Dynamic Conditional Optimal Transport through Simulation-Free Flows
<|reference_start|>Dynamic Conditional Optimal Transport through Simulation-Free Flows: 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.<|reference_end|>
@article{kerrigan2024dynamic,
    title={Dynamic Conditional Optimal Transport through Simulation-Free Flows},
    author={Gavin Kerrigan, Giosue Migliorini, Padhraic Smyth},
    journal={arXiv preprint arXiv:2404.04240},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.04240},
    primaryClass={cs.LG}
}