Work

Flow matching achieves almost minimax optimal convergence

Year: 2024

Type: preprint

Abstract: 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 $1 \leq p \leq 2$, 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2405.20879

Authors: Fukumizu, Kenji, Suzuki, Taiji, Isobe, Noboru, Oko, Kazusato, Koyama, Masanori

Institutions: The Institute of Statistical Mathematics, Preferred Networks (Japan), RIKEN, RIKEN Center for Advanced Intelligence Project, The University of Tokyo

Language: English

Topic: Generative Adversarial Networks and Image Synthesis

Subfield: Computer Vision and Pattern Recognition

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4399317849

Cites:

Cited by:

Related to: 10