Dynamic Conditional Optimal Transport through Simulation-Free Flows

• URL: http://arxiv.org/abs/2404.04240v2
• Date: Fri, 31 May 2024 17:43:54 GMT
• Title: Dynamic Conditional Optimal Transport through Simulation-Free Flows
• Authors: Gavin Kerrigan, Giosue Migliorini, Padhraic Smyth,
• Abstract summary: We study the geometry of conditional optimal transport (COT) and prove a dynamical formulation which generalizes the Benamou-Brenier Theorem. We propose a simulation-free flow-based method for conditional generative modeling.
• Score: 12.976042923229466
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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