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

2026-06-16

AI Summary

This work addresses the instability in image reconstruction and editing caused by the lack of an effective selection mechanism among multiple solutions in existing fixed-point inversion methods. To resolve this issue, we introduce trajectory linearity as a novel criterion for fixed-point selection, prioritizing solutions that yield straighter inverse trajectories during inversion. This principle-driven strategy enhances both accuracy and convergence, offering a superior inversion approach for Rectified Flows. Experimental results demonstrate that our method significantly outperforms current baselines on FLUX.1-dev and PIE-Bench, achieving higher-fidelity real-image reconstruction and more faithful prompt-based editing with improved source preservation.

Abstract

Finding the initial noise that generates a given data sample, known as inversion, is a key component for downstream applications such as training-free image editing. Existing fixed-point inversion methods improve inversion accuracy by formulating each inversion step as a fixed-point problem, but they lack a principled mechanism for selecting among multiple fixed-point solutions that can arise in practice. We observe that different selections induce different inversion trajectories, leading to substantial variation in reconstruction and editing quality. For rectified flows, we further find that this variation is closely associated with trajectory straightness, motivating straightness as a principled selection criterion. We propose SelFix, a fixed-point inversion method that selects fixed-point solutions inducing straighter inverse trajectories while retaining convergence to an exact inverse root under standard local assumptions. Experiments on FLUX.1-dev and PIE-Bench show that SelFix improves fixed-point inversion, achieving stronger real-image reconstruction and better source-preserving prompt-based editing than prior inversion baselines. The code is available at https://github.com/seminkim/selfix.

Problem

• inversion
• fixed-point
• rectified flows
• trajectory straightness
• image editing

Innovation

• fixed-point inversion
• rectified flows
• trajectory straightness
• image editing
• inversion trajectory