Flow Matching for Generative Modeling

TL;DR

This paper introduces Flow Matching, a novel training paradigm for Continuous Normalizing Flows that improves scalability, stability, and efficiency by using a simulation-free approach with various probability paths, including diffusion and optimal transport.

Contribution

The paper proposes Flow Matching, a new method for training CNFs that generalizes existing diffusion paths and introduces optimal transport paths for improved performance and efficiency.

Findings

Flow Matching enables stable, scalable training of CNFs.

Using optimal transport paths improves training speed and sample quality.

CNFs trained with Flow Matching outperform diffusion-based methods on ImageNet.

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.