AREX is a training‑free sampler for pretrained flow matching models that leverages the target mean and covariance to analytically capture part of the sampling dynamics. By showing that the velocity field of a moment‑matched Gaussian target is the $L^2$‑optimal affine approximation to the marginal velocity field, AREX decomposes the learned dynamics into an affine component—determined by the first two target moments—and a neural residual term. The affine component is integrated explicitly with a matrix‑valued propagator, leaving only the residual term to be integrated numerically, which consistently improves sample fidelity in few‑step image and text‑to‑image generation tasks without retraining the underlying model.
By Shizheng Lin, Soon Hoe Lim, 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:2610.08717v1 Announce Type: cross
Abstract: We study path-flow alignment as a unified training objective for flow matching. Instead of fixing the interpolation path and learning only the veloci...
By Zeyu Michael Li, William Xingxu Chen, Xiang Cheng
The paper introduces Cumulative Marginal Matching (CMM), a new objective for training few‑step diffusion and flow‑matching models. CMM treats flow‑matching as a sequence of intermediate marginal distributions and directly optimizes the cumulative Wasserstein‑2 discrepancy between the base and few‑step models across the entire trajectory. It derives a tractable surrogate for this objective, shows that Shortcut‑CSL is a first‑order approximation of CMM, and reports improved generation quality on standard benchmarks under the same training budget.
By Paribesh Regmi, Rui Li
arXiv:2610.02260v1 Announce Type: new
Abstract: Flow matching models excel at generative modeling, and many downstream applications require their samples to satisfy prescribed constraints, such as ob...
By Yesom Park, Kelvin Kan, Qifan Chen, Thomas Flynn, Hayden Schaeffer. Xihaier Luo
Preconditioned Flow Matching introduces a precondition-then-match framework that transforms target distributions into more isotropic representations before training flow matching models. By reshaping intermediate distributions, the method improves conditioning, leading to better low-eigenvalue recovery and enhanced performance metrics such as FID, MMD, precision, and recall across Gaussian, Gaussian-mixture, and high-resolution image datasets. The approach is theoretically justified and empirically validated, with ablations showing gains stem from improved geometry rather than extra parameters.
By Shadab Ahamed, Eshed Gal, Md Shahriar Rahim Siddiqui, Simon Ghyselincks, Moshe Eliasof, Eldad Haber