Root-Selecting Fixed-Point Inversion for Rectified Flows via Trajectory Straightness

2026-06-16 · Source: Computer Vision and Pattern Recognition · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Computer Vision & Pattern Recognition · Depth: Expert, quick

Summary

SelFix is a novel fixed-point inversion method designed for rectified flows, addressing the challenge of selecting among multiple fixed-point solutions in existing inversion techniques. Inversion, which identifies the initial noise generating a data sample, is crucial for applications like training-free image editing. The authors observed that different fixed-point selections lead to varying inversion trajectories and impact reconstruction and editing quality. For rectified flows, this variation correlates with trajectory straightness, which SelFix utilizes as a principled selection criterion. SelFix ensures convergence to an exact inverse root under standard local assumptions. Experiments on FLUX.1-dev and PIE-Bench demonstrate that SelFix enhances fixed-point inversion, yielding superior real-image reconstruction and more effective source-preserving prompt-based editing compared to prior inversion baselines.

Key takeaway

For Machine Learning Engineers developing generative models or image editing tools, SelFix offers a critical improvement for rectified flow inversion. If you are struggling with inconsistent reconstruction or editing quality due to arbitrary fixed-point selections, you should integrate SelFix. Its principled approach, based on trajectory straightness, directly enhances real-image reconstruction and source-preserving prompt-based editing, as shown on FLUX.1-dev and PIE-Bench.

Key insights

Trajectory straightness provides a principled criterion for selecting fixed-point solutions in rectified flow inversion, improving reconstruction and editing.

Principles

• Fixed-point selection impacts inversion trajectory quality.
• Trajectory straightness correlates with inversion accuracy.
• Principled selection improves downstream application quality.

Method

SelFix selects fixed-point solutions that induce straighter inverse trajectories, ensuring convergence to an exact inverse root under local assumptions for rectified flows.

In practice

• Apply SelFix for improved real-image reconstruction.
• Use SelFix for better source-preserving editing.
• Consider trajectory straightness in flow-based models.

Topics

• Fixed-Point Inversion
• Rectified Flows
• Image Editing
• Trajectory Straightness
• SelFix
• Generative Models

Code references

• seminkim/selfix

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

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Editorial summary, takeaway, and curation by AIssential. Original article published by Computer Vision and Pattern Recognition.