Dynamic Conditional Optimal Transport through Simulation-Free Flows
Keywords: flow matching, optimal transport, generative models, conditional generation
TL;DR: We study the geometry of conditional optimal transport from a dynamical perspective, and use our theory to build conditional generative models.
Abstract: We study the geometry of conditional optimal transport (COT) and prove a dynamic 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.
Primary Area: Generative models
Submission Number: 11358
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