Divergence-Suppressing Couplings for Rectified Flow

2026-05-18 · Source: Takara TLDR - Daily AI Papers · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

Rectified Flow (RF) models aim to generate straight trajectories for self-generated couplings, but practical implementations often suffer from bent and intertwined trajectories. This distortion is linked to regions of non-zero divergence in the learned velocity field, causing local expansion or contraction that steers particles away from ideal endpoints. Researchers propose "divergence-suppressing couplings" for Rectified Flow, an offline correction method that attenuates the divergent component of the learned velocity during coupling generation. This correction is applied once per coupling pair and amortized over training, meaning deployment uses standard Euler integration with no additional wall-clock cost compared to regular Rectified Flow. Empirical results show consistent improvements on 2D synthetic benchmarks and in image generation tasks.

Key takeaway

For research scientists developing or deploying Rectified Flow models, understanding that trajectory distortion stems from velocity field divergence is crucial. Implementing divergence-suppressing couplings as an offline correction can significantly improve model performance on tasks like image generation without incurring additional computational cost during inference. You should consider integrating this method to achieve straighter trajectories and more accurate outputs from your flow models.

Key insights

Trajectory entanglement in Rectified Flow is caused by divergent velocity fields, which can be corrected offline.

Principles

• Divergence in velocity fields distorts trajectories.
• Offline correction can improve flow model performance.

Method

An offline correction attenuates the divergent component of the learned velocity field during coupling generation, applied once per coupling pair and amortized over training.

In practice

• Improve Rectified Flow trajectory straightness.
• Enhance image generation quality.

Topics

• Rectified Flow
• Divergence Suppression
• Velocity Field Divergence
• Trajectory Entanglement
• Image Generation

Best for: Computer Vision Engineer, Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Takara TLDR - Daily AI Papers.