Poster
Theoretical guarantees in KL for Diffusion Flow Matching
Marta Gentiloni Silveri · Alain Durmus · Giovanni Conforti
East Exhibit Hall A-C #2611
Abstract:
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 with an auxiliary distribution leveraging a fixed coupling 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 , and 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 , and , and a standard -drift-approximation error assumption.
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