Rectified-Flow (RF)-based generative models have recently emerged as strong alternatives to traditional diffusion models, demonstrating state-of-the-art performance across various tasks. By learning a continuous velocity field that transforms simple noise into complex data, RF-based models not only enable high-quality generation, but also support training-free inversion, which facilitates downstream tasks such as reconstruction and editing. However, existing inversion methods, such as vanilla RF-based inversion, suffer from approximation errors that accumulate across timesteps, leading to unstable velocity fields and degraded reconstruction and editing quality. To address this challenge, we propose Proximal-Mean Inversion (PMI), a training-free gradient correction method that stabilizes the velocity field by guiding it toward a running average of past velocities, constrained within a theoretically derived spherical Gaussian. Furthermore, we introduce mimic-CFG, a lightweight velocity correction scheme for editing tasks, which interpolates between the current velocity and its projection onto the historical average, balancing editing effectiveness and structural consistency. Extensive experiments on PIE-Bench demonstrate that our methods significantly improve inversion stability, image reconstruction quality, and editing fidelity, while reducing the required number of neural function evaluations. Our approach achieves state-of-the-art performance on the PIE-Bench with enhanced efficiency and theoretical soundness.

翻译：基于整流流（RF）的生成模型近期已成为传统扩散模型的有力替代方案，在各类任务中展现出最先进的性能。通过学习将简单噪声转化为复杂数据的连续速度场，RF模型不仅能够实现高质量生成，还支持免训练反演，从而促进重建与编辑等下游任务。然而，现有反演方法（如基于RF的朴素反演）存在近似误差随时间步累积的问题，导致速度场失稳，并降低重建与编辑质量。为解决这一挑战，我们提出近端均值反演（PMI），这是一种免训练的梯度校正方法，通过将速度场引导至历史速度的滑动平均方向（约束在理论推导的球面高斯分布内）以实现稳定化。此外，我们提出mimic-CFG——一种面向编辑任务的轻量级速度校正方案，该方法在当前速度与其历史平均投影之间进行插值，以平衡编辑效果与结构一致性。在PIE-Bench上的大量实验表明，我们的方法显著提升了反演稳定性、图像重建质量与编辑保真度，同时减少了所需的神经网络函数评估次数。本方法在PIE-Bench上实现了最先进的性能，兼具更高的效率与理论严谨性。