Bridging the Manifold Gap: Riemannian Residual Line Search for One-Step Image Editing

2026-06-23

AI Summary

This work addresses the challenge in single-step image editing where fixed-intensity transport updates struggle to simultaneously achieve target prompt alignment and source image fidelity. To resolve this, the authors formulate edit intensity selection as a posterior candidate filtering problem and propose a Riemannian residual line search strategy. This approach constructs stronger editing directions by estimating local temporal curvature and optimizes CLIP semantic alignment along a residual path. Notably, the method requires no modification to the underlying diffusion model, instead integrating energy-field transport, Riemannian geometric projection, and residual search. Evaluated on PIE-Bench++ across 700 samples and 10 editing categories, it achieves state-of-the-art performance among single-step editing algorithms.

Abstract

One-step diffusion editors are fast because they avoid inversion and iterative optimization, but a single transport update must be aggressive enough to realize the target prompt and conservative enough to preserve the source image--and no fixed update strength satisfies both demands across edit types. We treat this tension as a post-hoc candidate-selection problem on top of energy-field transport rather than as a new editing model. Our proposed method, Riemannian Residual Line Search, first builds a stronger edit by estimating the local time curvature of the prompt-delta field and projecting the corrected direction back onto the update norm of the original first-order energy-field transport estimation. It then forms a small residual path from the source image to this strong edit, retains the original first-order output as one candidate, and picks the final image by maximizing target-prompt CLIP alignment. On a 700-sample PIE-Bench++ evaluation across 10 edit type IDs, our method achieves state-of-the-art (SOTA) performance among current one-step update algorithms.

Problem

• one-step image editing
• manifold gap
• transport update
• edit-consistency trade-off
• diffusion editors

Innovation

• Riemannian Residual Line Search
• one-step diffusion editing
• energy-field transport
• CLIP alignment
• manifold-aware editing