Flow Matching

Flow Matching is a generative modeling framework that learns a time-dependent vector field capable of transporting a simple prior distribution (such as a standard Gaussian) to the target data distribution. The core idea is to define a continuous-time probability flow — a deterministic ordinary differential equation (ODE) — whose trajectories map samples from the prior to samples from the data distribution. Training involves regressing a neural network against the target vector field that defines this transport.

Unlike diffusion models, which are restricted to noise-adding forward processes (and correspondingly noise-removing reverse processes), flow matching allows arbitrary transport paths between the prior and data distributions. This includes straight-line paths (optimal transport), which are more efficient to simulate and require fewer discretization steps. The greater flexibility in path design often translates to faster sampling — flow-matching models can generate high-quality samples in as few as 1–10 ODE steps compared to the hundreds of steps traditional diffusion models may require.

Flow matching has been adopted across diverse domains including voice synthesis (e.g., voice cloning and text-to-speech), image generation, video generation, and protein structure prediction. It provides a unified mathematical framework that subsumes several prior approaches, including score-based diffusion and rectified flow, under a common training objective.