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

Effective image inversion in rectified flow models—mapping real images to editable latent representations—is crucial for practical image editing applications, however achieving optimal balance between reconstruction fidelity and editing flexibility remains a fundamental challenge. In this work, we introduce the Optimal Transport Inversion Pipeline (OTIP), a zero-shot framework that leverages optimal transport theory to guide the inversion process in rectified flow models. Our underlying hypothesis is that incorporating transport-based guidance during the reverse diffusion process can effectively balance reconstruction accuracy and editing controllability through principled trajectory optimization. The method computes optimal transport paths between image and noise distributions while maintaining computational efficiency. Our approach achieves high-fidelity reconstruction with LPIPS scores of 0.001 and SSIM of 0.992 on face editing benchmarks, demonstrating superior preservation of fine-grained details compared to existing methods. We evaluate the framework across multiple editing tasks, observing 7.8\% to 12.9\% improvements in reconstruction loss over RF-Inversion on the LSUN-Bedroom and LSUN-Church datasets, respectively. For semantic face editing, our method achieves an 11.2\% improvement in identity preservation and a 1.6\% enhancement in perceptual quality, while maintaining computational efficiency comparable to baseline approaches. Qualitatively, our method produces visually compelling edits with superior semantic consistency and fine-grained detail preservation across diverse editing scenarios. Code is available at https://anonymous.4open.science/r/OT-Inversion.