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arXiv AI

AREX: Affine-Residual Exponential Integrator for Few-Step Sampling in Flow Matching

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.

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arXiv AI
Sep 2

Training-Free Refinement of Flow Matching with Divergence-based Sampling

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
diffusion
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arXiv Machine Learning
Sep 11

Prediction--Loss Alignment for Sampler--Robust Flow Matching Training

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
diffusionsafety
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arXiv Machine Learning
Sep 3

CAT-Flow: Curvature-Adaptive sTeps for Flow Matching

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%.

By Qinchan Li, Pedro Cisneros-Velarde, Keru Fu, Samuel Antunes Miranda, Sharan Vaswani, Hao Zhang
diffusionbenchmarks
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