通过抑制速度场发散，让流模型轨迹更直，提升生成质量。
Divergence-Suppressing Couplings for Rectified Flow
- 引入离线修正机制，抑制学习速度场中的发散成分。
- 在2D合成数据和图像生成任务上实现稳定性能提升。
- 无需增加推理成本，适合对轨迹精度要求高的生成场景。
Rectified Flow 的潜力在于生成轨迹近乎直线的自生成耦合。实际中，基础流模型生成的轨迹可能弯曲缠绕，导致耦合结果失真。本文发现，这种轨迹纠缠常与学习速度场中非零发散区域相关，局部扩张或收缩会扭曲轨迹，使粒子偏离理想终点。为此，提出用于 Rectified Flow 的发散抑制耦合方法，通过一次离线修正，衰减学习速度场中的发散分量。该修正每对耦合仅执行一次，可摊销到训练过程，部署时仍使用标准 Euler 积分，运行时间与传统 Rectified Flow 相同。实验表明，该离线修改在 2D 合成基准和图像生成任务上均带来一致性能提升。
原文摘要 · Abstract (English)
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.
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