Exponential Convergence Guarantees for Iterative Markovian Fitting

• URL: http://arxiv.org/abs/2510.20871v1
• Date: Thu, 23 Oct 2025 08:34:04 GMT
• Title: Exponential Convergence Guarantees for Iterative Markovian Fitting
• Authors: Marta Gentiloni Silveri, Giovanni Conforti, Alain Durmus,
• Abstract summary: We provide the first non-asymptotic exponential convergence guarantees for Iterative Proportional Fitting (IMF)<n>Our results encompass two key regimes: one where the marginals are log-concave, and another where they are weakly log-concave.<n>The analysis relies on new contraction results for the Markovian projection operator and paves the way to theoretical guarantees for DSBM.
• Score: 15.697611355182005
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Schr\"odinger Bridge (SB) problem has become a fundamental tool in computational optimal transport and generative modeling. To address this problem, ideal methods such as Iterative Proportional Fitting and Iterative Markovian Fitting (IMF) have been proposed-alongside practical approximations like Diffusion Schr\"odinger Bridge and its Matching (DSBM) variant. While previous work have established asymptotic convergence guarantees for IMF, a quantitative, non-asymptotic understanding remains unknown. In this paper, we provide the first non-asymptotic exponential convergence guarantees for IMF under mild structural assumptions on the reference measure and marginal distributions, assuming a sufficiently large time horizon. Our results encompass two key regimes: one where the marginals are log-concave, and another where they are weakly log-concave. The analysis relies on new contraction results for the Markovian projection operator and paves the way to theoretical guarantees for DSBM.

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