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Dynamic Conditional Optimal Transport through Simulation-Free Flows
April 8, 2024, 4:42 a.m. | Gavin Kerrigan, Giosue Migliorini, Padhraic Smyth
cs.LG updates on arXiv.org arxiv.org
Abstract: We study the geometry of conditional optimal transport (COT) and prove a dynamical formulation which generalizes the Benamou-Brenier Theorem. 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. We build on the framework of flow matching to train a conditional generative model by approximating the geodesic path of measures induced by this COT plan. …
abstract arxiv cs.lg distribution dynamic flow free generative generative modeling geometry modeling prove simulation study theorem through tools transport type
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