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
The paper introduces a penalized distributionally robust optimization framework that allows an adversary to choose any distribution while incurring a Wasserstein penalty for deviating from the empirical distribution. It shows that the adversary’s problem can be reformulated as optimizing transport maps that push empirical samples to adversarial ones, proving that optimal maps are cyclically monotone. The authors argue that standard per-sample adversarial training violates this property and propose two remedies—multi-start particle ascent and input-convex neural network parameterization—to enforce cyclical monotonicity, demonstrating improved robustness and generalization in experiments on regression, image classification, and control tasks.
By Alireza Abdollahpoorrostam, Ehsan Sharifian, Buse \c{S}en, Marco Cuturi, Daniel Kuhn
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:2510. 04602v4 Announce Type: replace-cross Abstract: Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space.
By Eduardo Fernandes Montesuma, Yassir Bendou, Mike Gartrell
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:2609.40075v1 Announce Type: new
Abstract: Partial Optimal Transport (POT) extends the classical optimal transport problem by relaxing the strict mass conservation constraint, enabling its use i...
By Khoa Nguyen, Dung T. Nguyen, Thong Huynh, Hoang-Hiep Nguyen-Mau, Anh Nguyen, Minh Ngoc Dinh, Juho Kannala