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

Recent advances in flow-based generative models have enabled training-free, text-guided image editing by inverting an image into its latent noise and regenerating it under a new target conditional guidance. However, existing methods struggle to preserve source fidelity: higher-order solvers incur additional model inferences, truncated inversion constrains editability, and feature injection methods lack architectural transferability. To address these limitations, we propose SteerFlow, a model-agnostic editing framework with strong theoretical guarantees on source fidelity. In the forward process, we introduce an Amortized Fixed-Point Solver that implicitly straightens the forward trajectory by enforcing velocity consistency across consecutive timesteps, yielding a high-fidelity inverted latent. In the backward process, we introduce Trajectory Interpolation, which adaptively blends target-editing and source-reconstruction velocities to keep the editing trajectory anchored to the source. To further improve background preservation, we introduce an Adaptive Masking mechanism that spatially constrains the editing signal with concept-guided segmentation and source-target velocity differences. Extensive experiments on FLUX.1-dev and Stable Diffusion 3.5 Medium demonstrate that SteerFlow consistently achieves better editing quality than existing methods. Finally, we show that SteerFlow extends naturally to a complex multi-turn editing paradigm without accumulating drift.

Flow-based image editing (FlowEdit) enables inversion-free semantic changes through the difference between source and target velocities. In this paper, we observe that FlowEdit's default classifier-free guidance (CFG) configuration, with asymmetric source and target scales, causes substantial background leakage. Matching these guidance scales, for example by removing CFG, improves edit-relevant localization but severely degrades editability. To get the best of both worlds, we propose DecFlowEdit, which decouples the optimal guidance scales for localization and for editing in flow-based generative models. In particular, DecFlowEdit first extracts an edit-relevant prior by temporally aggregating velocity differences evaluated without CFG, and then uses this prior to reweight the original updates under default CFG. Our method remains training-free and inversion-free, requiring neither external spatial masks nor attention manipulation. Experiments on PIE-Bench across FLUX, SD3, and SD3.5 show that DecFlowEdit improves background preservation, reducing structure distance by approximately 61 to 73 percent and background LPIPS by 68 to 80 percent relative to FlowEdit at comparable editing fidelity.

Generative models based on flow matching have emerged as a powerful paradigm for inverse problems, offering straighter trajectories and faster sampling compared to diffusion models. However, existing approaches often necessitate differentiating through unrolled paths, leading to numerical instability and prohibitive computational overhead. To address this, we propose P-Flow, a framework that stabilizes the reconstruction process by leveraging a proxy gradient to update the source point. This approach effectively circumvents the numerical instability and memory overhead of long-chain differentiation. To ensure consistency with the prior distribution, we employ a Gaussian spherical projection motivated by the concentration of measure phenomenon in high-dimensional spaces. We further provide a theoretical analysis for P-Flow based on Bayesian theory and Lipschitz continuity. Experiments across diverse restoration tasks demonstrate that P-Flow delivers competitive performance, especially under extreme degradations such as severely ill-posed conditions and high measurement noise.