Flow Matching

Generate samples by learning a continuous normalizing flow between a noise distribution and the data distribution, providing a simpler and more stable alternative to score-based diffusion. Flow matching replaces the diffusion SDE/ODE with a direct regression objective: given a linear interpolation between noise x₀ and data x₁, the model learns to predict the velocity field dx/dt that maps one to the other. Unlike score matching, flow matching has no time-dependent normalization constants and does not require solving a reverse SDE at inference. The result is simpler training, faster sampling, and better likelihood estimation.