Divergence-Suppressing Couplings for Rectified Flow

TL;DR

This paper introduces divergence-suppressing couplings for Rectified Flow, reducing trajectory distortion caused by divergence in the velocity field, leading to improved performance in synthetic benchmarks and image generation.

Contribution

It proposes an offline correction method to suppress divergence in learned velocity fields, enhancing Rectified Flow's trajectory accuracy without additional runtime cost.

Findings

Consistent improvements on 2D synthetic benchmarks.

Enhanced image generation quality.

Offline correction effectively reduces trajectory distortion.

Abstract

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.