An Introduction to Flow Matching and Diffusion Models

• URL: http://arxiv.org/abs/2506.02070v2
• Date: Sat, 12 Jul 2025 16:37:24 GMT
• Title: An Introduction to Flow Matching and Diffusion Models
• Authors: Peter Holderrieth, Ezra Erives,
• Abstract summary: This tutorial provides a self-contained introduction to diffusion and flow-based generative models from first principles.<n>We develop the necessary mathematical background in ordinary and differential equations and derive the core algorithms of flow matching and denoising diffusion models.<n>We then provide a step-by-step guide to building image and video generators, including training methods, guidance, and architectural design.
• Score: 1.2277343096128712
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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 tutorial 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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