# Diffusion models from scratch in PyTorch

TLDRThis tutorial video dives into the implementation of denoising diffusion models in PyTorch, a topic that has seen success in generative deep learning. The video provides both theoretical background and practical steps to build a simple diffusion model, with a focus on image data sets like Stanford Cars. It covers the forward process of adding noise to images, the backward process of recovering the original image from noise using a neural network, and the importance of the variance schedule in controlling the noise level. The U-Net architecture is introduced for the model, and the video explains how to encode the time step using positional embeddings. The loss function is derived from the variational lower bound, and the training process is demonstrated, showing initial disappointment with results that improved significantly with extended training. The video concludes by highlighting the potential of diffusion models in various domains beyond image data and the promising future of this generative model family.

### Takeaways

- 🎓 **Generative Deep Learning**: The tutorial focuses on diffusion models, a part of generative deep learning, which aim to learn a distribution over data to generate new data points.
- 🤖 **Model Comparison**: Generative Adversarial Networks (GANs) are known for high-quality outputs but can be difficult to train, while Variational Autoencoders (VAEs) are easier to train but may produce blurry outputs.
- 📈 **Diffusion Models**: These newer models have shown success in generating high-quality and diverse samples, with applications in text-guided image generation and modern deep learning architectures.
- 🔍 **Sequential Process**: Diffusion models work by gradually adding noise to an input (forward process) and then recovering the input from the noise (backward process), which is a Markov chain of stochastic events.
- 🔢 **Variance Scheduling**: A sequence of betas determines the amount of noise added at each time step, with the goal of reaching an isotropic Gaussian distribution with a mean of zero.
- 🛠️ **Model Components**: To implement a diffusion model, you need a noise scheduler, a neural network to predict noise, and a method to encode the current time step.
- 🖼️ **Dataset**: The Stanford Cars dataset, consisting of 16,000 images, is used for training the generative model, providing a diverse set of car images.
- 👀 **U-Net Architecture**: A U-Net structure is used for the neural network in the backward process, which is similar to an autoencoder and is popular for image segmentation tasks.
- ⏱️ **Time Step Consideration**: Positional embeddings are used to encode the discrete time step information, allowing the model to filter out noise from images with varying noise intensities.
- 🔧 **Model Simplification**: The tutorial aims to build a simple and understandable model rather than the latest state-of-the-art architecture, focusing on core components like down and upsampling and residual connections.
- 📉 **Loss Function**: The diffusion models are optimized using a loss function that calculates the L2 distance between the predicted noise and the actual noise in the image, aiming for denoising score matching.

### Q & A

### What is the main focus of the tutorial?

-The tutorial focuses on implementing a denoising diffusion model in PyTorch, covering both the theoretical aspects and practical implementation.

### What is generative deep learning?

-Generative deep learning is a domain of machine learning where the goal is to learn a distribution over the data in order to generate new, synthetic data points that are similar to the original data.

### How do diffusion models differ from other generative models like GANs and VAEs?

-Diffusion models have shown to produce high-quality samples that are also quite diverse. Unlike GANs, which can be difficult to train, and VAEs, which can produce blurry outputs, diffusion models offer a balance between quality and diversity.

### What are the downsides of diffusion models?

-One of the main downsides of diffusion models is their sampling speed. Due to the sequential reverse process, they are much slower compared to GANs or VAEs.

### What is the role of the neural network in the diffusion model?

-The neural network in a diffusion model is used to predict the noise in an image, which is then used to recover the input from the noise during the backward process.

### How does the forward process in a diffusion model work?

-The forward process involves gradually adding noise to the input image over a sequence of steps, creating a Markov chain of stochastic events, until only noise is left.

### What is a variance schedule in the context of diffusion models?

-A variance schedule is a sequence of beta values that determines how much noise is added to the image at each time step during the forward process.

### How does the U-Net architecture contribute to the diffusion model?

-The U-Net architecture, with its encoder-decoder structure and residual connections, is used in the backward process of the diffusion model to predict the noise in the image and help reconstruct the original image from the noisy version.

### What is the significance of the time step in the diffusion model?

-The time step is crucial as it represents the progression of the diffusion process. The model needs to consider the time step to correctly predict the noise at each stage of the backward process.

### How are positional embeddings used in the diffusion model?

-Positional embeddings are used to encode the discrete positional information, or time steps, in the diffusion model. They provide the model with a way to distinguish between different time steps during the backward process.

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

-The loss function used to optimize the diffusion model is based on the variational lower bound and is defined as the L2 distance between the predicted noise and the actual noise in the image.

### What are some potential improvements or extensions to the basic diffusion model presented in the tutorial?

-Potential improvements include adding group normalization, attention modules, or experimenting with different model architectures. The tutorial also suggests looking into more advanced implementations and research papers for further enhancements.

### Outlines

### 🎓 Introduction to Denoising Diffusion Models in PyTorch

The video begins with an introduction to denoising diffusion models, a type of generative deep learning model, and their place among other generative models like GANs and VAEs. The speaker discusses the advantages and limitations of these models, and introduces the concept of diffusion models which have shown success in generating high-quality and diverse data. The tutorial aims to provide both theoretical understanding and practical implementation details, referencing two key papers that form the basis of the model architecture.

### 🛠️ Setting Up the Diffusion Model Implementation

The second paragraph delves into the prerequisites for implementing a diffusion model, which include a noise scheduler, a neural network to predict noise, and a method to encode the current time step. The speaker then presents the Stanford Cars dataset from PyTorch, which will be used for training the model. The process of transforming the dataset into tensors and applying data augmentation is outlined, along with the forward diffusion process that adds noise to images in a controlled manner using a variance schedule.

### 🔢 Understanding the Mathematics of Diffusion Models

This paragraph focuses on the mathematical foundation of diffusion models, explaining the forward process and how noise is sampled from a conditional Gaussian distribution. The concept of a variance schedule and its role in controlling the noise level at each time step is discussed. The speaker also touches on the idea of alpha terms and how they can be used to calculate the noisy version of an image for any given time step without the need for sequential iteration.

### 🖼️ Preparing the Dataset and Converting Images for Training

The speaker details the process of preparing the dataset for training, including resizing images to a uniform size and converting them into tensors. Data augmentation techniques are applied, and the images are normalized to a range of -1 to 1 to align with the model's requirements. The paragraph also describes the creation of a function to reverse the process, converting tensor images back into a visual format for display purposes.

### 🤖 Neural Network Architecture for Backward Process

The paragraph introduces the U-Net architecture, a type of convolutional neural network used in the backward process of the diffusion model. The U-Net is chosen for its auto-encoder like structure and its use in image segmentation tasks. The speaker outlines the components of the U-Net, such as convolutional layers, downsampling, upsampling, residual connections, and discusses the use of positional embeddings to encode time step information into the model.

### 🏗️ Building the Backward Process and U-Net Implementation

The speaker provides a step-by-step guide to implementing the backward process and the U-Net architecture. The process involves increasing the depth of the tensor through convolutional layers, applying activation functions, and using batch normalization. Positional embeddings are calculated using sine and cosine functions and added to the noisy image input. The implementation details of the U-Net, including the use of residual connections and the structure of the blocks within the network, are explained.

### 📉 Defining the Loss Function and Sampling Process

The paragraph discusses the loss function used to optimize the diffusion model, which is based on the L2 distance between the predicted noise and the actual noise in the image. The speaker also explains the sampling process, which involves iteratively subtracting the predicted noise from the image to obtain less noisy versions. The training procedure is outlined, highlighting the need for memory management and the iterative optimization of the model using the data loader.

### 🚀 Training Results and Future Prospects of Diffusion Models

The speaker shares the results of training the diffusion model on the Stanford Cars dataset, noting initial disappointment with the results but eventual improvement over time. The limitations of the model's resolution are acknowledged, but the potential for higher quality images with further training and architectural refinements is emphasized. The video concludes with a positive outlook on the future of diffusion models and their applications in various domains beyond image data.

### Mindmap

### Keywords

### 💡Denoising Diffusion Model

### 💡Generative Adversarial Networks (GANs)

### 💡Variational Autoencoders (VAEs)

### 💡Markov Chain

### 💡U-Net

### 💡Positional Embeddings

### 💡Beta Schedule

### 💡Stanford Cars Dataset

### 💡Denoising Score Matching

### 💡Variational Lower Bound

### 💡Residual Connections

### Highlights

This tutorial introduces how to implement a denoising diffusion model in PyTorch.

Denoising diffusion models are part of generative deep learning, aiming to learn a distribution over data to generate new data.

Generative models like GANs and VAEs have trade-offs between sample diversity and quality.

Diffusion models have shown success in producing high-quality, diverse samples and are used in modern deep learning architectures.

Diffusion models work by gradually adding noise to an input and then recovering it, forming a Markov chain of stochastic events.

The tutorial provides a simple diffusion model implementation based on two foundational papers from Berkeley University and OpenAI.

The model architecture uses a U-Net structure, which is similar to auto-encoders and is popular for image segmentation.

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

The model predicts the noise in an image, which is called denoising score matching.

The tutorial demonstrates how to implement the forward and backward processes of the diffusion model.

The loss function is defined by the L2 distance between the predicted noise and the actual noise in the image.

The sampling process involves iteratively subtracting the predicted noise from the image to get less noisy images.

The tutorial uses the Stanford Cars dataset included in PyTorch, consisting of around 16,000 images.

The model is trained for 500 epochs on a personal GPU, resulting in generated images that resemble cars.

Diffusion models are not limited to image data and have applications in other domains such as molecule graphs and audio.

The tutorial provides a solid base model for those interested in the theoretical and practical aspects of diffusion models.

The author encourages looking into the literature for a deeper understanding of the theoretical details of diffusion models.

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