Exponential Convergence Guarantees for Iterative Markovian Fitting
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909867027988480 |
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| author | Silveri, Marta Gentiloni Conforti, Giovanni Durmus, Alain |
| author_facet | Silveri, Marta Gentiloni Conforti, Giovanni Durmus, Alain |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_20871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential Convergence Guarantees for Iterative Markovian Fitting Silveri, Marta Gentiloni Conforti, Giovanni Durmus, Alain Machine Learning Probability 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. |
| title | Exponential Convergence Guarantees for Iterative Markovian Fitting |
| topic | Machine Learning Probability |
| url | https://arxiv.org/abs/2510.20871 |