Divergence-Suppressing Couplings for Rectified Flow

Fuente: arXiv
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Main Authors: Min, Yimeng, Gomes, Carla P.
Format: Preprint
Published: 2026
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author Min, Yimeng
Gomes, Carla P.
author_facet Min, Yimeng
Gomes, Carla P.
contents The promise of Rectified Flow rests on producing self-generated couplings whose trajectories are straight, or nearly so. In practice, trajectories generated by the base flow model can bend and intertwine, and the resulting coupling inherits this distortion. In this paper, we identify that such trajectory entanglement is often associated with regions of nonzero divergence in the learned velocity field, where local expansion or contraction distorts trajectories and steers particles away from their ideal endpoints. We then propose divergence-suppressing couplings for Rectified Flow, an offline correction that attenuate the divergent component of the learned velocity during coupling generation. The correction is paid only once per coupling pair and amortized over training, so deployment runs plain Euler at identical wall-clock cost to standard Rectified Flow. Empirically, this offline modification yields consistent improvements on 2D synthetic benchmarks and on image generation.
format Preprint
id arxiv_https___arxiv_org_abs_2605_17733
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Divergence-Suppressing Couplings for Rectified Flow
Min, Yimeng
Gomes, Carla P.
Artificial Intelligence
Machine Learning
The promise of Rectified Flow rests on producing self-generated couplings whose trajectories are straight, or nearly so. In practice, trajectories generated by the base flow model can bend and intertwine, and the resulting coupling inherits this distortion. In this paper, we identify that such trajectory entanglement is often associated with regions of nonzero divergence in the learned velocity field, where local expansion or contraction distorts trajectories and steers particles away from their ideal endpoints. We then propose divergence-suppressing couplings for Rectified Flow, an offline correction that attenuate the divergent component of the learned velocity during coupling generation. The correction is paid only once per coupling pair and amortized over training, so deployment runs plain Euler at identical wall-clock cost to standard Rectified Flow. Empirically, this offline modification yields consistent improvements on 2D synthetic benchmarks and on image generation.
title Divergence-Suppressing Couplings for Rectified Flow
topic Artificial Intelligence
Machine Learning
url https://arxiv.org/abs/2605.17733