An Introduction to Flow Matching and Diffusion Models

2025/06/02 by Peter Holderrieth, Holderrieth, Peter, Ezra Erives +1 · 1 voice · 6 citations
Computer Science · Engineering · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Reservoir Engineering and Simulation Methods #cs.LG

paper · pdf · doi:10.48550/arxiv.2506.02070

openalex publication_date 2025/06/02 · arxiv published 2025/06/02 · openalex created_date 2025/10/14 · arxiv updated 2026/03/18 · openalex updated_date 2026/07/28

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.

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