2024/05/31 by Kenji Fukumizu, Fukumizu, Kenji, Taiji Suzuki +7 · 5 citations
Engineering · Computer Science · #Advanced Control Systems Optimization #Reinforcement Learning in Robotics
paper · pdf · doi:10.48550/arxiv.2405.20879
Flow matching (FM) has gained significant attention as a simulation-free generative model. Unlike diffusion models, which are based on stochastic differential equations, FM employs a simpler approach by solving an ordinary differential equation with an initial condition from a normal distribution, thus streamlining the sample generation process. This paper discusses the convergence properties of FM for large sample size under the p-Wasserstein distance, a measure of distributional discrepancy. We establish that FM can achieve an almost minimax optimal convergence rate for 1 ≤ p ≤ 2, presenting the first theoretical evidence that FM can reach convergence rates comparable to those of diffusion models. Our analysis extends existing frameworks by examining a broader class of mean and variance functions for the vector fields and identifies specific conditions necessary to attain almost optimal rates.