# Diffusion models from scratch in PyTorch

TLDRThis tutorial offers a hands-on guide to implementing a denoising diffusion model in PyTorch. It explores generative deep learning, comparing models like GANs and VAEs, and introduces diffusion models that generate high-quality, diverse samples. The video explains the theoretical foundation and practical steps to build a simple diffusion model, using the Stanford Cars dataset, and discusses the model's architecture, training process, and potential. The results, though in early stages, demonstrate the model's capability to generate recognizable car images, highlighting diffusion models as a promising approach in generative modeling.

### Takeaways

- 🧠 The tutorial covers how to implement a denoising diffusion model in PyTorch, focusing on both theory and practical implementation.
- 🌟 Diffusion models are a new class of generative deep learning models that have shown success in generating high-quality and diverse samples.
- 📈 The video discusses the limitations of other generative models like VAEs and GANs, highlighting the comparative strengths of diffusion models.
- 🛠️ The tutorial includes a hands-on implementation of a simple diffusion model using the Stanford Cars dataset, with an emphasis on the forward and backward processes.
- 📚 The content is inspired by two key papers from Berkeley University and OpenAI, which introduced and improved diffusion models for image generation.
- 🔢 The script explains the importance of the variance schedule in the forward process, which controls the amount of noise added to the images step by step.
- 🎨 The tutorial demonstrates the use of a U-Net architecture for the backward process, which predicts the noise in an image to reconstruct the original data.
- 🔄 The concept of positional embeddings is introduced to encode the time step information, allowing the model to handle different noise levels across steps.
- 🔧 The training process involves optimizing the model with a loss function based on the L2 distance between predicted and actual noise.
- 🖼️ The script showcases the results of training the model, indicating that with sufficient training epochs, the model can generate recognizable images of cars.
- 🚀 The tutorial concludes by highlighting the potential of diffusion models in various domains beyond images, such as molecules, graphs, audio, and more.

### Q & A

### What is the main topic of the tutorial video?

-The main topic of the tutorial video is the implementation of a denoising diffusion model in PyTorch.

### Why are diffusion models considered a new approach in generative deep learning?

-Diffusion models are considered a new approach in generative deep learning because they have shown to produce high-quality and diverse samples, and they are part of many modern deep learning architectures, including text-guided image generation models like DALL-E 2 andImagen.

### What are some of the challenges associated with training GANs?

-Some of the challenges associated with training GANs include vanishing gradients, mode collapse, and the adversarial setup, which can make the training process difficult.

### How does a diffusion model work in the context of image generation?

-A diffusion model works by gradually adding noise to an input image until only noise is left, and then using a neural network to recover the original input from the noise in a reverse process.

### What is the role of a noise scheduler in a diffusion model?

-The noise scheduler in a diffusion model is responsible for sequentially adding noise to the input data according to a predefined variance schedule, which dictates how much noise is added at each time step.

### What is the purpose of the backward process in a diffusion model?

-The purpose of the backward process in a diffusion model is to predict the noise in an image and use that prediction to reconstruct the original image from the noisy data.

### What is the significance of the variance schedule in the forward process of a diffusion model?

-The variance schedule, often represented by a sequence of betas, determines the amount of noise added at each time step in the forward process, which is crucial for ensuring the model can effectively learn to reverse the noise addition.

### What is the U-Net architecture used for in the backward process of a diffusion model?

-The U-Net architecture is used in the backward process of a diffusion model to predict the noise in the image. It has a structure similar to an autoencoder, with a bottleneck in the middle, and is known for its effectiveness in image segmentation tasks.

### How are positional embeddings used in the diffusion model to encode time steps?

-Positional embeddings are used in the diffusion model to provide the neural network with information about the time step, allowing it to distinguish between different noise intensities across the sequence of steps.

### What is the loss function used to optimize diffusion models?

-The loss function used to optimize diffusion models is typically based on the L2 distance between the predicted noise and the actual noise in the image, which encourages the model to accurately predict the noise for denoising.

### What are some potential improvements or extensions to a basic diffusion model architecture?

-Potential improvements or extensions to a basic diffusion model architecture include adding group normalization, attention modules, or other advanced components to enhance the model's performance and ability to generate high-quality images.

### Outlines

### 🤖 Introduction to Denoising Diffusion Models in PyTorch

This paragraph introduces the tutorial on implementing denoising diffusion models in PyTorch. The speaker has observed a gap in hands-on content for these models, which led them to create a collaborative notebook showcasing a simple diffusion model. The video aims to elucidate both the theoretical underpinnings and practical implementation of these models within the realm of generative deep learning. Generative models like GANs and VAEs are briefly compared, with a focus on the diffusion model's ability to generate high-quality and diverse samples. The tutorial will be based on two foundational papers, one from Berkeley University and another from OpenAI, which offer insights and improvements for image generation tasks.

### 🔍 Understanding Diffusion Models and Implementation Basics

The second paragraph delves into the specifics of diffusion models, explaining the process of gradually adding noise to an input and then recovering it, which is akin to a Markov chain of stochastic events. The importance of the variance schedule, beta, in controlling the noise level is highlighted. The paragraph also touches on the direct calculation of the noisy image at any time step without sequential iteration, thanks to the properties of Gaussian distributions. The concept of alpha, which represents the retention of original image information, is introduced, along with the practical aspects of training, including the use of the Stanford Cars dataset and the preparation of data for the diffusion process.

### 🖼️ Forward Process and Noise Scheduling in Diffusion Models

This section discusses the forward process of diffusion models, detailing how noise is added to images. It describes the conditional Gaussian distribution used for sampling noise and the role of the variance schedule in this process. The paragraph provides an intuitive explanation of how the noise level affects individual pixels and the overall image. It also explains the strategy for adding noise linearly and the alternative approaches found in literature, such as quadratic or sigmoidal schedules. The forward diffusion sample function is introduced, which calculates the noisy version of an image for a given time step, and the process of preparing the dataset for training is outlined.

### 🛠️ Building the Neural Network Model for Backward Process

The fourth paragraph focuses on constructing the neural network model for the backward process, which involves using a U-Net architecture known for its encoder-decoder structure with skip connections. The U-Net is ideal for the diffusion model due to its ability to maintain the input and output dimensions. The paragraph explains the model's task of predicting the noise in an image, referred to as denoising score matching, and the importance of incorporating the time step information into the model. Positional embeddings, inspired by the transformer model, are introduced as a method to encode the time step information for the model.

### 🔧 Implementing the Backward Process and Positional Embeddings

This paragraph provides a practical guide to implementing the backward process, including the creation and application of positional embeddings. It describes the calculation of these embeddings using sine and cosine functions and their integration into the model alongside the noisy image. The paragraph also outlines the structure of the U-Net, detailing the convolutional layers, downsampling, and upsampling processes, along with the use of residual connections. The code snippets provided offer a glimpse into the practical aspects of building the model, emphasizing simplicity and understandability.

### 📉 Loss Function and Sampling Process in Diffusion Models

The sixth paragraph discusses the loss function used for optimizing diffusion models, which is based on the variational lower bound similar to that used in variational autoencoders. It explains an alternative formulation related to denoising score matching and the straightforward nature of the L2 loss function that measures the difference between predicted and actual noise. The paragraph also covers the sampling process, which involves iteratively subtracting the predicted noise from the image to generate less noisy versions. The importance of pre-calculated noise levels for this process is highlighted, along with the practical implementation of sampling during training.

### 🚀 Training the Model and Exploring Variants of Diffusion Models

The final paragraph wraps up the tutorial by discussing the training process, which involves iterating over the data points and optimizing the model based on the defined loss function. It mentions the initial disappointment with the results and the subsequent improvement after extended training on a personal GPU. The speaker expresses optimism about the potential of diffusion models and their applications beyond image data, such as in molecules, graphs, audio, and more. They also mention interesting variants like diffusion GANs and conclude by looking forward to the future developments in this field.

### Mindmap

### Keywords

### 💡Denoising Diffusion Model

### 💡Generative Deep Learning

### 💡Generative Adversarial Networks (GANs)

### 💡Variational Autoencoders (VAEs)

### 💡Markov Chain

### 💡Latent Space

### 💡U-Net

### 💡Residual Connections

### 💡Positional Embeddings

### 💡Variational Lower Bound

### Highlights

Introduction to implementing a denoising diffusion model in PyTorch.

Denoising diffusion models are a new approach in generative deep learning.

Comparison of VAEs, GANs, and diffusion models in terms of sample diversity and quality.

Diffusion models have shown success in text-guided image generation.

The process of diffusion models involves destroying input with noise and recovering it.

Diffusion models are part of modern deep learning architectures.

The downside of diffusion models includes slower sampling speed due to the sequential reverse process.

Building a simple diffusion model to fit on an image dataset.

The importance of the variance schedule in the forward process of diffusion models.

How to start implementing a diffusion model with a scheduler, model, and time step encoding.

Using the Stanford Cars dataset for training the diffusion model.

The role of the U-Net architecture in the backward process of diffusion models.

Positional embeddings are used to encode time step information in the model.

The implementation of the backward process using a simplified U-Net.

The loss function for optimizing diffusion models is based on the L2 distance between predicted and actual noise.

Sampling new images from the diffusion model during training.

Early results from training the diffusion model on theCars dataset.

Potential for diffusion models to generate high-quality images with further training and refinement.

Diffusion models are not limited to image data and have applications in other domains.

The future potential and excitement surrounding the development of diffusion models.