Flow Matching

Flow matching is a method for training continuous normalizing flows, generative models that transform noise into data by integrating a learned vector field. Yaron Lipman and coauthors introduced it in 2022 (arXiv:2210.02747). Instead of the slow, simulation-based training that continuous normalizing flows previously required, flow matching regresses a neural network directly onto the vector field of a chosen, fixed probability path between noise and data, without running the ODE during training.

The method works with a broad family of these paths. The paths used in diffusion models are one special case, so training a diffusion model can itself be framed as an instance of flow matching, often with a more stable loss. Beyond that unification, the paper's central proposal is to use optimal transport paths instead: straight-line interpolations between a noise sample and a data sample. These train faster and let a trained model be sampled in far fewer integration steps than a typical diffusion model.

Flow matching's straight, deterministic paths make it a natural target for further speedups. It underlies rectified flow methods and the base architecture of image and video models including Stable Diffusion 3 and Meta's Movie Gen. It has since been extended to discrete data, such as text tokens, and used as a building block for one- and few-step generative models that try to avoid distilling a separately trained teacher model.