{"ID":2851060,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.20871","arxiv_id":"2510.20871","title":"Exponential Convergence Guarantees for Iterative Markovian Fitting","abstract":"The Schrödinger 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 Schrödinger 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.","short_abstract":"The Schrödinger 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 Schröding...","url_abs":"https://arxiv.org/abs/2510.20871","url_pdf":"https://arxiv.org/pdf/2510.20871v1","authors":"[\"Marta Gentiloni Silveri\",\"Giovanni Conforti\",\"Alain Durmus\"]","published":"2025-10-23T08:34:04Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.PR\"]","methods":"[\"Diffusion Model\"]","has_code":false}