steps) | |
| noisy_l = pipe.scheduler.add_noise(l, torch.randn_like(l), pipe.scheduler.timesteps[start_step]) | |
| sample(new_prompt, start_latents=noisy_l, start_step=start_step, num_inference_steps=num_inference_steps)[0] | |
| ``` | |
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|  | |
| 注意背景和草坪有着非常大的变化。 | |
| # 把它们都组装起来 | |
| 来把我们目前所写的代码都组装在一个简单的函数里，输入一张图像和两个prompts，就会得到一个通过反转得到的修改后的图片： | |
| ```python | |
| def edit(input_image, input_image_prompt, edit_prompt, num_steps=100, start_step=30, guidance_scale=3.5): | |
| with torch.no_grad(): latent = pipe.vae.encode(tfms.functional.to_tensor(input_image).unsqueeze(0).to(device)*2-1) | |
| l = 0.18215 * latent.latent_dist.sample() | |
| inverted_latents = invert(l, input_image_prompt,num_inference_steps=num_steps) | |
| final_im = sample(edit_prompt, start_latents=inverted_latents[-(start_step+1)][None], | |
| start_step=start_step, num_inference_steps=num_steps, guidance_scale=guidance_scale)[0] | |
| return final_im | |
| ``` | |
| And in action: | |
| 实际操作起来： | |
| ```python | |
| edit(input_image, 'A puppy on the grass', 'an old grey dog on the grass', num_steps=50, start_step=10) | |
| ``` | |
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|  | |
| ```python | |
| edit(input_image, 'A puppy on the grass', 'A blue dog on the lawn', num_steps=50, start_step=12, guidance_scale=6) | |
| ``` | |
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|  | |
| ```python | |
| # Exercise: Try this on some more images! Explore the different parameters | |
| ``` | |
| ## 更多迭代 = 更好的表现 | |
| 如果你因为反转结果不准确而烦恼，你可以试试多迭代几次（代价就是更长的运行时间）。为了测试一下反转过程，你可以使用这里的edit函数并输入相同的prompt： | |
| ```python | |
| # Inversion test with far more steps: | |
| edit(input_image, 'A puppy on the grass', 'A puppy on the grass', num_steps=350, start_step=1) | |
| ``` | |
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|  | |
| 好多了！来试试用它编辑图片： | |
| ```python | |
| edit(input_image, 'A photograph of a puppy', 'A photograph of a grey cat', num_steps=150, start_step=30, guidance_scale=5.5) | |
| ``` | |
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|  | |
| ```python | |
| # source: https://www.pexels.com/photo/girl-taking-photo-1493111/ | |
| face = load_image('https://images.pexels.com/photos/1493111/pexels-photo-1493111.jpeg', size=(512, 512)) | |
| face | |
| ``` | |
|  | |
| ```python | |
| edit(face, 'A photograph of a face', 'A photograph of a face with sunglasses', num_steps=250, start_step=30, guidance_scale=3.5) | |
| ``` | |
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|  | |
| ```python | |
| edit(face, 'A photograph of a face', 'Acrylic palette knife painting of a face, colorful', num_steps=250, start_step=65, guidance_scale=5.5) | |
| ``` | |
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|  | |
| # 接下来会是？ | |
| 有了此篇笔记的帮助，我建议你再研究下['Null-text Inversion'](https://null-text-inversion.github.io/)，它是基于DDIM来优化空文本（无条件文字prompt）的反转过程，有着更准确的反转与更好的编辑效果。 | |