Computing high-dimensional optimal transport by flow neural networks

Chen Xu, Xiuyuan Cheng, Yao Xie
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:2872-2880, 2025.

Abstract

Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT problem. The current work proposes to compute the dynamic OT between two arbitrary distributions $P$ and $Q$ by optimizing a flow model, where both distributions are only accessible via finite samples. Our method learns the dynamic OT by finding an invertible flow that minimizes the transport cost. The trained optimal transport flow subsequently allows for performing many downstream tasks, including infinitesimal density ratio estimation (DRE) and domain adaptation by interpolating distributions in the latent space. The effectiveness of the proposed model on high-dimensional data is demonstrated by strong empirical performance on OT baselines, image-to-image translation, and high-dimensional DRE.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-xu25f, title = {Computing high-dimensional optimal transport by flow neural networks}, author = {Xu, Chen and Cheng, Xiuyuan and Xie, Yao}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {2872--2880}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/xu25f/xu25f.pdf}, url = {https://proceedings.mlr.press/v258/xu25f.html}, abstract = {Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT problem. The current work proposes to compute the dynamic OT between two arbitrary distributions $P$ and $Q$ by optimizing a flow model, where both distributions are only accessible via finite samples. Our method learns the dynamic OT by finding an invertible flow that minimizes the transport cost. The trained optimal transport flow subsequently allows for performing many downstream tasks, including infinitesimal density ratio estimation (DRE) and domain adaptation by interpolating distributions in the latent space. The effectiveness of the proposed model on high-dimensional data is demonstrated by strong empirical performance on OT baselines, image-to-image translation, and high-dimensional DRE.} }
Endnote
%0 Conference Paper %T Computing high-dimensional optimal transport by flow neural networks %A Chen Xu %A Xiuyuan Cheng %A Yao Xie %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-xu25f %I PMLR %P 2872--2880 %U https://proceedings.mlr.press/v258/xu25f.html %V 258 %X Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT problem. The current work proposes to compute the dynamic OT between two arbitrary distributions $P$ and $Q$ by optimizing a flow model, where both distributions are only accessible via finite samples. Our method learns the dynamic OT by finding an invertible flow that minimizes the transport cost. The trained optimal transport flow subsequently allows for performing many downstream tasks, including infinitesimal density ratio estimation (DRE) and domain adaptation by interpolating distributions in the latent space. The effectiveness of the proposed model on high-dimensional data is demonstrated by strong empirical performance on OT baselines, image-to-image translation, and high-dimensional DRE.
APA
Xu, C., Cheng, X. & Xie, Y.. (2025). Computing high-dimensional optimal transport by flow neural networks. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:2872-2880 Available from https://proceedings.mlr.press/v258/xu25f.html.

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