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
The paper introduces Flow Divergence Sampler (FDS), a training‑free method that refines intermediate states in flow‑matching models by using the divergence of the marginal velocity field to detect and correct misguidance toward low‑density regions. FDS operates during inference, requires no additional training, and can be applied as a plug‑and‑play module with standard solvers and existing flow backbones. Experiments show that FDS consistently improves fidelity in tasks such as text‑to‑image synthesis and inverse problems.
By Yeonwoo Cha, Jaehoon Yoo, Semin Kim, Yunseo Park, Jinhyeon Kwon, Seunghoon Hong
arXiv:2607. 12171v1 Announce Type: cross Abstract: In rectified-flow-based generative models, the neural network can be trained to predict two different targets, such as the instantaneous velocity or the data endpoint, to perform denoising.
By Xu Han, Jiajing Hu, Li-Ping Liu
arXiv:2602.23188v2 Announce Type: replace
Abstract: We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while...
By Isma\"el Zighed, Andrea N\'ovoa, Luca Magri, Taraneh Sayadi
arXiv:2608. 14120v1 Announce Type: cross Abstract: Lagrangian modeling is vital to fluid dynamics, as it characterizes particle transport and complements the Eulerian description.
By Meng Li, Chuqi Chen, Zhengqing Gao, Xi Zhou, Xiao Sun, Yang Xiang, Huaxi Huang
The paper presents a lightweight retraining strategy for a parameterized Reduced Order Model (ROM) that achieves full‑model accuracy using only a fraction of the computational effort and sparse observations. The ROM architecture combines a Variational Autoencoder for dimensionality reduction with a transformer network that evolves latent states while accounting for the Reynolds number as an external control variable. By leveraging the probabilistic VAE, the method generates trajectory ensembles and uncertainty estimates, and adapts to out‑of‑sample parameters through sparse data assimilation with an ensemble Kalman filter, focusing retraining on the autoencoder to correct latent manifold distortions.
By Isma\"el Zighed, Andrea N\'ovoa, Luca Magri, Taraneh Sayadi
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
By Yilong Dai, Shengyu Chen, Xiaowei Jia, Runlong Yu
In rectified-flow-based generative models, the neural network can be trained to predict two different targets, such as the instantaneous velocity or the data endpoint, to perform denoising. Although prior work shows that these parameterizations lead to different empirical behaviors, the mechanisms underlying their respective advantages remain to be underexplored, and how to combine them effectively is still unclear.
arXiv:2601. 21542v3 Announce Type: replace-cross Abstract: Flow Matching (FM) models have emerged as a leading paradigm for high-fidelity synthesis.
By Hongxu Chen, Hongxiang Li, Zhen Wang, Long Chen
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
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
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