This repository contains educational Jupyter notebooks that explore the theory and implementation of generative models, specifically Variational Autoencoders (VAEs) and Diffusion Models. These notebooks are designed to provide a clear, step-by-step understanding of how these powerful generative AI techniques work.
📖 Blog Post: For a gist and overview of the concepts covered in this repository, check out the accompanying blog post: From VAEs to Diffusion Models: A Step-by-Step Journey
To run the notebooks in this repository, you'll need Python 3.8+ and the following dependencies:
pip install -r requirements.txtThe main dependencies are:
- PyTorch (for deep learning models)
- torchvision (for computer vision utilities)
- matplotlib (for visualization)
- tqdm (for progress bars)
- The mathematical foundations behind VAEs and diffusion models
- How to implement these models from scratch using PyTorch
- The connection between VAEs and diffusion models
- How to generate MNIST digits using these techniques
01.vae.ipynb – Variational Autoencoders
This notebook covers the fundamental concepts of Variational Autoencoders (VAEs):
- Motivation behind generative models and latent variable models
- The Evidence Lower Bound (ELBO) objective
- Reparameterization trick for training VAEs
- Implementation of VAEs using both Multi-Layer Perceptron (MLP) and Convolutional Neural Network (CNN) architectures
- Exploration of both Bernoulli and Gaussian likelihoods for the decoder
- Comparison of different likelihood models and architectures, and their effects on image generation quality for MNIST digits
02.vae-without-encoder.ipynb – Simplified VAE (Decoder-Only)
This notebook explores a "VAE-like" model that omits the encoder:
- One-step fixed corruption process as "inference"
- Connection between this simplified model and diffusion models
- Implementation of a noise prediction objective
- Demonstration of how this approach performs on MNIST data
- Compare the classical CNN architecture with the U-Net CNN architecture
03.diffusion.ipynb – Diffusion Models
This comprehensive notebook dives into diffusion models:
- Forward and reverse processes in diffusion models
- Beta schedules (linear)
- Variational inference and the ELBO objective for diffusion
- Simplified noise prediction objective
- Implementation of a diffusion model with:
- UNet architecture
- Time embedding and conditioning
- Linear beta schedule
- Conditional generation, e.g., class, text, with VAE and diffusion.
- VAE and diffusion working together, e.g., VAE as an encoder diffusion as a decoder.
- Discrete modality, e.g., table, graph, text, etc, with non Gaussian and continuous distributions, e.g., discrete categorical.