Flow Matching for Generative Modeling

Flow Matching introduces a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs) that can be trained without simulation. Instead of integrating an ODE during training, it regresses a neural vector field onto the vector fields of fixed conditional probability paths that transport noise to data. The formulation is compatible with a general family of Gaussian probability paths, which subsumes existing diffusion paths as special cases, and it can also express entirely non-diffusion paths such as those defined by Optimal Transport displacement interpolation.

Applying Flow Matching with diffusion paths gives a more robust and stable alternative to standard diffusion training, while the Optimal Transport paths are more efficient, enabling faster training and sampling and better generalization. Trained on ImageNet, Flow Matching consistently surpasses diffusion-based methods on both likelihood and sample quality and supports fast, reliable generation using off-the-shelf numerical ODE solvers. The method broadened the design space of continuous flows and became an influential, efficient alternative to diffusion models.