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.
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.
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.
The paper introduces a new optimal transport framework that uses the Barron energy—an intrinsic neural network complexity measure—instead of the traditional kinetic energy. By modeling transport as deep residual networks that map a reference distribution to a target distribution, the authors define a new metric on probability measures and analyze its properties for generative modeling. They demonstrate that diffusion generative models are suboptimal in this Barron geometry and explore how adaptivity can improve alternative generative approaches.
The paper introduces CAT-Flow, a pair of lightweight, training‑free algorithms—CAT‑OV and CAT‑OT—that adapt step‑sizes during Flow Matching inference by estimating curvature in time or state space. These methods avoid extra neural evaluations and achieve constant‑order truncation error bounds. Experiments show that CAT‑OV and CAT‑OT improve image quality metrics across four text‑to‑image Flow Matching models, cutting the required generation steps by up to 40%.
arXiv:2606. 06272v1 Announce Type: new Abstract: Generative Flow Networks (GFlowNets) are a framework for sampling structured objects via stochastic trajectories in a directed graph.
arXiv:2603. 00205v2 Announce Type: replace-cross Abstract: Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems.
arXiv:2606. 10450v1 Announce Type: cross Abstract: DiffC provides a principled way to reuse pre-trained diffusion models for lossy compression, but its encoding and decoding procedures remain slow because they require many discretized forward and reverse steps.
arXiv:2608. 02487v1 Announce Type: cross Abstract: Recently, rectified flow has emerged as a fundamental framework for large-scale image generation, powering state-of-the-art systems such as FLUX.
arXiv:2606. 03820v1 Announce Type: cross Abstract: We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps.
The paper investigates how one-step generative models, which compress multi-step diffusion processes, handle denoising across a single forward pass. It introduces the concept of "depth as time," showing that intermediate layers of a model can be decoded to reveal a denoising trajectory similar to multi-step diffusion. The study finds that models trained with a time-indexed transport task, such as MeanFlow, exhibit this depthwise denoising and can be highly compressed, whereas models without such a task do not show the same behavior.
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...