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Flow Matching for Generative Modeling

Lex Toumbourou · · revised

Flow Matching for Generative Modeling is a 2022 paper by Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel and Matt Le (arXiv). It introduces Flow Matching, a simulation-free way to train Continuous Normalizing Flows.

Instead of training the flow by simulating an ODE, Flow Matching trains a neural network to regress a vector field that moves samples along a chosen probability path from noise to data. The paths used by Diffusion Models are one special case. The paper also proposes optimal transport paths, which are straighter, and found they train faster and need fewer steps to sample.

Flow matching is now used in large image models such as FLUX.1.

arXiv listing for Flow Matching for Generative Modeling by Lipman, Chen, Ben-Hamu, Nickel and Le, with the abstract. Title block of the Flow Matching for Generative Modeling paper, with authors from Meta AI (FAIR) and the Weizmann Institute of Science.

Figure 1 from the paper: a grid of unconditional ImageNet-128 samples from a CNF trained with Flow Matching and Optimal Transport paths.

Figure 3 from the paper: diffusion trajectories curve and overshoot on their way to the target point, while OT trajectories are straight lines.

Figure 4 from the paper: a Gaussian turning into a 2D checkerboard under score matching, Flow Matching with diffusion paths and Flow Matching with OT paths; the OT path forms the checkerboard earliest and samples well with fewer function evaluations.