Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map. In applications like generative modeling, the transport cost itself is irrelevant, and this makes it natural to target maps which are more tractable from either a statistical or computational standpoint.
arXiv:2606. 30574v1 Announce Type: new Abstract: Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map.
By Sivaraman Balakrishnan
arXiv:2606. 05327v1 Announce Type: new Abstract: Flow matching (FM) has emerged as a powerful framework for learning dynamic transport maps between two empirical distributions.
By Raghav Kansal, David Crair, Nghia Nguyen, Scott Pope, Bradley Parry
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
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
arXiv:2608. 28262v1 Announce Type: new Abstract: Entropic optimal transport (EOT) has been shown to offer a computationally tractable approximation to exact optimal transport.
By Ian Hsieh, Soumya Snigdha Kundu, Tom Vercauteren, Reuben Dorent
arXiv:2602. 24201v2 Announce Type: replace Abstract: Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions.
By Egor Antipov, Alessandro Palma, Lorenzo Consoli, Stephan G\"unnemann, Andrea Dittadi, Fabian J. Theis
arXiv:2609.37424v1 Announce Type: cross
Abstract: Optimal Transport (OT) provides a principled framework for learning transformations between probability distributions from unpaired samples. In many...
By Milena Gazdieva, Kirill Sokolov, Jiawei Chen, Evgeny Burnaev, Alexander Korotin
Particle-based variational inference (ParVI) methods approximate an intractable target distribution by evolving an ensemble of interacting samples. Existing approaches rely predominantly on kernel-based repulsion (e.
The paper introduces multifidelity techniques for building triangular transport maps when high‑fidelity data are limited but low‑fidelity data are plentiful. Two strategies are proposed: a hierarchical approach that composes maps across fidelity levels, and a non‑hierarchical method that uses monotonicity‑preserving corrections to incorporate low‑fidelity information. Numerical tests show these methods outperform single‑fidelity transport and, when applied to amortized simulation‑based inference, improve conditional sampling and uncertainty quantification in data‑scarce regimes.
By Owen Davis, Daniel Sharp, Youssef Marzouk, Gianluca Geraci
arXiv:2609.16622v1 Announce Type: cross
Abstract: Parameter estimation in finite mixture models can exhibit highly heterogeneous convergence behavior: locally isolated components may be estimated sub...
By Dung Le, Huy Nguyen, Trang Pham, Alessandro Rinaldo, Nhat Ho
arXiv:2609.15072v1 Announce Type: cross
Abstract: Methods of Branched Optimal Transport (BOT) mimic the economy and efficiency of natural tree-like structures, such as those found in rivers and biolo...
By Semyon Semenov, Viktor Kovalchuk, Meir Roketlishvili, Albert Baichorov, Fakhri Karray, Martin Takac, Arip Asadulaev