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This paper addresses the instability issues in Rectified Flow (RF) inversion, which arise from accumulated approximation errors during the inversion process. They introduce Proximal-Mean Inversion (PMI), a training-free gradient correction method that stabilizes the velocity field by guiding it towards a running average of past velocities within a theoretically-motivated spherical Gaussian constraint. The authors further propose mimic-CFG, a velocity correction scheme for editing tasks that interpolates between the current velocity and its projection onto the historical average.
Rectified Flow inversion gets a free lunch: stabilizing the velocity field with a simple running average of past velocities dramatically improves reconstruction and editing quality.
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.