Theoretical guarantees in KL for Diffusion Flow Matching
<|reference_start|>Theoretical guarantees in KL for Diffusion Flow Matching: 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 assumptions 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, we establish 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 $L^2$-drift-approximation error assumption.<|reference_end|>
@article{silveri2024theoretical,
    title={Theoretical guarantees in KL for Diffusion Flow Matching},
    author={Marta Gentiloni Silveri, Giovanni Conforti, Alain Durmus},
    journal={arXiv preprint arXiv:2409.08311},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.08311},
    primaryClass={stat.ML cs.LG math.PR}
}