arXiv:2602. 02241v2 Announce Type: replace Abstract: Entropic optimal transport (EOT) in continuous spaces with quadratic cost is a classical tool for solving the domain translation problem.
By Roman Dyachenko, Nikita Gushchin, Kirill Sokolov, Petr Mokrov, Evgeny Burnaev, Alexander Korotin
arXiv:2606. 24987v1 Announce Type: cross Abstract: Optimal transport (OT) has become a central language for comparing probability measures, but exact balanced OT is often both too rigid for data with missing, created, or destroyed mass and subject to unfavorable high-dimensional sample complexity.
By Francisco Andrade, Gabriel Peyr\'e, Clarice Poon
The paper introduces Distribution‑Conditioned Transport (DCT), a framework that learns transport maps conditioned on embeddings of source and target distributions, allowing generalization to unseen distribution pairs. DCT supports semi‑supervised learning for distributional forecasting by leveraging distributions observed at only one condition. It is agnostic to the transport mechanism and is demonstrated on synthetic benchmarks and four biological applications, including batch effect transfer in single‑cell genomics and modeling T‑cell receptor sequence evolution.
By Nic Fishman, Gokul Gowri, Paolo L. B. Fischer, Marinka Zitnik, Omar Abudayyeh, Jonathan Gootenberg
The paper introduces BROT, a two‑step approach for estimating optimal transport maps. First, it computes the unregularized OT plan, then fits a deep neural network to the resulting barycentric targets using least‑squares regression. The authors prove that, under standard regularity conditions, BROT achieves the minimax convergence rate when the true OT map is Lipschitz, and demonstrate its effectiveness on synthetic data, images, and downstream tasks such as single‑cell perturbation prediction and unsupervised domain adaptation.
By Kunwoong Kim, Insung Kong, Yongdai Kim
arXiv:2606. 14023v1 Announce Type: cross Abstract: Optimal Transport has become recently a powerful method for domain adaptation by aligning source and target distributions.
By Brian Britos, Mathias Bourel
The paper introduces COFM, a framework for consistent optimal transport flow matching that uses partially input convex neural networks (PICNN) to parameterize the transport potential. By adding a Hamilton‑Jacobi residual to the training objective, COFM enforces dynamical consistency and supports both one‑step transport and multi‑step ODE sampling without costly inner optimization. Experiments on benchmark datasets show that COFM achieves competitive performance while reducing L^2‑UVP by over 2× and cutting computational time by about 9× compared to state‑of‑the‑art models.
By Fanghui Song, Zhongjian Wang, Jiebao Sun