Application of Computer Vision 20-Detailed explanation of the principles of image generation model (Stable Diffusion) and introduction to related projects

Hello everyone, I am Wei Xue AI. Today I will introduce to you the application of computer vision 20-image generation model: a detailed explanation of the principles of the Stable Diffusion model and an introduction to related projects. Do you know how these beautiful pictures of beautiful girls posted on various platforms are generated? In fact, their underlying principle is to use the Stable Diffusion model.
Stable Diffusion is a deep learning-based image generation method designed to generate high-quality, realistic images. This project utilizes the process of steady diffusion, a process of image generation by gradually blurring and sharpening the image. This method has a wide range of applications in the field of image generation, including artistic creation, virtual scene generation, data enhancement, etc.
Here are the cute girl pictures I generated based on some prompt words:

I. Introduction

In the field of deep learning, image generation has always been a popular research direction. It has been very popular in recent years, and most image generation functions mainly use the Stable Diffusion model. This article will introduce the depth principle of the Stable Diffusion model in detail, and demonstrate how to use PyTorch to build the model and generate images through actual combat.

2. Depth principle of Stable Diffusion model

2.1 Model Overview

Stable Diffusion model, a name that sounds extremely scientific and enigmatic. However, this complex process becomes vivid and visual if we compare it to cooking a dish.

Imagine you are preparing to make a delicious soup. You need a variety of ingredients: vegetables, meats, spices, and more. These raw ingredients are like our initial data distribution. All ingredients are served raw without any seasoning or processing before cooking begins.

Next, you start putting various ingredients into the pot and add water (this is like us adding Gaussian noise). Then you start to heat the pot slowly (that is, gradually change the time t), let the water temperature gradually increase (equivalent to the alpha coefficient gradually increasing), and let all the ingredients spread in the water. The original vegetables and meat are now completely dissolved in the soup - they have transformed from their original state into a new state.

However, there's a problem with this process: if we simply heat and diffuse, the soup we end up with might not be that tasty. Because each ingredient requires a specific time and temperature to cook to achieve the best taste - that is, each time step corresponds to a specific "noise". Similarly, in the Stable Diffusion model, we use the neural network q_\theta(epsilon|x, t) to learn to find the best "noise" corresponding to each time step.

Going back to the scene where we are making soup, you may find that certain spices need to be added later to better retain their aroma. At this time, you can take the pot off the heat (equivalent to stopping the diffusion process), add New spices (i.e. introducing new information) before continuing to heat. This is very similar to the Stable Diffusion model for back diffusion.

Backdiffusion is exactly what it sounds like: it is the reverse of the diffusion process. If we continue with the metaphor of cooking soup, backdiffusion is like separating the various original ingredients from a pot of mixed soup. But in practice, we do not We don't really need to completely isolate all the ingredients - we just need to find those key factors that will help us better understand and generate new soups.

This reverse diffusion process is implemented through a neural network. This neural network can be understood as our "chef". He knows how to adjust each ingredient according to the current "soup" status and time point to obtain the best results. Best taste.

Training the Stable Diffusion model is like training the chef to better understand how to make delicious soup based on original ingredients and cooking conditions. Through continuous experimentation (i.e., forward and backward propagation), the chef (i.e., the model) will gradually master how to cook a delicious soup with full color and aroma from a pot of seemingly ordinary water (i.e., Gaussian noise) (i.e., generate images).

The Stable Diffusion model is like a chef who is good at cooking and turning waste into treasure. He is able to transform seemingly unrelated, ordinary ingredients into mouth-watering, ever-changing dishes. Similarly, the Stable Diffusion model is able to generate expressive images with rich diversity and high-quality detailed features from simple and ubiquitous noise. Although this process may be full of challenges and difficulties, as long as we learn patiently and keep trying, we will always find the mysterious formula that can generate the ideal image "recipe" in our minds.

2.2 Diffusion and counter-diffusion processes

In Stable Diffusion, we first define a random variable x_t that obeys the conditional distribution p(x_t|x_{t-1}) at time t. This conditional distribution is defined as a Gaussian noise plus a linear interpolation of the original data x_{t-1}:

$$x_t=\sqrt{(}1-a_t)\ast x_{t-1}+\sqrt{(}{a}_t)\ast ϵ$$,

Naka $ϵN(0,I)$，$a_t$is a coefficient between 0 and 1.

Correspondingly, we can define the reverse diffusion process as:

$$x_{t-1}=(x_t-\sqrt{(}{a}_t)\ast ϵ)/\sqrt{(}1-a_t)$$.

2.3 Network structure and training objectives

In Stable Diffusion, we use a neural network $q_{\theta }(ϵ|x,$$x$ 和时间 $t$ , the output is the distribution of noise epsilon. The network structure usually chooses Transformer or CNN.

The training goal is to minimize the following loss function:

$$L(\theta )={AND}_{p(x_0)}[E_{p_T(x_T|x_0)}[KL(q_{\theta }(ϵ|x_T,T)||p(ϵ))]]$$,

$ KL $display $KL$ 散度，$p\left(x_0\right)$ is the distribution of real samples in the data set.

3. Code implementation and running results

Next we will show how to use PyTorch to implement Stable Diffusion and generate images.

# 导入必要的库
import torch
from torch import nn
import math
from torch.utils.data import DataLoader
from torchvision import datasets, transforms

# 定义数据预处理操作：转换为 Tensor 并归一化到 [0, 1]
transform = transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.5,), (0.5,))
])

# 加载 MNIST 数据集
train_dataset = datasets.MNIST(root='./data', train=True, download=True, transform=transform)

# 创建数据加载器
batch_size = 64  # 可以根据你的硬件条件调整批次大小
dataloader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)

# 定义模型参数
T = 1000  # 扩散步数
alpha = torch.linspace(0, 1, T + 1)  # alpha 系数

# 定义网络结构，这里简单地使用一个全连接网络作为示例
class Net(nn.Module):
    def __init__(self):
        super().__init__()
        self.fc1 = nn.Linear(784, 256)
        self.fc2 = nn.Linear(256, 784)

    def forward(self, x, t):
        x = x.view(x.size(0), -1)
        h = torch.relu(self.fc1(x))
        return self.fc2(h).view(x.size(0), 1, 28, 28)

# 初始化模型和优化器
net = Net()
optimizer = torch.optim.Adam(net.parameters())

# 定义扩散过程和逆扩散过程
def diffusion(x_t_minus_1, t):
    epsilon_t = torch.randn_like(x_t_minus_1)
    x_t = torch.sqrt(1 - alpha[t] + 1e-6) * x_t_minus_1 + torch.sqrt(alpha[t] + 1e-6) * epsilon_t
    return x_t

def reverse_diffusion(x_t, t):
    epsilon_hat_T = net(x_t.detach(), t)
    return (x_t - torch.sqrt(alpha[t] + 1e-6) * epsilon_hat_T) / torch.sqrt(1 - alpha[t] + 1e-6)


# 训练过程，假设 dataloader 是已经定义好的数据加载器
num_epochs =100
for epoch in range(num_epochs):
    for batch_idx, data in enumerate(dataloader):
        optimizer.zero_grad()
        # 执行扩散过程得到噪声数据x_T
        data_noise = diffusion(data[0],T)

        # 执行逆扩散过程进行恢复
        data_recover = reverse_diffusion(data_noise,T)
        #print(data_recover)

        loss_func = nn.MSELoss()

        loss = loss_func(data[0], data_recover)

        loss.backward()

        optimizer.step()

        if batch_idx % 100 == 0:
            print('Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                epoch, batch_idx * len(data), len(dataloader.dataset),
                       100. * batch_idx / len(dataloader), loss.item()))

The above introduces the basic framework of Stable Diffusion. Specifically, in actual applications, the network structure, loss function, etc. may need to be adjusted based on data characteristics.

The most detailed code of Stable Diffusion can be found at: "Deep Learning Practice 51-Detailed Explanation of Image Generation Principles and Project Practice Based on Stable Diffusion Model"

4. Summary

Stable Diffusion is a novel image generation method that generates new images by establishing a mapping relationship between original data and noise, and learning this mapping relationship. Although the theory and implementation of Stable Diffusion are relatively complex, its excellent generation effects make it worthy of further research and exploration. In the future, we look forward to seeing more applications based on Stable Diffusion emerge to achieve high-quality image generation in various scenarios.