Flow Matching for Generative Modeling | alphaXiv

View recent discussion. Abstract: We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

Problem Setup and Motivation Flow Matching (FM) addresses a fundamental challenge in deep generative modeling: how to efficiently train Continuous Normalizing Flows (CNFs) at scale. CNFs are theoretically elegant models that learn time-dependent vector fields to transform simple prior distributions (like Gaussian noise) into complex data distributions through deterministic ordinary differential equations (ODEs). While CNFs offer exact likelihood computation and deterministic generation, their practical application has been severely limited by the computational cost of training, which…

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