Flow matching achieves almost minimax optimal convergence
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914969822429184 |
|---|---|
| author | Fukumizu, Kenji Suzuki, Taiji Isobe, Noboru Oko, Kazusato Koyama, Masanori |
| author_facet | Fukumizu, Kenji Suzuki, Taiji Isobe, Noboru Oko, Kazusato Koyama, Masanori |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20879 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Flow matching achieves almost minimax optimal convergence Fukumizu, Kenji Suzuki, Taiji Isobe, Noboru Oko, Kazusato Koyama, Masanori Machine Learning 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. |
| title | Flow matching achieves almost minimax optimal convergence |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2405.20879 |