Score-Guided Proximal Projection: A Unified Geometric Framework for Rectified Flow Editing

Abstract: Rectified Flow (RF) models achieve state-of-the-art generation quality, yet controlling them for precise tasks -- such as semantic editing or blind image recovery -- remains a challenge. Current approaches bifurcate into inversion-based guidance, which suffers from "geometric locking" by rigidly adhering to the source trajectory, and posterior sampling approximations (e.g., DPS), which are computationally expensive and unstable. In this work, we propose Score-Guided Proximal Projection (SGPP), a unified framework that bridges the gap between deterministic optimization and stochastic sampling. We reformulate the recovery task as a proximal optimization problem, defining an energy landscape that balances fidelity to the input with realism from the pre-trained score field. We theoretically prove that this objective induces a normal contraction property, geometrically guaranteeing that out-of-distribution inputs are snapped onto the data manifold, and it effectively reaches the posterior mode constrained to the manifold. Crucially, we demonstrate that SGPP generalizes state-of-the-art editing methods: RF-inversion is effectively a limiting case of our framework. By relaxing the proximal variance, SGPP enables "soft guidance," offering a continuous, training-free trade-off between strict identity preservation and generative freedom.