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.

翻译：寻找生成给定数据样本的初始噪声（即反演）是无需训练图像编辑等下游应用的关键组成部分。现有定点反演方法通过将每个反演步骤建模为定点问题来提高反演精度，但缺乏一种原则性机制来选择实践中可能出现的多个定点解。我们观察到，不同的选择会产生不同的反演轨迹，导致重建和编辑质量出现显著差异。对于矫正流，我们进一步发现这种差异与轨迹直线度密切相关，这促使我们将直线度作为原则性的选择标准。我们提出SelFix，一种定点反演方法，它在标准局部假设下选择能生成更直反演轨迹的定点解，同时保持收敛到精确逆根。在FLUX.1-dev和PIE-Bench上的实验表明，SelFix改进了定点反演，比以往的反演基线实现了更强的真实图像重建和更好的源保留提示驱动编辑。代码可在https://github.com/seminkim/selfix获取。