The paper studies how flow‑matching schedules influence sampling dynamics and regression variance. For centered commuting Gaussians, it shows that a direction‑dependent schedule splits into a variance path that determines intermediate laws and a factorization that keeps the flow unchanged while controlling irreducible regression variance. The authors analyze finite‑step Euler accuracy, derive a drift bound for exact N‑step sampling, and provide closed‑form factorizations that either minimize time‑averaged regression variance or keep it constant along a fixed path.
By Ars\`ene Claustre (DI-ENS), Hugo Negrel (DMA, CFM), Claire Boyer (LMO, IUF), Kimia Nadjahi (DI-ENS), Eric Vanden-Eijnden (DMA, CFM, CIMS)
arXiv:2602. 10691v2 Announce Type: replace-cross Abstract: We study the slice-matching scheme, an efficient iterative method for distribution matching based on sliced optimal transport.
By Gauthier Thurin (ENS-PSL), Claire Boyer (LMO, IUF, CELESTE), Kimia Nadjahi (ENS-PSL)
arXiv:2609.38918v1 Announce Type: cross
Abstract: Flow Matching (FM) learns a velocity field whose ODE transports a simple source distribution to a target law. Existing finite-sample theory largely t...
By Lifeng Hao, Shaolin Ji
arXiv:2607. 13841v1 Announce Type: new Abstract: Heavy-tailed data arise in many domains where rare events carry disproportionate importance, such as imbalanced image datasets, financial returns, and weather extremes.
By Zhouhao Yang, Yezhen Wang, Kenji Kawaguchi, Vladimir Braverman, Haoyang Cao
The paper examines the common practice in diffusion and flow matching of predicting the clean signal, converting it to a velocity, and training with a velocity-space loss. It shows that this conversion can cause unstable optimization due to singular endpoint amplification, but that prediction–loss alignment removes this source of non‑integrability and ensures a finite second moment for all timesteps, even with uniform sampling. Experiments confirm that aligned objectives remain trainable across different samplers, reconciling theoretical concerns with empirical success.
By Jiadong Hong, Lei Liu, Xinyu Bian, Wenjie Wang, Zhaoyang Zhang
Discrete flow matching (DFM) provides a principled framework for generative modeling on discrete state spaces via continuous-time Markov chain dynamics. In practice, sampling for DFM commonly employs discretizations such as $τ$-leaping, yet efficient sampling methods under a limited number of function evaluations (NFE) remain less studied.
arXiv:2606. 24140v1 Announce Type: new Abstract: Discrete flow matching (DFM) provides a principled framework for generative modeling on discrete state spaces via continuous-time Markov chain dynamics.
By Feiyang Fu, Hehe Fan
arXiv:2509. 02971v2 Announce Type: replace-cross Abstract: Flow-based generative models can face numerical challenges on scientific data with multiscale Fourier spectra, often producing large errors at fine scales.
By Yifan Chen, Eric Vanden-Eijnden
arXiv:2602.12624v2 Announce Type: replace
Abstract: Diffusion-based generative models have achieved remarkable performance across various domains, yet their practical deployment is often limited by h...
By Sangwoo Jo, Sungjoon Choi
arXiv:2605. 12951v2 Announce Type: replace-cross Abstract: We propose Coreset-Induced Conditional Velocity Flow Matching (CCVFM), a generative model that augments hierarchical rectified flow with a data-informed source distribution.
By Xiao Wang, Zihua She, Jianxi Su
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: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