Score-Guided Proximal Projection: A Unified Geometric Framework for Rectified Flow Editing
arXiv:2603.05761v1 Announce Type: new 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 man
arXiv:2603.05761v1 Announce Type: new 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.
Executive Summary
This article proposes a novel framework, Score-Guided Proximal Projection (SGPP), for rectified flow editing. SGPP bridges the gap between deterministic optimization and stochastic sampling by reformulating the recovery task as a proximal optimization problem. This approach balances fidelity to the input with realism from the pre-trained score field, inducing a normal contraction property that guarantees out-of-distribution inputs are snapped onto the data manifold. The authors demonstrate that SGPP generalizes state-of-the-art editing methods and offers a continuous trade-off between strict identity preservation and generative freedom. This framework has significant implications for applications such as semantic editing and blind image recovery, where precise control over generative models is essential. By providing a unified geometric framework, SGPP offers a promising solution to the challenges faced by current approaches.
Key Points
- ▸ SGPP reformulates the recovery task as a proximal optimization problem, balancing fidelity and realism.
- ▸ SGPP induces a normal contraction property, snapping out-of-distribution inputs onto the data manifold.
- ▸ SGPP generalizes state-of-the-art editing methods and offers a continuous trade-off between identity preservation and generative freedom.
Merits
Unified Geometric Framework
SGPP provides a unified geometric framework that bridges the gap between deterministic optimization and stochastic sampling, offering a promising solution to the challenges faced by current approaches.
Normal Contraction Property
The normal contraction property induced by SGPP guarantees that out-of-distribution inputs are snapped onto the data manifold, ensuring that the model remains grounded in the data.
Generalizability
SGPP generalizes state-of-the-art editing methods, offering a continuous trade-off between strict identity preservation and generative freedom.
Demerits
Computational Complexity
The proximal optimization problem reformulated by SGPP may be computationally expensive, particularly for large-scale datasets.
Hyperparameter Sensitivity
The performance of SGPP may be sensitive to the choice of hyperparameters, particularly the relaxation of the proximal variance.
Expert Commentary
The proposed framework, SGPP, offers a promising solution to the challenges faced by current approaches to rectified flow editing. By providing a unified geometric framework, SGPP bridges the gap between deterministic optimization and stochastic sampling, inducing a normal contraction property that guarantees out-of-distribution inputs are snapped onto the data manifold. The authors' demonstration of SGPP's generalizability to state-of-the-art editing methods and its ability to offer a continuous trade-off between identity preservation and generative freedom further solidifies its potential. However, the computational complexity and hyperparameter sensitivity of SGPP require careful consideration and may limit its widespread adoption. Nonetheless, SGPP represents a significant advancement in the field of generative modeling and has the potential to revolutionize applications such as semantic editing and blind image recovery.
Recommendations
- ✓ Further research is needed to explore the computational complexity and hyperparameter sensitivity of SGPP and to develop more efficient and stable methods for controlling generative models.
- ✓ The development of SGPP highlights the need for more efficient and stable methods for controlling generative models, particularly in high-stakes applications such as healthcare and finance.