Mirror Flow Matching with Heavy-Tailed Priors for Generative Modeling on Convex Domains
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| Format: | Preprint |
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2025
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| _version_ | 1866915543434395648 |
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| author | Guan, Yunrui Balasubramanian, Krishnakumar Ma, Shiqian |
| author_facet | Guan, Yunrui Balasubramanian, Krishnakumar Ma, Shiqian |
| contents | We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics. Second, coupling with Gaussian priors performs poorly when matching heavy-tailed targets. To address these issues, we propose Mirror Flow Matching based on a \emph{regularized mirror map} that controls dual tail behavior and guarantees finite moments, together with coupling to a Student-$t$ prior that aligns with heavy-tailed targets and stabilizes training. We provide theoretical guarantees, including spatial Lipschitzness and temporal regularity of the velocity field, Wasserstein convergence rates for flow matching with Student-$t$ priors and primal-space guarantees for constrained generation, under $\varepsilon$-accurate learned velocity fields. Empirically, our method outperforms baselines in synthetic convex-domain simulations and achieves competitive sample quality on real-world constrained generative tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08929 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mirror Flow Matching with Heavy-Tailed Priors for Generative Modeling on Convex Domains Guan, Yunrui Balasubramanian, Krishnakumar Ma, Shiqian Machine Learning We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics. Second, coupling with Gaussian priors performs poorly when matching heavy-tailed targets. To address these issues, we propose Mirror Flow Matching based on a \emph{regularized mirror map} that controls dual tail behavior and guarantees finite moments, together with coupling to a Student-$t$ prior that aligns with heavy-tailed targets and stabilizes training. We provide theoretical guarantees, including spatial Lipschitzness and temporal regularity of the velocity field, Wasserstein convergence rates for flow matching with Student-$t$ priors and primal-space guarantees for constrained generation, under $\varepsilon$-accurate learned velocity fields. Empirically, our method outperforms baselines in synthetic convex-domain simulations and achieves competitive sample quality on real-world constrained generative tasks. |
| title | Mirror Flow Matching with Heavy-Tailed Priors for Generative Modeling on Convex Domains |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.08929 |