Optimal Transport for Rectified Flow Image Editing: Unifying Inversion-Based and Direct Methods

Image editing in rectified flow models remains challenging due to the fundamental trade-off between reconstruction fidelity and editing flexibility. While inversion-based methods suffer from trajectory deviation, recent inversion-free approaches like FlowEdit offer direct editing pathways but can benefit from additional guidance to improve structure preservation. In this work, we demonstrate that optimal transport theory provides a unified framework for improving both paradigms in rectified flow editing. We introduce a zero-shot transport-guided inversion framework that leverages optimal transport during the reverse diffusion process, and extend optimal transport principles to enhance inversion-free methods through transport-optimized velocity field corrections. Incorporating transport-based guidance can effectively balance reconstruction accuracy and editing controllability across different rectified flow editing approaches. For inversion-based editing, our method achieves high-fidelity reconstruction with LPIPS scores of 0.001 and SSIM of 0.992 on face editing benchmarks, observing 7.8% to 12.9% improvements over RF-Inversion on LSUN datasets. For inversion-free editing with FlowEdit on FLUX and Stable Diffusion 3, we demonstrate consistent improvements in semantic consistency and structure preservation across diverse editing scenarios. Our semantic face editing experiments show an 11.2% improvement in identity preservation and enhanced perceptual quality. The unified optimal transport framework produces visually compelling edits with superior detail preservation across both inversion-based and direct editing paradigms. Code is available for RF-Inversion and FlowEdit at: https://github.com/marianlupascu/OT-RF