Flow matching is a simple yet effective generative modeling paradigm that has found widespread adoption in diverse domains and large-scale applications. It is inspired by the efficient training of diffusion models, but offers a simpler perspective and enables easy implementation and generalization. At its core, flow matching follows a simple blueprint: regress onto conditional velocities that generate single data examples, and the result is a model that generates the full distribution.

Our objective in this tutorial is to provide a comprehensive yet self-contained introduction to flow matching, beginning with the continuous Euclidean setting. Afterwards, we will explore extensions and generalizations, including adaptations to non-Euclidean geometries, as well as generalizations to discrete domains and even arbitrary Markov processes. Lastly, we will discuss post-training and fine-tuning methodologies for improved inference and conditioning. The tutorial will survey applications of flow matching ranging from image and video generation to molecule generation and language modeling, and will be accompanied by coding examples and a release of an open source flow matching library. We hope this tutorial will serve as a soft entry point for researchers, as well as provide all attendees with both a theoretical and practical understanding of flow matching with an outlook for future advancements.