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. 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
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: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
We introduce Potential Matching Optimal Transport (PMOT), a potential-flow framework for general $p$-cost optimal transport with $c_p(x,y)=\|x-y\|^p$. PMOT parameterizes the CNF velocity field with a scalar potential in the generalized Benamou--Brenier form for the chosen exponent $p$.
arXiv:2607. 26398v1 Announce Type: new Abstract: Diffusion and flow-based models benefit from simple regression losses, but inference incurs significant overhead because sampling requires integration.
By Mark Goldstein, Anshuk Uppal, Raghav Singhal, Aahlad Puli, Rajesh Ranganath
arXiv:2605. 08328v3 Announce Type: replace Abstract: Generative models based on flow matching have emerged as a powerful paradigm for inverse problems, offering straighter trajectories and faster sampling compared to diffusion models.
By Zehua Jiang, Fenghao Zhu, Xinquan Wang, Chongwen Huang, Zhaoyang Zhang
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)
arXiv:2606. 08953v1 Announce Type: new Abstract: Modern generative models often define an entire probability path from a simple prior to the data law, rather than only an endpoint map.
By Lei Luo, Yingzhen Zhang, Jian Yang
Blind image restoration requires recovering clean images from observations corrupted by unknown and potentially mixed degradations. While recent deterministic flow-based methods model restoration as transport processes that map degraded images to clean ones, they typically rely on Euclidean interpolation, implicitly assuming linear degradation geometry.
arXiv:2608. 07042v1 Announce Type: cross Abstract: Rectified flows, also called flow matching or stochastic interpolants, are generative models that learn a time-dependent vector field steering a probability curve between two probability distributions, usually referred to as latent and target distributions.
By Antonin Chambolle, Johannes Hertrich