Dynamic Conditional Optimal Transport through Simulation-Free Flows

arXiv:2404.04240v1 Announce Type: new
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