mlsanityData to 14 Oct 2026

Computing high-dimensional optimal transport by flow neural networks

arXiv 2305.11857 ↗First posted 19 May 2023stat.ML cs.LG stat.MEcited by 8

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Abstract (arXiv)

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.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 51 of its 83 references that are in the map. First posted on arXiv 19 May 2023.

Builds on

51 of 83 references.

References · 51

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38 more
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50 most cited of 51 All 51 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 2; 2025: 3; 2026: 1.

8 papers.

  1. 2023Convergence of flow-based generative models via proximal gradient descent in Wasserstein spacecited by 34
  2. 2023Flow-based Distributionally Robust Optimizationcited by 13
  3. 2025Density Ratio Estimation with Conditional Probability Pathscited by 13
  4. 2024Annealing Flow Generative Models Towards Sampling High-Dimensional and Multi-Modal Distributionscited by 11
  5. 2024Local Flow Matching Generative Modelscited by 5
  6. 2026Generative models for decision-making under distributional shiftcited by 4
  7. 2025High-dimensional Mean-Field Games by Particle-based Flow Matchingcited by 3
  8. 2025Flow-based generative models as iterative algorithms in probability spacecited by 2