Error Bounds for Flow Matching Methods

Fuente: arXiv
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Autores principales: Benton, Joe, Deligiannidis, George, Doucet, Arnaud
Formato: Preprint
Publicado: 2023
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author Benton, Joe
Deligiannidis, George
Doucet, Arnaud
author_facet Benton, Joe
Deligiannidis, George
Doucet, Arnaud
contents Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary differential equations (ODE) rather than SDE. This led to the introduction of the probability flow ODE approach and denoising diffusion implicit models. Flow matching methods have recently further extended these ODE-based approaches and approximate a flow between two arbitrary probability distributions. Previous work derived bounds on the approximation error of diffusion models under the stochastic sampling regime, given assumptions on the $L^2$ loss. We present error bounds for the flow matching procedure using fully deterministic sampling, assuming an $L^2$ bound on the approximation error and a certain regularity condition on the data distributions.
format Preprint
id arxiv_https___arxiv_org_abs_2305_16860
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Error Bounds for Flow Matching Methods
Benton, Joe
Deligiannidis, George
Doucet, Arnaud
Machine Learning
Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary differential equations (ODE) rather than SDE. This led to the introduction of the probability flow ODE approach and denoising diffusion implicit models. Flow matching methods have recently further extended these ODE-based approaches and approximate a flow between two arbitrary probability distributions. Previous work derived bounds on the approximation error of diffusion models under the stochastic sampling regime, given assumptions on the $L^2$ loss. We present error bounds for the flow matching procedure using fully deterministic sampling, assuming an $L^2$ bound on the approximation error and a certain regularity condition on the data distributions.
title Error Bounds for Flow Matching Methods
topic Machine Learning
url https://arxiv.org/abs/2305.16860