arXiv:2608. 19783v1 Announce Type: new Abstract: Existing optimal transport (OT) models primarily seek an OT map or plan between distributions by minimizing a prescribed transport cost or distortion.
By Xiang Gu, Jian Sun, Zongben Xu
arXiv:2608. 16506v1 Announce Type: cross Abstract: Dataset alignment is a central step in data analysis across science and engineering, where the goal is to match observations between datasets.
By Keyi Li, Yuval Kluger, Boris Landa
arXiv:2606. 04092v1 Announce Type: cross Abstract: Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution.
By Shimon Malnick, Matan Rusanovsky, Ohad Fried, Shai Avidan
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: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
BridgeMatch is a two‑stage generative solver that preserves the full soft matching matrix for 3D deformable registration. Stage I uses denoising diffusion to estimate a global matching matrix at a coarse resolution, then lifts it to high resolution while maintaining hierarchy and rank constraints. Stage II refines this lifted matrix via a conditional transport bridge, implemented with either a deterministic Flow Matching ODE or a stochastic Brownian‑bridge SDE, and demonstrates improved correspondence accuracy and registration performance on 4DMatch, 4DLoMatch, CAPE, and DeepDeform datasets, especially in low‑overlap scenarios.
By Qianliang Wu, Haobo Jiang, Guangwei Gao, Shuo Chen, Jin Xie, Jian Yang, Yaqing Ding