Dynamic Conditional Optimal Transport through Simulation-Free Flows
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910465123155968 |
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| author | Kerrigan, Gavin Migliorini, Giosue Smyth, Padhraic |
| author_facet | Kerrigan, Gavin Migliorini, Giosue Smyth, Padhraic |
| contents | We study the geometry of conditional optimal transport (COT) and prove a dynamical formulation which generalizes the Benamou-Brenier Theorem. Equipped with these tools, we propose a simulation-free flow-based method for conditional generative modeling. Our method couples an arbitrary source distribution to a specified target distribution through a triangular COT plan, and a conditional generative model is obtained by approximating the geodesic path of measures induced by this COT plan. Our theory and methods are applicable in infinite-dimensional settings, making them well suited for a wide class of Bayesian inverse problems. Empirically, we demonstrate that our method is competitive on several challenging conditional generation tasks, including an infinite-dimensional inverse problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04240 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamic Conditional Optimal Transport through Simulation-Free Flows Kerrigan, Gavin Migliorini, Giosue Smyth, Padhraic Machine Learning We study the geometry of conditional optimal transport (COT) and prove a dynamical formulation which generalizes the Benamou-Brenier Theorem. Equipped with these tools, we propose a simulation-free flow-based method for conditional generative modeling. Our method couples an arbitrary source distribution to a specified target distribution through a triangular COT plan, and a conditional generative model is obtained by approximating the geodesic path of measures induced by this COT plan. Our theory and methods are applicable in infinite-dimensional settings, making them well suited for a wide class of Bayesian inverse problems. Empirically, we demonstrate that our method is competitive on several challenging conditional generation tasks, including an infinite-dimensional inverse problem. |
| title | Dynamic Conditional Optimal Transport through Simulation-Free Flows |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2404.04240 |