Divergence-Suppressing Couplings for Rectified Flow
For practitioners of generative modeling using Rectified Flow, this work offers a simple, cost-free modification that improves coupling quality and generation performance.
The paper identifies that trajectory entanglement in Rectified Flow arises from nonzero divergence in the learned velocity field, and proposes an offline correction that suppresses divergence during coupling generation. This yields consistent improvements on 2D synthetic benchmarks and image generation.
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.