An Introduction to Flow Matching and Diffusion Models

TL;DR

This tutorial offers a comprehensive introduction to diffusion and flow-based generative models, covering their mathematical foundations, core algorithms, and practical implementation for image and video generation.

Contribution

It systematically develops the mathematical background and provides a detailed guide to building and training flow matching and diffusion models from first principles.

Findings

Provides a unified framework for diffusion and flow models

Details algorithms for training and sampling in generative models

Includes practical guidance for building image and video generators

Abstract

Diffusion and flow-based models have become the state of the art for generative AI across a wide range of data modalities, including images, videos, shapes, molecules, music, and more. This tutorial provides a self-contained introduction to diffusion and flow-based generative models from first principles. We systematically develop the necessary mathematical background in ordinary and stochastic differential equations and derive the core algorithms of flow matching and denoising diffusion models. We then provide a step-by-step guide to building image and video generators, including training methods, guidance, and architectural design. This course is ideal for machine learning researchers who want to develop a principled understanding of the theory and practice of generative AI.