@inproceedings{
silveri2024theoretical,
title={Theoretical guarantees in {KL} for Diffusion Flow Matching},
author={Marta Gentiloni Silveri and Alain Oliviero Durmus and Giovanni Conforti},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=ia4WUCwHA9}
}
Flow Matching (FM) (also referred to as stochastic interpolants or rectified flows)  stands out as a class of generative models that aims to bridge in finite time the target distribution $\nu^\star$ with an auxiliary distribution $\mu$ leveraging a fixed coupling $\pi$ and a bridge which can either be deterministic or stochastic. These two ingredients define a path measure which can then be approximated by learning the drift of its Markovian projection. The main contribution of this paper is to provide relatively mild assumption on $\nu^\star$, $\mu$ and $\pi$ to obtain non-asymptotics guarantees for Diffusion Flow Matching (DFM) models using as bridge the conditional distribution associated with the Brownian motion. More precisely, it establishes bounds on the Kullback-Leibler divergence between the target distribution and the one generated by such DFM models under moment conditions on the score of $\nu^\star$, $\mu$ and $\pi$, and a standard $\mathrm{L}^2$-drift-approximation error assumption.
Theoretical guarantees in KL for Diffusion Flow Matching
Marta Gentiloni Silveri Alain Oliviero Durmus Giovanni Conforti