arXiv:2605. 10792v2 Announce Type: replace-cross Abstract: We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches.
By Yesom Park, Eric Gelphman, Stanley Osher, Samy Wu Fung
The paper introduces the Variational Incompressible Optimal Transport (VIOT) operator, a generative neural operator that predicts divergence‑free velocity fields for incompressible density transport. VIOT combines a stream‑function representation, a regularized transport objective, and a Fourier Neural Operator backbone to amortize the solve across new source‑target pairs and grid resolutions. Experiments on 2D and 3D benchmarks show that VIOT produces full transport trajectories in seconds, achieving roughly a $10^4 imes$ speedup over per‑instance baselines that require hours of optimization.
By Jinjin He, Shenyifan Lu, Sinan Wang, Zhiqi Li, Duowen Chen, Bo Zhu
The paper introduces a new optimal transport framework that uses the Barron energy—an intrinsic neural network complexity measure—instead of the traditional kinetic energy. By modeling transport as deep residual networks that map a reference distribution to a target distribution, the authors define a new metric on probability measures and analyze its properties for generative modeling. They demonstrate that diffusion generative models are suboptimal in this Barron geometry and explore how adaptivity can improve alternative generative approaches.
By Evan Dogariu, Joan Bruna
arXiv:2609.38049v1 Announce Type: new
Abstract: Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite...
By Fred Xu, Thomas Markovich, Barbora Barancikova, Yizhou Sun
Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite-dimensional spaces. Functional Flow Matching (FF...
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