Dynamic Conditional Optimal Transport through Simulation-Free Flows

Gavin Kerrigan, Giosue Migliorini, Padhraic Smyth
4/5/2024
cs.LG

No official code found. Best implementation: GavinKerrigan/cot_fm (4 stars, last commit 2024-06-03).

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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Code Implementations(1)

GavinKerrigan/cot_fmCommunity100%
44PythonApr 23, 20242 years ago

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Cite this paper

@article{kerrigan2024dynamic,
  title  = {Dynamic Conditional Optimal Transport through Simulation-Free Flows},
  author = {Gavin Kerrigan and Giosue Migliorini and Padhraic Smyth},
  year   = {2024},
  eprint = {2404.04240},
  archivePrefix = {arXiv},
  doi    = {10.48550/arXiv.2404.04240},
  url    = {http://arxiv.org/abs/2404.04240v2},
  journal = {NEURIPS 2024 2024}
}

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