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+# 《从零开始学扩散模型》
+
+## 术语表
+
+| 词汇                    | 翻译 | 
+| :---------------------- | :--- | 
+| Corruption Process      |  退化过程  |
+| Pipeline      |  管线  |
+| Timestep      |  时间步  |
+| Scheduler      |  调度器  |
+| Gradient Accumulation      |  梯度累加  |
+| Fine-Tuning      |  微调  |
+| Guidance      |  引导  |
+# 目录
+
+## 第一部分 基础知识
+
+### 第一章 扩散模型的原理、发展和应用
+
+#### 1.1 扩散模型的原理
+#### 1.2 扩散模型的发展
+#### 1.3 扩散模型的应用
+
+### 第二章 HuggingFace介绍与环境准备
+
+#### 2.1 HuggingFace Space
+#### 2.2 Transformer 与 diffusers 库
+#### 2.3 环境准备
+
+## 第二部分 扩散模型实战
+
+### 第三章 从零开始做扩散模型
+
+#### 3.1 章节概述
+有时，只考虑一些事务最简单的情况反而会更有助于理解其工作原理。我们将在本章中进行尝试，从一个简单的扩散模型开始，了解不同部分的工作原理，然后再对比它们与更复杂的实现有何不同。
+首先，我们将学习如下知识点：
+- 损坏过程(向数据添加噪声)；
+- 什么是UNet模型，以及如何从零开始实现一个简单的UNet；
+- 扩散模型训练；
+- 采样理论。
+
+然后，我们将对比我们的版本与使用diffusers库中DDPM实现的区别，知识点如下：
+- 对小型UNet模型的改进；
+- DDPM噪声计划；
+- 训练目标的差异；
+- timestep调节；
+- 采样方法。
+
+值得注意的是，这里的大多数代码都是为了说明与讲解，我不建议直接将其用于自己的工作(除非你只是为了学习而尝试改进本章展示的示例)。
+
+
+#### 3.2 环境准备
+#### 3.2.1 环境的创建与导入
+```python
+!pip install -q diffusers
+```
+
+
+```python
+import torch
+import torchvision
+from torch import nn
+from torch.nn import functional as F
+from torch.utils.data import DataLoader
+from diffusers import DDPMScheduler, UNet2DModel
+from matplotlib import pyplot as plt
+
+device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
+print(f'Using device: {device}')
+```
+
+#### 3.2.2 数据集测试
+在这里，我们将使用一个非常小的经典数据集mnist来进行测试。如果您想在不改变任何其他内容的情况下，给模型一个更困难的挑战，请使用torchvision.dataset中FashionMNIST来代替。
+
+```python
+dataset = torchvision.datasets.MNIST(root="mnist/", train=True, download=True, transform=torchvision.transforms.ToTensor())
+```
+
+```python
+train_dataloader = DataLoader(dataset, batch_size=8, shuffle=True)
+```
+
+```python
+x, y = next(iter(train_dataloader))
+print('Input shape:', x.shape)
+print('Labels:', y)
+plt.imshow(torchvision.utils.make_grid(x)[0], cmap='Greys');
+```
+
+该数据集中的每张图都是一个阿拉伯数字的28x28像素的灰度图，像素值的范围是从0到1。
+
+#### 3.3 扩散模型-退化过程
+假设你没有读过任何扩散模型相关的论文，但你知道在这个过程是在给内容增加噪声。你会怎么做？
+
+你可能想要一个简单的方法来控制损坏的程度。那么如果需要引入一个参数，用来控制输入的“噪声量”，那么我们会这么做：
+
+`noise = torch.rand_like(x)` 
+
+`noisy_x =  (1-amount)*x + amount*noise`
+
+如果 amount = 0，则返回输入而不做任何更改。如果 amount = 1，我们将得到一个纯粹的噪声。通过这种方式将输入内容与噪声混合，再把混合后的结果仍然保持在相同的范围（0 to 1）。
+
+我们可以很容易地实现这一点（但是要注意tensor的shape，以防被广播(broadcasting)机制不正确的影响到）：
+
+
+```python
+def corrupt(x, amount):
+  """Corrupt the input `x` by mixing it with noise according to `amount`"""
+  noise = torch.rand_like(x)
+  amount = amount.view(-1, 1, 1, 1) # Sort shape so broadcasting works
+  return x*(1-amount) + noise*amount 
+```
+
+我们来可视化一下输出的结果，来看看它是否符合预期：
+
+
+```python
+# Plotting the input data
+fig, axs = plt.subplots(2, 1, figsize=(12, 5))
+axs[0].set_title('Input data')
+axs[0].imshow(torchvision.utils.make_grid(x)[0], cmap='Greys')
+
+# Adding noise
+amount = torch.linspace(0, 1, x.shape[0]) # Left to right -> more corruption
+noised_x = corrupt(x, amount)
+
+# Plottinf the noised version
+axs[1].set_title('Corrupted data (-- amount increases -->)')
+axs[1].imshow(torchvision.utils.make_grid(noised_x)[0], cmap='Greys');
+```
+
+当噪声量接近1时，我们的数据开始看起来像纯粹的随机噪声。但对于大多数的噪声情况下，您还是可以很好地识别出数字。但这样你认为是最佳的结果吗？
+
+#### 3.4 扩散模型训练
+#### 3.4.1 Unet模型
+我们想要一个模型，它可以接收28px的噪声图像，并输出相同形状的预测。一个比较流行的选择是一个叫做UNet的架构。[最初被发明用于医学图像中的分割任务](https://arxiv.org/abs/1505.04597)，UNet由一个“压缩路径”和一个“扩展路径”组成。“压缩路径”会使通过该路径的数据纬度被压缩，而通过“扩展路径”会将数据扩展回原始维度（类似于自动编码器）。模型中的残差连接也允许信息和梯度在不同层级之间流动。
+
+一些UNet的设计在每个阶段都有复杂的blocks，但对于这个玩具demo，我们只会构建一个最简单的示例，它接收一个单通道图像，并通过下行路径的3个卷积层（图和代码中的down_layers）和上行路径的3个卷积层，且在下行和上行层之间有残差连接。我们将使用max pooling进行下采样和`nn.Upsample`用于上采样。某些更复杂的UNets的设计会使用带有可学习参数的上采样和下采样layer。下面的结构图大致展示了每个layer的输出通道数：
+
+![unet_diag.png](data:image/png;base64,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)
+
+代码实现如下：
+
+
+```python
+class BasicUNet(nn.Module):
+    """A minimal UNet implementation."""
+    def __init__(self, in_channels=1, out_channels=1):
+        super().__init__()
+        self.down_layers = torch.nn.ModuleList([ 
+            nn.Conv2d(in_channels, 32, kernel_size=5, padding=2),
+            nn.Conv2d(32, 64, kernel_size=5, padding=2),
+            nn.Conv2d(64, 64, kernel_size=5, padding=2),
+        ])
+        self.up_layers = torch.nn.ModuleList([
+            nn.Conv2d(64, 64, kernel_size=5, padding=2),
+            nn.Conv2d(64, 32, kernel_size=5, padding=2),
+            nn.Conv2d(32, out_channels, kernel_size=5, padding=2), 
+        ])
+        self.act = nn.n() # The activation function
+        self.downscale = nn.MaxPool2d(2)
+        self.upscale = nn.Upsample(scale_factor=2)
+
+    def forward(self, x):
+        h = []
+        for i, l in enumerate(self.down_layers):
+            x = self.act(l(x)) # Through the layer and the activation function
+            if i < 2: # For all but the third (final) down layer:
+              h.append(x) # Storing output for skip connection
+              x = self.downscale(x) # Downscale ready for the next layer
+              
+        for i, l in enumerate(self.up_layers):
+            if i > 0: # For all except the first up layer
+              x = self.upscale(x) # Upscale
+              x += h.pop() # Fetching stored output (skip connection)
+            x = self.act(l(x)) # Through the layer and the activation function
+            
+        return x
+```
+
+我们可以验证输出的shape是否如我们期望的那样是与输入相同的：
+
+
+```python
+net = BasicUNet()
+x = torch.rand(8, 1, 28, 28)
+net(x).shape
+```
+
+
+
+
+    torch.Size([8, 1, 28, 28])
+
+
+
+该网络有30多万个参数：
+
+
+```python
+sum([p.numel() for p in net.parameters()])
+```
+
+
+
+
+    309057
+
+
+
+您可以尝试更改每个layer中的通道数或直接尝试不同的结构设计。
+
+#### 3.4.2 开始训练模型
+那么，扩散模型到底应该做什么呢？对这个问题有各种不同的看法，但对于这个演示，我们来选择一个简单的框架：给定一个带噪的输入noisy_x，模型应该输出它对原本x的最佳预测。我们会通过均方误差将预测与真实值进行比较。
+
+我们现在可以尝试来训练网络了。
+- 获取一批数据
+- 添加随机噪声
+- 将数据输入模型
+- 将模型预测与干净图像进行比较，以计算loss
+- 更新模型的参数。
+
+你可以自由进行修改来看看怎样获得更好的结果！
+
+
+```python
+# Dataloader (you can mess with batch size)
+batch_size = 128
+train_dataloader = DataLoader(dataset, batch_size=batch_size, shuffle=True)
+
+# How many runs through the data should we do?
+n_epochs = 3
+
+# Create the network
+net = BasicUNet()
+net.to(device)
+
+# Our loss finction
+loss_fn = nn.MSELoss()
+
+# The optimizer
+opt = torch.optim.Adam(net.parameters(), lr=1e-3) 
+
+# Keeping a record of the losses for later viewing
+losses = []
+
+# The training loop
+for epoch in range(n_epochs):
+
+    for x, y in train_dataloader:
+
+        # Get some data and prepare the corrupted version
+        x = x.to(device) # Data on the GPU
+        noise_amount = torch.rand(x.shape[0]).to(device) # Pick random noise amounts
+        noisy_x = corrupt(x, noise_amount) # Create our noisy x
+
+        # Get the model prediction
+        pred = net(noisy_x)
+
+        # Calculate the loss
+        loss = loss_fn(pred, x) # How close is the output to the true 'clean' x?
+
+        # Backprop and update the params:
+        opt.zero_grad()
+        loss.backward()
+        opt.step()
+
+        # Store the loss for later
+        losses.append(loss.item())
+
+    # Print our the average of the loss values for this epoch:
+    avg_loss = sum(losses[-len(train_dataloader):])/len(train_dataloader)
+    print(f'Finished epoch {epoch}. Average loss for this epoch: {avg_loss:05f}')
+
+# View the loss curve
+plt.plot(losses)
+plt.ylim(0, 0.1);
+```
+
+    Finished epoch 0. Average loss for this epoch: 0.026736
+    Finished epoch 1. Average loss for this epoch: 0.020692
+    Finished epoch 2. Average loss for this epoch: 0.018887
+
+
+
+    
+![png](02_diffusion_models_from_scratch_CN_files/02_diffusion_models_from_scratch_CN_24_1.png)
+    
+
+
+我们可以尝试通过抓取一批数据，拿不同程度的损坏数据，喂进模型获得预测来观察结果：
+
+
+```python
+#@markdown Visualizing model predictions on noisy inputs:
+
+# Fetch some data
+x, y = next(iter(train_dataloader))
+x = x[:8] # Only using the first 8 for easy plotting
+
+# Corrupt with a range of amounts
+amount = torch.linspace(0, 1, x.shape[0]) # Left to right -> more corruption
+noised_x = corrupt(x, amount)
+
+# Get the model predictions
+with torch.no_grad():
+  preds = net(noised_x.to(device)).detach().cpu()
+
+# Plot
+fig, axs = plt.subplots(3, 1, figsize=(12, 7))
+axs[0].set_title('Input data')
+axs[0].imshow(torchvision.utils.make_grid(x)[0].clip(0, 1), cmap='Greys')
+axs[1].set_title('Corrupted data')
+axs[1].imshow(torchvision.utils.make_grid(noised_x)[0].clip(0, 1), cmap='Greys')
+axs[2].set_title('Network Predictions')
+axs[2].imshow(torchvision.utils.make_grid(preds)[0].clip(0, 1), cmap='Greys');
+```
+
+
+    
+![png](02_diffusion_models_from_scratch_CN_files/02_diffusion_models_from_scratch_CN_26_0.png)
+    
+
+
+你可以看到，对于较低噪声量的输入，预测的结果相当不错！但是，当噪声量非常高时，模型能够获得的信息就开始逐渐减少。而当我们达到amount = 1时，模型会输出一个模糊的预测，该预测会很接近数据集的平均值。模型正是通过这样的方式来猜测原始输入。
+
+
+#### 3.5 扩散模型-采样（取样）过程
+#### 3.5.1 采样（取样）过程
+如果我们在高噪声量下的预测结果不是很好，又如何来解决呢？
+
+如果我们从完全随机的噪声开始，先检查一下模型预测的结果，然后只朝着预测方向移动一小部分，比如说20%。现在我们有一个夹杂很多噪声的图像，其中可能隐藏了一些输入数据结构的提示，我们来把它输入到模型中来获得新的预测。希望这个新的预测比上一步稍微好一点（因为我们这一次的输入稍微减少了一点噪声），所以我们可以再用这个新的，更好一点的预测往前再迈出一小步。
+
+如果一切顺利的话，以上过程重复几次以后我们就会得到一个全新的图像！以下图例是迭代了五次以后的结果，左侧是每个阶段的模型输入的可视化，右侧则是预测的去噪图像。要注意即使模型在第一步后就能输出一个去掉一些噪声的图像，但也只是向最终目标前进了一点点。如此重复几次后，图像的结构开始逐渐出现并得到改善,直到获得我们的最终结果为止。
+
+
+```python
+#@markdown Sampling strategy: Break the process into 5 steps and move 1/5'th of the way there each time:
+n_steps = 5
+x = torch.rand(8, 1, 28, 28).to(device) # Start from random
+step_history = [x.detach().cpu()]
+pred_output_history = []
+
+for i in range(n_steps):
+    with torch.no_grad(): # No need to track gradients during inference
+        pred = net(x) # Predict the denoised x0
+    pred_output_history.append(pred.detach().cpu()) # Store model output for plotting
+    mix_factor = 1/(n_steps - i) # How much we move towards the prediction
+    x = x*(1-mix_factor) + pred*mix_factor # Move part of the way there
+    step_history.append(x.detach().cpu()) # Store step for plotting
+
+fig, axs = plt.subplots(n_steps, 2, figsize=(9, 4), sharex=True)
+axs[0,0].set_title('x (model input)')
+axs[0,1].set_title('model prediction')
+for i in range(n_steps):
+    axs[i, 0].imshow(torchvision.utils.make_grid(step_history[i])[0].clip(0, 1), cmap='Greys')
+    axs[i, 1].imshow(torchvision.utils.make_grid(pred_output_history[i])[0].clip(0, 1), cmap='Greys')
+```
+
+
+    
+![png](02_diffusion_models_from_scratch_CN_files/02_diffusion_models_from_scratch_CN_29_0.png)
+    
+
+
+我们可以将流程分成更多步骤，并期望通过这种方式来获得质量更高的图像：
+
+
+```python
+#@markdown Showing more results, using 40 sampling steps
+n_steps = 40
+x = torch.rand(64, 1, 28, 28).to(device)
+for i in range(n_steps):
+  noise_amount = torch.ones((x.shape[0], )).to(device) * (1-(i/n_steps)) # Starting high going low
+  with torch.no_grad():
+    pred = net(x)
+  mix_factor = 1/(n_steps - i)
+  x = x*(1-mix_factor) + pred*mix_factor
+fig, ax = plt.subplots(1, 1, figsize=(12, 12))
+ax.imshow(torchvision.utils.make_grid(x.detach().cpu(), nrow=8)[0].clip(0, 1), cmap='Greys')
+```
+
+
+
+
+    <matplotlib.image.AxesImage at 0x7f27567d8210>
+
+
+
+
+    
+![png](02_diffusion_models_from_scratch_CN_files/02_diffusion_models_from_scratch_CN_31_1.png)
+    
+
+
+结果并不是非常好，但是已经有了几个可以被认出来的数字！您可以尝试训练更长时间（例如，10或20个epoch），并调整模型配置、学习率、优化器等。此外，如果您想尝试稍微困难一点的数据集，您可以尝试一下fashionMNIST，只需要调整一行代码来替换就可以了。
+
+
+#### 3.5.2 与DDPM的区别
+
+在本节中，我们将看看我们的“玩具”实现与其他笔记中使用的基于DDPM论文的方法有何不同（[扩散器简介](https://github.com/huggingface/diffusion-models-class/blob/main/unit1/01_introduction_to_diffusers.ipynb))。
+
+我们将会看到
+
+*   模型的表现受限于随迭代周期(timesteps)变化的控制条件，在前向传到中时间步(t)是作为一个参数被传入的
+*   有很多不同的取样策略可选择，可能会比我们上面所使用的最简单的版本更好
+*   diffusers`UNet2DModel`比我们的BasicUNet更先进
+*   损坏过程的处理方式不同
+*   训练目标不同，包括预测噪声而不是去噪图像
+*   该模型通过调节timestep来调节噪声水平, 其中t作为一个附加参数传入前向过程中。
+*   有许多不同的采样策略可供选择，它们应该比我们上面简单的版本更有效。
+
+自DDPM论文发表以来，已经有人提出了许多改进建议，但这个例子对于不同的设计决策具有指导意义。读完这篇文章后，你可能会想要深入了解这篇论文['Elucidating the Design Space of Diffusion-Based Generative Models'](https://arxiv.org/abs/2206.00364)它对所有这些组件进行了详细的探讨，并就如何获得最佳性能提出了些新的建议。
+
+如果你觉得这些内容对你来说过于深奥了，请不要担心！你大可先跳过本笔记的其余部分，或将其保存以需要时再来回顾。
+
+
+#### 3.5.3 UNet2DModel模型
+diffusers中的UNet2DModel模型比上述基本UNet模型有许多改进：
+
+*   GroupNorm层对每个blocks的输入进行了组标准化（group normalization）
+*   Dropout层能使训练更平滑
+*   每个块有多个resnet层（如果layers_per_block未设置为1）
+*   注意力机制（通常仅用于输入分辨率较低的blocks）
+*   timestep的调节。
+*   具有可学习参数的下采样和上采样块
+
+让我们来创建并仔细研究一下UNet2DModel：
+
+
+```python
+model = UNet2DModel(
+    sample_size=28,           # the target image resolution
+    in_channels=1,            # the number of input channels, 3 for RGB images
+    out_channels=1,           # the number of output channels
+    layers_per_block=2,       # how many ResNet layers to use per UNet block
+    block_out_channels=(32, 64, 64), # Roughly matching our basic unet example
+    down_block_types=( 
+        "DownBlock2D",        # a regular ResNet downsampling block
+        "AttnDownBlock2D",    # a ResNet downsampling block with spatial self-attention
+        "AttnDownBlock2D",
+    ), 
+    up_block_types=(
+        "AttnUpBlock2D", 
+        "AttnUpBlock2D",      # a ResNet upsampling block with spatial self-attention
+        "UpBlock2D",          # a regular ResNet upsampling block
+      ),
+)
+print(model)
+```
+
+    UNet2DModel(
+      (conv_in): Conv2d(1, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+      (time_proj): Timesteps()
+      (time_embedding): TimestepEmbedding(
+        (linear_1): Linear(in_features=32, out_features=128, bias=True)
+        (act): SiLU()
+        (linear_2): Linear(in_features=128, out_features=128, bias=True)
+      )
+      (down_blocks): ModuleList(
+        (0): DownBlock2D(
+          (resnets): ModuleList(
+            (0): ResnetBlock2D(
+              (norm1): GroupNorm(32, 32, eps=1e-05, affine=True)
+              (conv1): Conv2d(32, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=32, bias=True)
+              (norm2): GroupNorm(32, 32, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(32, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+            )
+            (1): ResnetBlock2D(
+              (norm1): GroupNorm(32, 32, eps=1e-05, affine=True)
+              (conv1): Conv2d(32, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=32, bias=True)
+              (norm2): GroupNorm(32, 32, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(32, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+            )
+          )
+          (downsamplers): ModuleList(
+            (0): Downsample2D(
+              (conv): Conv2d(32, 32, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1))
+            )
+          )
+        )
+        (1): AttnDownBlock2D(
+          (attentions): ModuleList(
+            (0): AttentionBlock(
+              (group_norm): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (query): Linear(in_features=64, out_features=64, bias=True)
+              (key): Linear(in_features=64, out_features=64, bias=True)
+              (value): Linear(in_features=64, out_features=64, bias=True)
+              (proj_attn): Linear(in_features=64, out_features=64, bias=True)
+            )
+            (1): AttentionBlock(
+              (group_norm): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (query): Linear(in_features=64, out_features=64, bias=True)
+              (key): Linear(in_features=64, out_features=64, bias=True)
+              (value): Linear(in_features=64, out_features=64, bias=True)
+              (proj_attn): Linear(in_features=64, out_features=64, bias=True)
+            )
+          )
+          (resnets): ModuleList(
+            (0): ResnetBlock2D(
+              (norm1): GroupNorm(32, 32, eps=1e-05, affine=True)
+              (conv1): Conv2d(32, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=64, bias=True)
+              (norm2): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+              (conv_shortcut): Conv2d(32, 64, kernel_size=(1, 1), stride=(1, 1))
+            )
+            (1): ResnetBlock2D(
+              (norm1): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (conv1): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=64, bias=True)
+              (norm2): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+            )
+          )
+          (downsamplers): ModuleList(
+            (0): Downsample2D(
+              (conv): Conv2d(64, 64, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1))
+            )
+          )
+        )
+        (2): AttnDownBlock2D(
+          (attentions): ModuleList(
+            (0): AttentionBlock(
+              (group_norm): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (query): Linear(in_features=64, out_features=64, bias=True)
+              (key): Linear(in_features=64, out_features=64, bias=True)
+              (value): Linear(in_features=64, out_features=64, bias=True)
+              (proj_attn): Linear(in_features=64, out_features=64, bias=True)
+            )
+            (1): AttentionBlock(
+              (group_norm): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (query): Linear(in_features=64, out_features=64, bias=True)
+              (key): Linear(in_features=64, out_features=64, bias=True)
+              (value): Linear(in_features=64, out_features=64, bias=True)
+              (proj_attn): Linear(in_features=64, out_features=64, bias=True)
+            )
+          )
+          (resnets): ModuleList(
+            (0): ResnetBlock2D(
+              (norm1): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (conv1): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=64, bias=True)
+              (norm2): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+            )
+            (1): ResnetBlock2D(
+              (norm1): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (conv1): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=64, bias=True)
+              (norm2): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+            )
+          )
+        )
+      )
+      (up_blocks): ModuleList(
+        (0): AttnUpBlock2D(
+          (attentions): ModuleList(
+            (0): AttentionBlock(
+              (group_norm): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (query): Linear(in_features=64, out_features=64, bias=True)
+              (key): Linear(in_features=64, out_features=64, bias=True)
+              (value): Linear(in_features=64, out_features=64, bias=True)
+              (proj_attn): Linear(in_features=64, out_features=64, bias=True)
+            )
+            (1): AttentionBlock(
+              (group_norm): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (query): Linear(in_features=64, out_features=64, bias=True)
+              (key): Linear(in_features=64, out_features=64, bias=True)
+              (value): Linear(in_features=64, out_features=64, bias=True)
+              (proj_attn): Linear(in_features=64, out_features=64, bias=True)
+            )
+            (2): AttentionBlock(
+              (group_norm): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (query): Linear(in_features=64, out_features=64, bias=True)
+              (key): Linear(in_features=64, out_features=64, bias=True)
+              (value): Linear(in_features=64, out_features=64, bias=True)
+              (proj_attn): Linear(in_features=64, out_features=64, bias=True)
+            )
+          )
+          (resnets): ModuleList(
+            (0): ResnetBlock2D(
+              (norm1): GroupNorm(32, 128, eps=1e-05, affine=True)
+              (conv1): Conv2d(128, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=64, bias=True)
+              (norm2): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+              (conv_shortcut): Conv2d(128, 64, kernel_size=(1, 1), stride=(1, 1))
+            )
+            (1): ResnetBlock2D(
+              (norm1): GroupNorm(32, 128, eps=1e-05, affine=True)
+              (conv1): Conv2d(128, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=64, bias=True)
+              (norm2): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+              (conv_shortcut): Conv2d(128, 64, kernel_size=(1, 1), stride=(1, 1))
+            )
+            (2): ResnetBlock2D(
+              (norm1): GroupNorm(32, 128, eps=1e-05, affine=True)
+              (conv1): Conv2d(128, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=64, bias=True)
+              (norm2): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+              (conv_shortcut): Conv2d(128, 64, kernel_size=(1, 1), stride=(1, 1))
+            )
+          )
+          (upsamplers): ModuleList(
+            (0): Upsample2D(
+              (conv): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+            )
+          )
+        )
+        (1): AttnUpBlock2D(
+          (attentions): ModuleList(
+            (0): AttentionBlock(
+              (group_norm): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (query): Linear(in_features=64, out_features=64, bias=True)
+              (key): Linear(in_features=64, out_features=64, bias=True)
+              (value): Linear(in_features=64, out_features=64, bias=True)
+              (proj_attn): Linear(in_features=64, out_features=64, bias=True)
+            )
+            (1): AttentionBlock(
+              (group_norm): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (query): Linear(in_features=64, out_features=64, bias=True)
+              (key): Linear(in_features=64, out_features=64, bias=True)
+              (value): Linear(in_features=64, out_features=64, bias=True)
+              (proj_attn): Linear(in_features=64, out_features=64, bias=True)
+            )
+            (2): AttentionBlock(
+              (group_norm): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (query): Linear(in_features=64, out_features=64, bias=True)
+              (key): Linear(in_features=64, out_features=64, bias=True)
+              (value): Linear(in_features=64, out_features=64, bias=True)
+              (proj_attn): Linear(in_features=64, out_features=64, bias=True)
+            )
+          )
+          (resnets): ModuleList(
+            (0): ResnetBlock2D(
+              (norm1): GroupNorm(32, 128, eps=1e-05, affine=True)
+              (conv1): Conv2d(128, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=64, bias=True)
+              (norm2): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+              (conv_shortcut): Conv2d(128, 64, kernel_size=(1, 1), stride=(1, 1))
+            )
+            (1): ResnetBlock2D(
+              (norm1): GroupNorm(32, 128, eps=1e-05, affine=True)
+              (conv1): Conv2d(128, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=64, bias=True)
+              (norm2): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+              (conv_shortcut): Conv2d(128, 64, kernel_size=(1, 1), stride=(1, 1))
+            )
+            (2): ResnetBlock2D(
+              (norm1): GroupNorm(32, 96, eps=1e-05, affine=True)
+              (conv1): Conv2d(96, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=64, bias=True)
+              (norm2): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+              (conv_shortcut): Conv2d(96, 64, kernel_size=(1, 1), stride=(1, 1))
+            )
+          )
+          (upsamplers): ModuleList(
+            (0): Upsample2D(
+              (conv): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+            )
+          )
+        )
+        (2): UpBlock2D(
+          (resnets): ModuleList(
+            (0): ResnetBlock2D(
+              (norm1): GroupNorm(32, 96, eps=1e-05, affine=True)
+              (conv1): Conv2d(96, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=32, bias=True)
+              (norm2): GroupNorm(32, 32, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(32, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+              (conv_shortcut): Conv2d(96, 32, kernel_size=(1, 1), stride=(1, 1))
+            )
+            (1): ResnetBlock2D(
+              (norm1): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (conv1): Conv2d(64, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=32, bias=True)
+              (norm2): GroupNorm(32, 32, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(32, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+              (conv_shortcut): Conv2d(64, 32, kernel_size=(1, 1), stride=(1, 1))
+            )
+            (2): ResnetBlock2D(
+              (norm1): GroupNorm(32, 64, eps=1e-05, affine=True)
+              (conv1): Conv2d(64, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (time_emb_proj): Linear(in_features=128, out_features=32, bias=True)
+              (norm2): GroupNorm(32, 32, eps=1e-05, affine=True)
+              (dropout): Dropout(p=0.0, inplace=False)
+              (conv2): Conv2d(32, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+              (nonlinearity): SiLU()
+              (conv_shortcut): Conv2d(64, 32, kernel_size=(1, 1), stride=(1, 1))
+            )
+          )
+        )
+      )
+      (mid_block): UNetMidBlock2D(
+        (attentions): ModuleList(
+          (0): AttentionBlock(
+            (group_norm): GroupNorm(32, 64, eps=1e-05, affine=True)
+            (query): Linear(in_features=64, out_features=64, bias=True)
+            (key): Linear(in_features=64, out_features=64, bias=True)
+            (value): Linear(in_features=64, out_features=64, bias=True)
+            (proj_attn): Linear(in_features=64, out_features=64, bias=True)
+          )
+        )
+        (resnets): ModuleList(
+          (0): ResnetBlock2D(
+            (norm1): GroupNorm(32, 64, eps=1e-05, affine=True)
+            (conv1): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+            (time_emb_proj): Linear(in_features=128, out_features=64, bias=True)
+            (norm2): GroupNorm(32, 64, eps=1e-05, affine=True)
+            (dropout): Dropout(p=0.0, inplace=False)
+            (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+            (nonlinearity): SiLU()
+          )
+          (1): ResnetBlock2D(
+            (norm1): GroupNorm(32, 64, eps=1e-05, affine=True)
+            (conv1): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+            (time_emb_proj): Linear(in_features=128, out_features=64, bias=True)
+            (norm2): GroupNorm(32, 64, eps=1e-05, affine=True)
+            (dropout): Dropout(p=0.0, inplace=False)
+            (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+            (nonlinearity): SiLU()
+          )
+        )
+      )
+      (conv_norm_out): GroupNorm(32, 32, eps=1e-05, affine=True)
+      (conv_act): SiLU()
+      (conv_out): Conv2d(32, 1, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
+    )
+
+
+正如你所看到的，而且！它比我们的BasicUNet有多得多的参数量：
+
+
+```python
+sum([p.numel() for p in model.parameters()]) # 1.7M vs the ~309k parameters of the BasicUNet
+```
+
+
+
+
+    1707009
+
+
+
+我们可以用这个模型来代替之前的模型重复一遍上面展示的训练过程。我们需要将x和timestep传递进去（这里我会传递t = 0，以表明它在没有timestep条件的情况下工作，并保持采样代码足够简单，但您也可以尝试输入 `(amount*1000)`，使timestep与噪声水平相当）。如果要检查代码，更改的行将显示为“`#<<<`。
+
+
+```python
+#@markdown Trying UNet2DModel instead of BasicUNet:
+
+# Dataloader (you can mess with batch size)
+batch_size = 128
+train_dataloader = DataLoader(dataset, batch_size=batch_size, shuffle=True)
+
+# How many runs through the data should we do?
+n_epochs = 3
+
+# Create the network
+net = UNet2DModel(
+    sample_size=28,  # the target image resolution
+    in_channels=1,  # the number of input channels, 3 for RGB images
+    out_channels=1,  # the number of output channels
+    layers_per_block=2,  # how many ResNet layers to use per UNet block
+    block_out_channels=(32, 64, 64),  # Roughly matching our basic unet example
+    down_block_types=( 
+        "DownBlock2D",  # a regular ResNet downsampling block
+        "AttnDownBlock2D",  # a ResNet downsampling block with spatial self-attention
+        "AttnDownBlock2D",
+    ), 
+    up_block_types=(
+        "AttnUpBlock2D", 
+        "AttnUpBlock2D",  # a ResNet upsampling block with spatial self-attention
+        "UpBlock2D",   # a regular ResNet upsampling block
+      ),
+) #<<<
+net.to(device)
+
+# Our loss finction
+loss_fn = nn.MSELoss()
+
+# The optimizer
+opt = torch.optim.Adam(net.parameters(), lr=1e-3) 
+
+# Keeping a record of the losses for later viewing
+losses = []
+
+# The training loop
+for epoch in range(n_epochs):
+
+    for x, y in train_dataloader:
+
+        # Get some data and prepare the corrupted version
+        x = x.to(device) # Data on the GPU
+        noise_amount = torch.rand(x.shape[0]).to(device) # Pick random noise amounts
+        noisy_x = corrupt(x, noise_amount) # Create our noisy x
+
+        # Get the model prediction
+        pred = net(noisy_x, 0).sample #<<< Using timestep 0 always, adding .sample
+
+        # Calculate the loss
+        loss = loss_fn(pred, x) # How close is the output to the true 'clean' x?
+
+        # Backprop and update the params:
+        opt.zero_grad()
+        loss.backward()
+        opt.step()
+
+        # Store the loss for later
+        losses.append(loss.item())
+
+    # Print our the average of the loss values for this epoch:
+    avg_loss = sum(losses[-len(train_dataloader):])/len(train_dataloader)
+    print(f'Finished epoch {epoch}. Average loss for this epoch: {avg_loss:05f}')
+
+# Plot losses and some samples
+fig, axs = plt.subplots(1, 2, figsize=(12, 5))
+
+# Losses
+axs[0].plot(losses)
+axs[0].set_ylim(0, 0.1)
+axs[0].set_title('Loss over time')
+
+# Samples
+n_steps = 40
+x = torch.rand(64, 1, 28, 28).to(device)
+for i in range(n_steps):
+  noise_amount = torch.ones((x.shape[0], )).to(device) * (1-(i/n_steps)) # Starting high going low
+  with torch.no_grad():
+    pred = net(x, 0).sample
+  mix_factor = 1/(n_steps - i)
+  x = x*(1-mix_factor) + pred*mix_factor
+
+axs[1].imshow(torchvision.utils.make_grid(x.detach().cpu(), nrow=8)[0].clip(0, 1), cmap='Greys')
+axs[1].set_title('Generated Samples');
+```
+
+    Finished epoch 0. Average loss for this epoch: 0.018925
+    Finished epoch 1. Average loss for this epoch: 0.012785
+    Finished epoch 2. Average loss for this epoch: 0.011694
+
+
+
+    
+![png](02_diffusion_models_from_scratch_CN_files/02_diffusion_models_from_scratch_CN_39_1.png)
+    
+
+
+这看起来比我们的��一组的结果好多了！您可以尝试调整UNet的配置或更使用长的时间训练，以获得更好的性能。
+
+
+#### 3.6 扩散模型-退化过程示例
+#### 3.6.1 退化过程
+DDPM论文描述了一个为每个“timestep”添加少量噪声的损坏过程。 为某些timestep给定 $x_{t-1}$ ,我们可以得到一个噪声稍稍增加的 $x_t$:<br><br>
+
+$q(\mathbf{x}_t \vert \mathbf{x}_{t-1}) = \mathcal{N}(\mathbf{x}_t; \sqrt{1 - \beta_t} \mathbf{x}_{t-1}, \beta_t\mathbf{I}) \quad
+q(\mathbf{x}_{1:T} \vert \mathbf{x}_0) = \prod^T_{t=1} q(\mathbf{x}_t \vert \mathbf{x}_{t-1})$<br><br>
+
+
+这就是说，我们取 $x_{t-1}$, 给他一个$\sqrt{1 - \beta_t}$ 的系数，然后加上带有 $\beta_t$系数的噪声。 这里 $\beta$ 是根据一些管理器来为每一个t设定的，来决定每一个迭代周期中添加多少噪声。 现在，我们不想把这个推演进行500次来得到 $x_{500}$，所以我们用另一个公式来根据给出的 $x_0$ 计算得到任意t时刻的 $x_t$: <br><br>
+
+$\begin{aligned}
+q(\mathbf{x}_t \vert \mathbf{x}_0) &= \mathcal{N}(\mathbf{x}_t; \sqrt{\bar{\alpha}_t} \mathbf{x}_0, \sqrt{(1 - \bar{\alpha}_t)} \mathbf{I})
+\end{aligned}$ where $\bar{\alpha}_t = \prod_{i=1}^T \alpha_i$ and $\alpha_i = 1-\beta_i$<br><br>
+
+数学符号看起来总是很吓人！幸运的是，调度器为我们处理了所有这些（取消下一个单元格的注释来试试代码）。我们可以画出 $\sqrt{\bar{\alpha}_t}$ (标记为 `sqrt_alpha_prod`) 和 $\sqrt{(1 - \bar{\alpha}_t)}$ (标记为 `sqrt_one_minus_alpha_prod`) 来看一下输入(x)与噪声是如何在不同迭代周期中量化和叠加的:
+
+
+
+```python
+#??noise_scheduler.add_noise
+```
+
+
+```python
+noise_scheduler = DDPMScheduler(num_train_timesteps=1000)
+plt.plot(noise_scheduler.alphas_cumprod.cpu() ** 0.5, label=r"${\sqrt{\bar{\alpha}_t}}$")
+plt.plot((1 - noise_scheduler.alphas_cumprod.cpu()) ** 0.5, label=r"$\sqrt{(1 - \bar{\alpha}_t)}$")
+plt.legend(fontsize="x-large");
+```
+
+
+    
+![png](02_diffusion_models_from_scratch_CN_files/02_diffusion_models_from_scratch_CN_43_0.png)
+    
+
+
+一开始, 噪声x里绝大部分都是x自身的值  (sqrt_alpha_prod ~= 1)，但是随着时间的推移，x的成分逐渐降低而噪声的成分逐渐增加。与我们根据`amount`对x和噪声进行线性混合不同，这个噪声的增加相对较快。我们可以在一些数据上看到这一点：
+
+
+```python
+#@markdown visualize the DDPM noising process for different timesteps:
+
+# Noise a batch of images to view the effect
+fig, axs = plt.subplots(3, 1, figsize=(16, 10))
+xb, yb = next(iter(train_dataloader))
+xb = xb.to(device)[:8]
+xb = xb * 2. - 1. # Map to (-1, 1)
+print('X shape', xb.shape)
+
+# Show clean inputs
+axs[0].imshow(torchvision.utils.make_grid(xb[:8])[0].detach().cpu(), cmap='Greys')
+axs[0].set_title('Clean X')
+
+# Add noise with scheduler
+timesteps = torch.linspace(0, 999, 8).long().to(device)
+noise = torch.randn_like(xb) # << NB: randn not rand
+noisy_xb = noise_scheduler.add_noise(xb, noise, timesteps)
+print('Noisy X shape', noisy_xb.shape)
+
+# Show noisy version (with and without clipping)
+axs[1].imshow(torchvision.utils.make_grid(noisy_xb[:8])[0].detach().cpu().clip(-1, 1),  cmap='Greys')
+axs[1].set_title('Noisy X (clipped to (-1, 1)')
+axs[2].imshow(torchvision.utils.make_grid(noisy_xb[:8])[0].detach().cpu(),  cmap='Greys')
+axs[2].set_title('Noisy X');
+```
+
+    X shape torch.Size([8, 1, 28, 28])
+    Noisy X shape torch.Size([8, 1, 28, 28])
+
+
+
+    
+![png](02_diffusion_models_from_scratch_CN_files/02_diffusion_models_from_scratch_CN_45_1.png)
+    
+
+
+在运行中的另一个变化：在DDPM版本中，加入的噪声是取自一个高斯分布（来自均值0方差1的torch.randn），而不是在我们原始 `corrupt`函数中使用的 0-1之间的均匀分布（torch.rand），当然对训练数据做正则化也可以理解。在另一篇笔记中，你会看到 `Normalize(0.5, 0.5)`函数在变化列表中，它把图片数据从(0, 1) 区间映射到 (-1, 1)，对我们的目标来说也‘足够用了’。我们在此篇笔记中没使用这个方法，但在上面的可视化中为了更好的展示添加了这种做法。
+
+
+#### 3.6.2 最终的训练目标
+在我们的玩具示例中，我们让模型尝试预测去噪图像。在DDPM和许多其他扩散模型实现中，模型则会预测损坏过程中使用的噪声（在缩放之前，因此是单位方差噪声）。在代码中，它看起来像使这样：
+
+```python
+noise = torch.randn_like(xb) # << NB: randn not rand
+noisy_x = noise_scheduler.add_noise(x, noise, timesteps)
+model_prediction = model(noisy_x, timesteps).sample
+loss = mse_loss(model_prediction, noise) # noise as the target
+```
+
+你可能认为预测噪声（我们可以从中得出去噪图像的样子）等同于直接预测去噪图像。那么，为什么要这么做呢？这仅仅是为了数学上的方便吗？
+
+这里其实还有另一些精妙之处。我们在训练过程中，会计算不同（��机选择）timestep的loss。这些不同的目标将导致这些loss的不同的“隐含权重”，其中预测噪声会将更多的权重放在较低的噪声水平上。你可以选择更复杂的目标来改变这种“隐性损失权重”。或者，您选择的噪声管理器将在较高的噪声水平下产生更多的示例。也许你让模型设计成预测“velocity”v，我们将其定义为由噪声水平影响的图像和噪声组合（请参阅“扩散模型快速采样的渐进蒸馏”- 'PROGRESSIVE DISTILLATION FOR FAST SAMPLING OF DIFFUSION MODELS'）。也许你将模型设计成预测噪声，然后基于某些因子来对loss进行缩放：比如有些理论指出可以参考噪声水平（参见“扩散模型的感知优先训练”-'Perception Prioritized Training of Diffusion Models'），或者基于一些探索模型最佳噪声水平的实验（参见“基于扩散的生成模型的设计空间说明”-'Elucidating the Design Space of Diffusion-Based Generative Models'）。
+
+一句话解释：选择目标对模型性能有影响，现在有许多研究者正在探索“最佳”选项是什么。
+目前，预测噪声（epsilon或eps）是最流行的方法，但随着时间的推移，我们很可能会看到库中支持的其他目标，并在不同的情况下使用。
+
+
+#### 3.7 拓展知识
+#### 3.7.1 迭代周期（Timestep）的调节
+
+UNet2DModel以x和timestep为输入。后者被转化为一个嵌入（embedding），并在多个地方被输入到模型中。
+
+这背后的理论支持是这样的：通过向模型提供有关噪声量的信息，它可以更好地执行任务。虽然在没有这种timestep条件的情况下也可以训练模型，但在某些情况下，它似乎确实有助于性能，目前来说绝大多数的模型实现都包括了这一输入。
+
+
+#### 3.7.2 采样（取样）的关键问题
+
+有一个模型可以用来预测在带噪样本中的噪声（或者说能预测其去噪版本），我们怎么用它来生成图像呢？
+
+我们可以给入纯噪声，然后就希望模型能一步就输出一个不带噪声的好图像。但是，就我们上面所见到的来看，这通常行不通。所以，我们在模型预测的基础上使用足够多的小步，迭代着来每次去除一点点噪声。
+
+具体我们怎么走这些小步，取决于使用上面取样方法。我们不会去深入讨论太多的理论细节，但是一些顶层想法是这样：
+- 每一步你想走多大？也就是说，你遵循什么样的“噪声计划（噪声管理）”？
+- 你只使用模型当前步的预测结果来指导下一步的更新方向吗（像DDPM，DDIM或是其他的什么那样）？你是否要使用模型来多预测几次来估计一个更高阶的梯度来更新一步更大更准确的结果（更高阶的方法和一些离散ODE处理器）？或者保留历史预测值来尝试更好的指导当前步的更新（线性多步或遗传取样器）？
+- 你是否会在取样过程中额外再加一些随机噪声，或你完全已知得（deterministic）来添加噪声？许多取样器通过参数（如DDIM中的'eta'）来供用户选择。
+
+对于扩散模型取样器的研究演进的很快，随之开发出了越来越多可以使用更少步就找到好结果的方法。勇敢和有好奇心的人可能会在浏览diffusers library中不同部署方法时感到非常有意思 [here](https://github.com/huggingface/diffusers/tree/main/src/diffusers/schedulers) 或看看 [docs](https://huggingface.co/docs/diffusers/api/schedulers) 这里经常有一些相关的paper.
+
+
+#### 3.8 本章小结
+
+希望这可以从一些不同的角度来审视扩散模型提供一些帮助。
+这篇笔记是Jonathan Whitaker为Hugging Face 课程所写的，同时也有 [version included in his own course](https://johnowhitaker.github.io/tglcourse/dm1.html),“风景的生成”- 'The Generative Landscape'。如果你对从噪声和约束分类来生成样本的例子感兴趣。问题与bug可以通过GitHub issues 或 Discord来交流。 也同时欢迎通过Twitter联系 [@johnowhitaker](https://twitter.com/johnowhitaker).
+
+
+
+### 第四章 Diffusers实战
+#### 4.1 章节概述
+![diffusers_library](https://github.com/huggingface/diffusers/raw/main/docs/source/imgs/diffusers_library.jpg)
+
+在这个 Notebook 中，我们将介绍如何训练你的第一个扩散模型来 **生成美丽的蝴蝶的图片 🦋**。在此过程中，你将了解 🤗 Diffuers 库的相关内容，这将为我们之后课程中介绍的更高级的应用打下坚实的基础 
+
+让我们开始吧！
+
+在这个 Notebook 中，你将能够:
+
+- 学习如何使用一个功能强大的自定义扩散模型管线（Pipeline），并了解如何制作一个自己的版本
+- 通过以下方式创建你自己的迷你管线:
+  - 复习扩散模型的核心概念 
+  - 从 Hub 中加载数据以进行训练
+  - 探索如何使用 scheduler 将噪声添加到你的数据中 
+  - 创建并训练一个 UNet 模型 
+  - 将各个模块组���在一起来形成一个工作管线 (working pipelines)
+- 编辑并运行一段代码，用于初始化一个较长的训练，该代码将处理以下过程： 
+  - 使用 Accelerate 库来调用多个 GPU 以加速模型的训练过程 
+  - 记录并查阅实验日志以跟踪关键统计数据 
+  - 将最终的模型上传到 Hugging Face Hub
+
+
+#### 4.2 环境准备
+#### 4.2.1 安装Diffusers库
+运行以下代码来安装包括 diffusers 在内的第三方库：
+
+
+```python
+%pip install -qq -U diffusers datasets transformers accelerate ftfy pyarrow
+```
+
+然后请前往 https://huggingface.co/settings/tokens 创建具有写权限的访问令牌：
+
+![Screenshot from 2022-11-10 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)
+
+你可以使用命令行来通过此令牌进行登录 (`huggingface-cli login`) ，也可以通过运行以下单元来登录：
+
+
+```python
+from huggingface_hub import notebook_login
+
+notebook_login()
+```
+
+    Login successful
+    Your token has been saved to /root/.huggingface/token
+
+
+接下来你需要安装 Git LFS 来上传模型检查点：
+
+
+```python
+%%capture
+!sudo apt -qq install git-lfs
+!git config --global credential.helper store
+```
+
+最后让我们导入将要使用的库，并定义一些简单的支持函数，稍后我们将会在 Notebook 中使用这些函数：
+
+
+```python
+import numpy as np
+import torch
+import torch.nn.functional as F
+from matplotlib import pyplot as plt
+from PIL import Image
+
+
+def show_images(x):
+    """Given a batch of images x, make a grid and convert to PIL"""
+    x = x * 0.5 + 0.5  # Map from (-1, 1) back to (0, 1)
+    grid = torchvision.utils.make_grid(x)
+    grid_im = grid.detach().cpu().permute(1, 2, 0).clip(0, 1) * 255
+    grid_im = Image.fromarray(np.array(grid_im).astype(np.uint8))
+    return grid_im
+
+
+def make_grid(images, size=64):
+    """Given a list of PIL images, stack them together into a line for easy viewing"""
+    output_im = Image.new("RGB", (size * len(images), size))
+    for i, im in enumerate(images):
+        output_im.paste(im.resize((size, size)), (i * size, 0))
+    return output_im
+
+
+# Mac users may need device = 'mps' (untested)
+device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
+```
+
+好了，万��俱备，只欠东风！
+
+#### 4.2.2 Dreambooth-全新的扩散模型
+在过去的几个月中，如果你关注过人工智能相关的社交媒体，你就会听说过 Stable Diffusion 模型。这是一个功能强大的文图生成模型，但它有一个缺点：除非我们足够出名以至于互联网上经常出现我们的照片，它无法知道你或我长什么样
+
+Dreambooth 方法允许我们自己微调 Stable Diffusion 模型，引入对特定的面部、对象或样式的额外知识。Corridor Crew 制作了一段出色的视频，说明如何用一致的人物形象来讲故事，很好的说明了这种技术的能力：
+
+
+```python
+from IPython.display import YouTubeVideo
+
+YouTubeVideo("W4Mcuh38wyM")
+```
+
+
+
+
+
+<iframe
+width="400"
+height="300"
+src="https://www.youtube.com/embed/W4Mcuh38wyM"
+frameborder="0"
+allowfullscreen
+
+></iframe>
+
+
+
+
+这是一个使用了 [这个模型](https://huggingface.co/sd-dreambooth-library/mr-potato-head) 的例子。该模型的训练仅仅使用了 5 张著名的儿童玩具 "Mr Potato Head"的照片。
+
+首先让我们来加载这个管道。这些代码会自动从 Hub 下载模型权重等需要的文件。这个 demo 需要下载数 GB 的数据，所以如果你不想等待也可以跳过此单元格，只需欣赏样例输出即可！
+
+
+```python
+from diffusers import StableDiffusionPipeline
+
+# Check out https://huggingface.co/sd-dreambooth-library for loads of models from the community
+model_id = "sd-dreambooth-library/mr-potato-head"
+
+# Load the pipeline
+pipe = StableDiffusionPipeline.from_pretrained(model_id, torch_dtype=torch.float16).to(
+    device
+)
+```
+
+
+    Fetching 15 files:   0%|          | 0/15 [00:00<?, ?it/s]
+
+
+管道加载完成后，我们可以使用以下代码生成图像：
+
+
+```python
+prompt = "an abstract oil painting of sks mr potato head by picasso"
+image = pipe(prompt, num_inference_steps=50, guidance_scale=7.5).images[0]
+image
+```
+
+
+    0%|          | 0/51 [00:00<?, ?it/s]
+
+
+
+
+
+    
+![png](01_introduction_to_diffusers_CN_files/01_introduction_to_diffusers_CN_22_1.png)
+    
+
+
+
+**练习:** 你可以使用不同的提示 (prompt) 自行进行尝试。在这个 demo 中，`sks`是一个新概念的唯一标识符 (UID) - 那么如果把它留空的话会发生什么事呢？你还可以尝试改变`num_inference_steps`和`guidance_scale`。这两个参数分别代表了采样步骤的数量（试试最多可以设为多低？）和模型的输出与提示的匹配程度。
+
+有许多复杂而又神奇的事情发生在这条管线之中！在我们的课程结束之后，你就会清晰的了解这一切是如何运作的。现在，让我们先看看如何从头开始训练扩散模型。
+
+
+#### 4.2.3 Diffusers核心API
+🤗 Diffusers 的核心 API 被分为三个主要部分:
+1. **管线**: 从高层出发设计的多种类函数，旨在以易部署的方式，能够做到快速通过主流预训练好的扩散模型来生成样本。
+2. **模型**: 训练新的扩散模型时用到的主流网络架构，*e.g.* [UNet](https://arxiv.org/abs/1505.04597).
+3. **管理器 (or 调度器)**: 在 *推理* 中使用多种不同的技巧来从噪声中生成图像，同时也可以生成在 *训练* 中所需的带噪图像。
+
+管线对于终端使用者来说已经非常棒，但你既然已经参加了这门课程，我们就假定你想了解更多其中的机制！在此篇笔记结束之后，我们会来构建属于你自己的、能够生成小蝴蝶图片的管线。下面这里会是最终的结果：
+
+
+```python
+from diffusers import DDPMPipeline
+
+# Load the butterfly pipeline
+butterfly_pipeline = DDPMPipeline.from_pretrained(
+    "johnowhitaker/ddpm-butterflies-32px"
+).to(device)
+
+# Create 8 images
+images = butterfly_pipeline(batch_size=8).images
+
+# View the result
+make_grid(images)
+```
+
+
+    Fetching 4 files:   0%|          | 0/4 [00:00<?, ?it/s]
+
+
+
+    0%|          | 0/1000 [00:00<?, ?it/s]
+
+
+
+
+
+    
+![png](01_introduction_to_diffusers_CN_files/01_introduction_to_diffusers_CN_26_2.png)
+    
+
+
+
+也许这里看起来还不如 DreamBooth 所展示的样例那样惊艳，但要知道我们在训练这些图画时只用了不到训练稳定扩散模型用到数据的 0.0001%。
+
+到目前为止，训练一个扩散模型的流程看起来像是这样：
+
+1.   从训练集中加载一些图像 
+2.   加入各种不同级别的噪声 
+3.   将已经被引入了不同级别噪声的数据输入模型中 
+4.   评估模型在对这些数据做增强去噪时的表现 
+5.   使用这个信息来更新模型权重，然后重复此步骤 
+
+我们会在接下来几节中逐一实现这些步骤，直至训练循环可以完整的运行，在这之后我们会来探索如何使用训练好的模型来生成样本，还有如何封装模型到管道中，从而可以轻松的分享给别人。下面让我我们先从从数据开始入手吧。
+
+
+#### 4.3 实战：生成美丽的蝴蝶图片
+#### 4.3.1 下载蝴蝶图像集
+在这个例子中，我们会用到一个来自 Hugging Face Hub 的图像集。具体来说，[是个 1000 张蝴蝶图像收藏集](https://huggingface.co/datasets/huggan/smithsonian_butterflies_subset). 请注意，这是个非常小的数据集。我们在下面的单元格中中注释掉的几行指向了一些规模更大的数据集。你也可以使用这里被注释掉的示例代码，从一个指定的路径来装载图片，从而使用你自己收藏的图像数据。
+
+
+```python
+import torchvision
+from datasets import load_dataset
+from torchvision import transforms
+
+dataset = load_dataset("huggan/smithsonian_butterflies_subset", split="train")
+
+# Or load images from a local folder
+# dataset = load_dataset("imagefolder", data_dir="path/to/folder")
+
+# We'll train on 32-pixel square images, but you can try larger sizes too
+image_size = 32
+# You can lower your batch size if you're running out of GPU memory
+batch_size = 64
+
+# Define data augmentations
+preprocess = transforms.Compose(
+    [
+        transforms.Resize((image_size, image_size)),  # Resize
+        transforms.RandomHorizontalFlip(),  # Randomly flip (data augmentation)
+        transforms.ToTensor(),  # Convert to tensor (0, 1)
+        transforms.Normalize([0.5], [0.5]),  # Map to (-1, 1)
+    ]
+)
+
+
+def transform(examples):
+    images = [preprocess(image.convert("RGB")) for image in examples["image"]]
+    return {"images": images}
+
+
+dataset.set_transform(transform)
+
+# Create a dataloader from the dataset to serve up the transformed images in batches
+train_dataloader = torch.utils.data.DataLoader(
+    dataset, batch_size=batch_size, shuffle=True
+)
+```
+
+我们可以从中取出一批图像数据来做一下可视化:
+
+
+```python
+xb = next(iter(train_dataloader))["images"].to(device)[:8]
+print("X shape:", xb.shape)
+show_images(xb).resize((8 * 64, 64), resample=Image.NEAREST)
+```
+
+    X shape: torch.Size ([8, 3, 32, 32])
+
+
+    /tmp/ipykernel_4278/3975082613.py:3: DeprecationWarning: NEAREST is deprecated and will be removed in Pillow 10 (2023-07-01). Use Resampling.NEAREST or Dither.NONE instead.
+    show_images (xb).resize ((8 * 64, 64), resample=Image.NEAREST)
+
+
+
+
+
+    
+![png](01_introduction_to_diffusers_CN_files/01_introduction_to_diffusers_CN_31_2.png)
+    
+
+
+在这篇笔记中，我们使用的是一个图像尺寸为 32 像素的小数据集，从而保证训练时长在可接受的范围内。
+
+
+#### 4.3.2 扩散模型-调度器
+
+我们计划取出这些输入图片然后对它们增添噪声，然后把带噪的图像送入模型。在推理阶段，我们将用模型的预测结果来不断迭代的去除这些噪声。在`diffusers`中，这两个步骤都是由 **调度器（scheduler）** 来处理的。
+
+噪声管理器决定在不同的迭代周期时分别加入多少噪声。下面是我们如何使用 'DDPM' 训练和采样的默认设置创建调度程序。 (基于此篇论文 ["Denoising Diffusion Probabalistic Models"](https://arxiv.org/abs/2006.11239):
+
+
+```python
+from diffusers import DDPMScheduler
+
+noise_scheduler = DDPMScheduler(num_train_timesteps=1000)
+```
+
+DDPM论文描述了一个为每个”时间步“添加少量噪音的退化过程。假设在某个迭代周期，带噪的图像数据为 $x_{t-1}$, 我们可以通过以下方式获得 $x_t$ （比之前更多一点点噪声）:<br><br>
+
+$q (\mathbf {x}_t \vert \mathbf {x}_{t-1}) = \mathcal {N}(\mathbf {x}_t; \sqrt {1 - \beta_t} \mathbf {x}_{t-1}, \beta_t\mathbf {I}) \quad
+q (\mathbf {x}_{1:T} \vert \mathbf {x}_0) = \prod^T_{t=1} q (\mathbf {x}_t \vert \mathbf {x}_{t-1})$<br><br>
+
+
+这就是说，我们取 $x_{t-1}$, 给他一个 $\sqrt {1 - \beta_t}$ 的系数，然后加上带有 $\beta_t$ 系数的噪声。 这里 $\beta$ 是根据一些管理器来为每一个 t 设定的，来决定每一个迭代周期中添加多少噪声。 现在，我们不想把这个推演进行 500 次来得到 $x_{500}$，所以我们用另一个公式来根据给出的 $x_0$ 计算得到任意 t 时刻的 $x_t$: <br><br>
+
+$\begin {aligned}
+q (\mathbf {x}_t \vert \mathbf {x}_0) &= \mathcal {N}(\mathbf {x}_t; \sqrt {\bar {\alpha}_t} \mathbf {x}_0, {(1 - \bar {\alpha}_t)} \mathbf {I})
+\end {aligned}$ where $\bar {\alpha}_t = \prod_{i=1}^T \alpha_i$ and $\alpha_i = 1-\beta_i$<br><br>
+
+这些数学过程看起来真是可怕！好在有调度器来为我们完成这些运算。我们可以画出 $\sqrt {\bar {\alpha}_t}$ (标记为`sqrt_alpha_prod`) 和 $\sqrt {(1 - \bar {\alpha}_t)}$ (标记为`sqrt_one_minus_alpha_prod`) 来看一下输入 (x) 与噪声是如何在不同迭代周期中量化和叠加的:
+
+
+```python
+plt.plot(noise_scheduler.alphas_cumprod.cpu() ** 0.5, label=r"${\sqrt{\bar{\alpha}_t}}$")
+plt.plot((1 - noise_scheduler.alphas_cumprod.cpu()) ** 0.5, label=r"$\sqrt{(1 - \bar{\alpha}_t)}$")
+plt.legend(fontsize="x-large");
+```
+
+**练习:** 你可以探索一下使用不同的 beta_start 时曲线是如何变化的，beta_end 与 beta_schedule 可以通过以下被注释掉的内容来修改:
+
+
+```python
+# One with too little noise added:
+# noise_scheduler = DDPMScheduler(num_train_timesteps=1000, beta_start=0.001, beta_end=0.004)
+# The 'cosine' schedule, which may be better for small image sizes:
+# noise_scheduler = DDPMScheduler(num_train_timesteps=1000, beta_schedule='squaredcos_cap_v2')
+```
+
+不论你选择了哪一个调度器，我们现在都可以使用 `noise_scheduler.add_noise` 功能来添加不同程度的噪声，就像这样：
+
+
+```python
+timesteps = torch.linspace(0, 999, 8).long().to(device)
+noise = torch.randn_like(xb)
+noisy_xb = noise_scheduler.add_noise(xb, noise, timesteps)
+print("Noisy X shape", noisy_xb.shape)
+show_images(noisy_xb).resize((8 * 64, 64), resample=Image.NEAREST)
+```
+
+    Noisy X shape torch.Size ([8, 3, 32, 32])
+
+
+
+
+
+    
+![png](01_introduction_to_diffusers_CN_files/01_introduction_to_diffusers_CN_40_1.png)
+    
+
+
+
+你可以在这里反复探索使用不同噪声调度器和预设参数带来的效果。 [这个视频](https://www.youtube.com/watch?v=fbLgFrlTnGU) 很好的解释了一些上述数学运算的细节，同时也是对此类概念的一个很好引入介绍。
+
+
+#### 4.3.3 定义扩散模型
+现在我们来到了本章节的核心部分：模型。 
+
+大多数扩散模型使用的模型结构都是一些 [U-net] 的变种 (https://arxiv.org/abs/1505.04597) 也是我们在这里会用到的结构。
+
+![](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/unet-model.png)
+
+简单来说，一个U-net模型大致会有以下三个特征:
+- 输入模型中的图片会经过几个由 ResNetLayer 构成的层，其中每层都使图片的尺寸减半。
+- 在这之后，同样数量的上采样层会将图片的尺寸恢复到原始规模。
+- 残差连接模块会将特征图分辨率相同的上采样层和下采样层连接起来。
+
+U-net模型一个关键特征是输出图片的尺寸与输入图片相同，而这正是我们在扩散模型中所需要的。
+
+Diffusers 为我们提供了一个易用的`UNet2DModel`类，用来在 PyTorch 中创建我们所需要的结构。
+
+我们来使用 U-net 为我们生成目标大小的图片吧。
+注意这里 `down_block_types` 对应下采样模块 (上图中绿色部分), 而 `up_block_types` 对应上采样模块 (上图中红色部分):
+
+
+```python
+from diffusers import UNet2DModel
+
+# Create a model
+model = UNet2DModel(
+    sample_size=image_size,  # the target image resolution
+    in_channels=3,  # the number of input channels, 3 for RGB images
+    out_channels=3,  # the number of output channels
+    layers_per_block=2,  # how many ResNet layers to use per UNet block
+    block_out_channels=(64, 128, 128, 256),  # More channels -> more parameters
+    down_block_types=(
+        "DownBlock2D",  # a regular ResNet downsampling block
+        "DownBlock2D",
+        "AttnDownBlock2D",  # a ResNet downsampling block with spatial self-attention
+        "AttnDownBlock2D",
+    ),
+    up_block_types=(
+        "AttnUpBlock2D",
+        "AttnUpBlock2D",  # a ResNet upsampling block with spatial self-attention
+        "UpBlock2D",
+        "UpBlock2D",  # a regular ResNet upsampling block
+    ),
+)
+model.to(device);
+```
+
+当我们在处理更高分辨率的图像时，你可能会想尝试使用更多的下、上采样模块，并只在分辨率最低的（最底）层处保留注意力模块，从而降低内存负担。我们会在这之后讨论如何通过实验来找到最适合数据场景的配置方法。
+
+我们可以通过输入一批数据和随机的迭代周期数来看看输出是否与输入尺寸相同：
+
+
+```python
+with torch.no_grad():
+    model_prediction = model(noisy_xb, timesteps).sample
+model_prediction.shape
+```
+
+
+
+
+    torch.Size ([8, 3, 32, 32])
+
+
+
+接下来让我们来看看如何训练这个模型。
+
+#### 4.3.4 创建扩散模型训练循环
+做完了准备工作以后，我们终于可以开始训练了！下面是PyTorch中的一个典型的迭代优化循环过程的步骤，我们在其中逐批（batch）的输入数据，并使用优化器一步步更新模型的参数 - 在这个样例中我们使用学习率为 0.0004 的 AdamW 优化器。 
+
+对于每一批的数据，我们会： 
+- 随机取样几个迭代周期 
+- 对数据进行相应的噪声处理 
+- 把带噪数据输入模型 
+- 使用 MSE 作为损失函数来比较目标结果与模型预测结果，在这个样例中，即是比较真实噪声和模型预测的噪声之间的差距。
+- 通过`loss.backward ()`与`optimizer.step ()`来更新模型参数 
+
+在这个过程中我们需要记录下每一步中的损失函数的值，用来后续绘制损失的曲线图。
+
+NB: 这段代码大概需要十分钟左右来运行 - 如果你想节省时间，你也可以跳过以下两块操作直接使用预训练好的模型。或者，您可以探索如何通过上面的模型定义来减少每一层中的通道数量，从而加快训练速度。
+
+官方的扩散器训练示例 [official diffusers training example](https://colab.research.google.com/github/huggingface/notebooks/blob/main/diffusers/training_example.ipynb) 以更高的分辨率在这个数据集上训练一个更大的模型，方便大家了解一个不那么小的训练过程是什么样子：
+
+
+```python
+# Set the noise scheduler
+noise_scheduler = DDPMScheduler(
+    num_train_timesteps=1000, beta_schedule="squaredcos_cap_v2"
+)
+
+# Training loop
+optimizer = torch.optim.AdamW(model.parameters(), lr=4e-4)
+
+losses = []
+
+for epoch in range(30):
+    for step, batch in enumerate(train_dataloader):
+        clean_images = batch["images"].to(device)
+        # Sample noise to add to the images
+        noise = torch.randn(clean_images.shape).to(clean_images.device)
+        bs = clean_images.shape[0]
+
+        # Sample a random timestep for each image
+        timesteps = torch.randint(
+            0, noise_scheduler.num_train_timesteps, (bs,), device=clean_images.device
+        ).long()
+
+        # Add noise to the clean images according to the noise magnitude at each timestep
+        noisy_images = noise_scheduler.add_noise(clean_images, noise, timesteps)
+
+        # Get the model prediction
+        noise_pred = model(noisy_images, timesteps, return_dict=False)[0]
+
+        # Calculate the loss
+        loss = F.mse_loss(noise_pred, noise)
+        loss.backward(loss)
+        losses.append(loss.item())
+
+        # Update the model parameters with the optimizer
+        optimizer.step()
+        optimizer.zero_grad()
+
+    if (epoch + 1) % 5 == 0:
+        loss_last_epoch = sum(losses[-len(train_dataloader) :]) / len(train_dataloader)
+        print(f"Epoch:{epoch+1}, loss: {loss_last_epoch}")
+```
+
+    Epoch:5, loss: 0.16273280512541533
+    Epoch:10, loss: 0.11161588924005628
+    Epoch:15, loss: 0.10206522420048714
+    Epoch:20, loss: 0.08302505919709802
+    Epoch:25, loss: 0.07805309211835265
+    Epoch:30, loss: 0.07474562455900013
+
+
+上面就是绘制出来的损失函数的曲线，我们能看到模型在一开始快速的收敛，接下来以一个较慢的速度持续优化（我们用右边 log 坐标轴的视图可以看的更清楚）：
+
+
+```python
+fig, axs = plt.subplots(1, 2, figsize=(12, 4))
+axs[0].plot(losses)
+axs[1].plot(np.log(losses))
+plt.show()
+```
+
+
+
+
+    [<matplotlib.lines.Line2D at 0x7f40fc40b7c0>]
+
+
+
+
+    
+![png](01_introduction_to_diffusers_CN_files/01_introduction_to_diffusers_CN_54_1.png)
+    
+
+
+作为运行上述训练代码的替代方案，你可以像这样使用管道中的模型:
+
+
+```python
+# Uncomment to instead load the model I trained earlier:
+# model = butterfly_pipeline.unet
+```
+
+#### 4.3.5 图像的生成
+接下来的问题是，我们怎么通过这个模型生成图像呢？
+
+##### 方法 1：建立一个管道：
+
+
+```python
+from diffusers import DDPMPipeline
+
+image_pipe = DDPMPipeline(unet=model, scheduler=noise_scheduler)
+```
+
+
+```python
+pipeline_output = image_pipe()
+pipeline_output.images[0]
+```
+
+
+    0%|          | 0/1000 [00:00<?, ?it/s]
+
+
+
+
+
+    
+![png](01_introduction_to_diffusers_CN_files/01_introduction_to_diffusers_CN_60_1.png)
+    
+
+
+
+我们可以像这样将管线保存到本地文件夹:
+
+
+```python
+image_pipe.save_pretrained("my_pipeline")
+```
+
+检查文件夹的内容：
+
+
+```python
+!ls my_pipeline/
+```
+
+    model_index.json  scheduler  unet
+
+
+这里`scheduler`与`unet`子文件夹中包含了生成图像所需的全部组件。比如，在`unet`文件中能看到模型参数 (`diffusion_pytorch_model.bin`) 与描述模型结构的配置文件。
+
+
+```python
+!ls my_pipeline/unet/
+```
+
+    config.json  diffusion_pytorch_model.bin
+
+
+这些文件包含了重新创建管线所需的所有内容。您可以手动将它们上传到 Hub 以与其他人共享管线，或者在下一节中通过 API 检查代码来完成此操作。
+
+##### 方法 2：写一个取样循环 
+如果你观察了管道中的 forward 方法，你可以看到在运行`image_pipe ()`时发生了什么：
+
+
+```python
+# ??image_pipe.forward
+```
+
+我们从完全随机的噪声图像开始，从最大噪声往最小噪声方向运行调度器，根据模型的预测每一步去除少量噪声:
+
+```python
+# Random starting point (8 random images):
+sample = torch.randn(8, 3, 32, 32).to(device)
+
+for i, t in enumerate(noise_scheduler.timesteps):
+
+    # Get model pred
+    with torch.no_grad():
+        residual = model(sample, t).sample
+
+    # Update sample with step
+    sample = noise_scheduler.step(residual, t, sample).prev_sample
+
+show_images(sample)
+
+```
+
+
+
+
+    
+![png](01_introduction_to_diffusers_CN_files/01_introduction_to_diffusers_CN_71_0.png)
+    
+
+
+
+`noise_scheduler.step ()` 执行更新”样本“所需的数学运算。事实上有很多种不同的采样方法 - 在下一单元中，我们将看到如何通过使用不同的采样器，来加速现有模型中的图像生成过程，并更多地讨论从扩散模型中采样背后的理论。
+
+
+#### 4.4 拓展知��
+#### 4.4.1 将模型上传到Hub上
+在上面的例子中，我们将管道保存到本地文件夹中。为了将模型推送到 Hub，我们需要将文件推送到模型存储库中。我们根据你的选择（模型 ID）来决定仓库的名字（您可以随意替换 model_name;它只需要包含您的用户名，而这就是函数get_full_repo_name()所做的）：
+
+
+```python
+from huggingface_hub import get_full_repo_name
+
+model_name = "sd-class-butterflies-32"
+hub_model_id = get_full_repo_name(model_name)
+hub_model_id
+```
+
+
+
+
+    'lewtun/sd-class-butterflies-32'
+
+
+
+接下来，在 🤗 Hub 上创建模型仓库并 push 它吧：
+
+
+```python
+from huggingface_hub import HfApi, create_repo
+
+create_repo(hub_model_id)
+api = HfApi()
+api.upload_folder(
+    folder_path="my_pipeline/scheduler", path_in_repo="", repo_id=hub_model_id
+)
+api.upload_folder(folder_path="my_pipeline/unet", path_in_repo="", repo_id=hub_model_id)
+api.upload_file(
+    path_or_fileobj="my_pipeline/model_index.json",
+    path_in_repo="model_index.json",
+    repo_id=hub_model_id,
+)
+```
+
+
+
+
+    'https://huggingface.co/lewtun/sd-class-butterflies-32/blob/main/model_index.json'
+
+
+
+最后一件事是创建一个超棒的模型卡，如此，我们的蝴蝶生成器就可以轻松的在 Hub 上被找到（请在描述中随意发挥！）：
+
+
+```python
+from huggingface_hub import ModelCard
+
+content = f"""
+---
+license: mit
+tags:
+- pytorch
+- diffusers
+- unconditional-image-generation
+- diffusion-models-class
+---
+
+# Model Card for Unit 1 of the [Diffusion Models Class 🧨](https://github.com/huggingface/diffusion-models-class)
+
+This model is a diffusion model for unconditional image generation of cute 🦋.
+
+## Usage
+
+```python
+from diffusers import DDPMPipeline
+
+pipeline = DDPMPipeline.from_pretrained('{hub_model_id}')
+image = pipeline().images[0]
+image
+```
+"""
+
+card = ModelCard(content)
+card.push_to_hub(hub_model_id)
+```
+
+现在模型已经在 Hub 上了，你可以这样从任何地方使用 `DDPMPipeline` 的 `from_pretrained ()` 方法来下载它：
+
+
+```python
+from diffusers import DDPMPipeline
+
+image_pipe = DDPMPipeline.from_pretrained(hub_model_id)
+pipeline_output = image_pipe()
+pipeline_output.images[0]
+```
+
+
+    Fetching 4 files:   0%|          | 0/4 [00:00<?, ?it/s]
+
+
+
+    0%|          | 0/1000 [00:00<?, ?it/s]
+
+
+
+
+
+    
+![png](01_introduction_to_diffusers_CN_files/01_introduction_to_diffusers_CN_80_2.png)
+    
+
+
+
+太棒了，我们成功了！
+
+#### 4.4.2 扩大训练模型的规模
+这个笔记本是为了学习而制作的，因此我尽量保持代码的简洁。正因如此，我们省略了一些能让你在更多数据上训练更大模型的内容，比如多gpu支持、进度记录和示例图像、支持更大批量的梯度检查点、自动上传模型等等。好在这些特性在示例训练代码中都有。 [here](https://github.com/huggingface/diffusers/raw/main/examples/unconditional_image_generation/train_unconditional.py).
+
+你可以这样下载该文件：
+
+
+```python
+!wget https://github.com/huggingface/diffusers/raw/main/examples/unconditional_image_generation/train_unconditional.py
+```
+
+打开文件，你就可以看到模型是怎么定义的，以及有哪些可选的配置参数。我使用如下命令运行了该代码：
+
+
+```python
+# Let's give our new model a name for the Hub
+model_name = "sd-class-butterflies-64"
+hub_model_id = get_full_repo_name(model_name)
+hub_model_id
+```
+
+
+
+
+    'lewtun/sd-class-butterflies-64'
+
+
+
+
+```python
+!accelerate launch train_unconditional.py \
+  --dataset_name="huggan/smithsonian_butterflies_subset" \
+  --resolution=64 \
+  --output_dir={model_name} \
+  --train_batch_size=32 \
+  --num_epochs=50 \
+  --gradient_accumulation_steps=1 \
+  --learning_rate=1e-4 \
+  --lr_warmup_steps=500 \
+  --mixed_precision="no"
+```
+
+如之前一样，把模型 push 到 hub，并且创建一个超酷的模型卡（请按你的想法随意填写！）：
+
+
+```python
+create_repo(hub_model_id)
+api = HfApi()
+api.upload_folder(
+    folder_path=f"{model_name}/scheduler", path_in_repo="", repo_id=hub_model_id
+)
+api.upload_folder(
+    folder_path=f"{model_name}/unet", path_in_repo="", repo_id=hub_model_id
+)
+api.upload_file(
+    path_or_fileobj=f"{model_name}/model_index.json",
+    path_in_repo="model_index.json",
+    repo_id=hub_model_id,
+)
+
+content = f"""
+---
+license: mit
+tags:
+- pytorch
+- diffusers
+- unconditional-image-generation
+- diffusion-models-class
+---
+
+# Model Card for Unit 1 of the [Diffusion Models Class 🧨](https://github.com/huggingface/diffusion-models-class)
+
+This model is a diffusion model for unconditional image generation of cute 🦋.
+
+## Usage
+
+```python
+from diffusers import DDPMPipeline
+
+pipeline = DDPMPipeline.from_pretrained('{hub_model_id}')
+image = pipeline().images[0]
+image
+```
+"""
+
+card = ModelCard(content)
+card.push_to_hub(hub_model_id)
+```
+
+
+
+
+    'https://huggingface.co/lewtun/sd-class-butterflies-64/blob/main/README.md'
+
+
+
+大概 45 分钟之后，我们将得到这样的结果：
+
+
+```python
+pipeline = DDPMPipeline.from_pretrained(hub_model_id).to(device)
+images = pipeline(batch_size=8).images
+make_grid(images)
+```
+
+
+    0%|          | 0/1000 [00:00<?, ?it/s]
+
+
+
+
+
+    
+![png](01_introduction_to_diffusers_CN_files/01_introduction_to_diffusers_CN_90_1.png)
+    
+
+
+
+**练习:** 看看你是否能在尽可能短的时间内找到优秀好用的训练/模型设置，并与社区分享你的发现。请尝试阅读一下这些脚本，看看你能不能读懂它们。如果遇到任何难以理解的地方，你可以通过向大家提问来寻求解答。
+
+
+#### 4.5 本章小结
+希望这些能够让你初步了解如何使用 🤗 Diffusers library ！这里有一些你接下来可以尝试的东西：
+
+- 尝试在新的数据集上训练一个无条件扩散模型 - 如果你能直接自己完成那就太好了 [create one yourself](https://huggingface.co/docs/datasets/image_dataset). 你可以在 Hub 这里找到一些能完成这个任务的超棒图像数据集 [HugGan organization](https://huggingface.co/huggan). 如果你不想等待模型训练太久的话，一定记得对图片做下采样！
+- 试试用 DreamBooth 来创建你自己定制的扩散模型管线，看看 [这个 Space](https://huggingface.co/spaces/multimodalart/dreambooth-training) 或者 [这个 notebook](https://colab.research.google.com/github/huggingface/notebooks/blob/main/diffusers/sd_dreambooth_training.ipynb)
+- 修改训练脚本来探索不同的 UNet 超参数（例如层数、深度或者通道数），不同的噪声管理器等等。
+- 来瞧瞧 [Diffusion Models from Scratch](https://github.com/huggingface/diffusion-models-class/blob/main/unit1/02_diffusion_models_from_scratch.ipynb) 在本单元的核心思想之上的一些不同看法。
+
+
+
+
+### 第五章 微调和引导
+#### 5.1 章节概述
+#### 5.2 环境准备
+#### 5.3 载入一个预训练过的管线
+#### 5.4 DDIM-更快的采样过程
+#### 5.5 扩散模型-微调
+#### 5.5.1 实战：微调
+#### 5.5.2 使用最小化样例脚本微调模型
+#### 5.5.3 保存和载入微调过的管线
+#### 5.6 扩散模型-引导
+#### 5.6.1 实战：引导
+#### 5.6.2 CLIP 引导
+#### 5.7 分享你的自定义采样训练
+#### 5.7.1 环境准备
+#### 5.7.2 创建一个以类别为条件的UNet
+#### 5.7.3 训练与采样
+#### 5.8 本章小结
+#### 5.9 实战：创建一个类别条件扩散模型
+
+### 第六章 Stable Diffusion
+#### 6.1 章节概述
+#### 6.2 环境准备
+#### 6.3 从文本生成图像
+#### 6.4 Stable Diffusion Pipeline
+#### 6.4.1 可变分自编码器(VAE)
+#### 6.4.2 分词器(Tokenizer)和文本编码器(Text Encoder)
+#### 6.4.3 UNet
+#### 6.4.4 调度器(Scheduler)
+#### 6.4.5 DIY一个采样循环
+#### 6.5 其他管线介绍
+#### 6.5.1 Img2Img
+#### 6.5.2 In-Painting
+#### 6.5.3 Depth2Image
+#### 6.5.4 拓展：管理你的模型缓存
+#### 6.6 本章小结
+
+### 第七章 DDIM反转 
+#### 7.1 本章概述
+#### 7.2 实战：反转
+#### 7.2.1 设置
+#### 7.2.2 加载一个已训练的管道 
+#### 7.2.3 DDIM采样 
+#### 7.2.4 反转
+#### 7.3 组合封装
+#### 7.4 本章小结
+
+### 第八章 音频扩散模型
+#### 8.1 本章概述
+#### 8.2 实战：音频扩散模型
+#### 8.2.1 设置与导入
+#### 8.2.2 从预先训练的音频管道采样 
+#### 8.2.3 从音频到频谱的转换 
+#### 8.2.4 微调管道
+#### 8.2.5 循环训练
+#### 8.3 将模型上传到Hub上 
+#### 8.4 本章小结
+
+### 第九章 ControlNet和LoRa
+#### 9.1 ControlNet
+#### 9.2 LoRa
+
+## 附录 精美图像集展示
\ No newline at end of file