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 ReCouple, a framework that constructs coarse-grained optimal transport (OT) couplings to improve flow matching without requiring rollouts. Extensions ReCouple+ and ReCouple++ address continuous-source settings and add spatial regularization, respectively. Experiments show that these methods balance coupling optimality, neural network realizability, and generation quality, especially in low NFE regimes.
By Soon Hoe Lim, Aditi Gupta, Michael W. Mahoney, N. Benjamin Erichson
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:2611.06711v1 Announce Type: new
Abstract: Deep generative models, particularly Flow Matching frameworks, have emerged as powerful tools for synthesizing complex physical systems. However, stand...
By Giuliano Galadini, Aurelio Uncini, Danilo Comminiello
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
The paper introduces a density‑level backward‑error framework for low‑NFE generative ODE sampling, identifying the part of a solver’s modified‑equation defect that alters the evolving marginal while ignoring solenoidal trajectory distortion. This leads to a solver‑order‑aware compute‑allocation rule and an objective for choosing numerically favorable velocity representatives, distinct from schedule search or higher‑order solver design. Experiments on Gaussian, mixture models, and a pretrained CIFAR‑10 EDM probability‑flow ODE show that density‑aware allocation consistently improves fixed‑update Euler sampling in the low‑NFE regime and accelerates convergence to a dense Euler reference.
By Ewsey Obzherin, Valentin Khrulkov
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:2610.01408v1 Announce Type: new
Abstract: Trajectory crossing remains a critical bottleneck in Flow Matching (FM), and previous works typically view these crossings from a theoretical optimizat...
By Ziqi Jiang, Zhenqi He, Long Chen
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.