Dynamic Conditional Optimal Transport through Simulation-Free Flows
Gavin Kerrigan, Giosue Migliorini, Padhraic Smyth
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.
BibTeX
@inproceedings{
kerrigan2024dynamic,
title={Dynamic Conditional Optimal Transport through Simulation-Free Flows},
author={Gavin Kerrigan and Giosue Migliorini and Padhraic Smyth},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=tk0uaRynhH}
}