arXiv:2608. 05666v1 Announce Type: new Abstract: We introduce Potential Matching Optimal Transport (PMOT), a potential-flow framework for general $p$-cost optimal transport with $c_p(x,y)=\|x-y\|^p$.
By Lishuo Zhang (School of Mathematical Sciences, Shanghai Jiao Tong University), Ruizhi Huang (School of Mathematical Sciences, Shanghai Jiao Tong University), Yang Yu (School of Mathematical Sciences, Shanghai Jiao Tong University), Lei Li (School of Mathematical Sciences, Shanghai Jiao Tong University, Institute of Natural Sciences, MOE-LSC, Shanghai Jiao Tong University)
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
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...
arXiv:2602. 22265v2 Announce Type: replace Abstract: Modern vision generators transport a base distribution to data through time-indexed measures, implemented as deterministic flows (ODEs) or stochastic diffusions (SDEs).
By Chika Maduabuchi
arXiv:2608. 01692v1 Announce Type: new Abstract: We propose an instantiation of flow matching that relies on a time-independent velocity field (an \emph{autonomous flow}) to exactly map between two distributions, so long as the target is singular, i.
By Lee Cheuk-Kit, Florentin Coeurdoux, Peter Potaptchik, Yilun Du, Michael Samuel Albergo, Eric Vanden-Eijnden
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