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

arXiv: https://arxiv.org/abs/2508.02363 · HTML: https://mlsanity.com/paper/2508.02363/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Image generation, text-to-image and editing, one of 14 directions in Diffusion models.
- Builds on 36 of its 43 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Placed in

- Diffusion models / [Image generation, text-to-image and editing](https://mlsanity.com/diffusion/image-generation-text-to-image-and-editing/)

## Builds on (most cited first, 30 of 36)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [InstructPix2Pix: Learning to Follow Image Editing Instructions](https://mlsanity.com/paper/2211.09800/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [MasaCtrl: Tuning-Free Mutual Self-Attention Control for Consistent Image Synthesis and Editing](https://mlsanity.com/paper/2304.08465/) (2023)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [EDICT: Exact Diffusion Inversion via Coupled Transformations](https://mlsanity.com/paper/2211.12446/) (2022)
- [HyperDreamBooth: HyperNetworks for Fast Personalization of Text-to-Image Models](https://mlsanity.com/paper/2307.06949/) (2023)
- [FlowEdit: Inversion-Free Text-Based Editing Using Pre-Trained Flow Models](https://mlsanity.com/paper/2412.08629/) (2024)
- [Style Aligned Image Generation via Shared Attention](https://mlsanity.com/paper/2312.02133/) (2023)
- [Taming Rectified Flow for Inversion and Editing](https://mlsanity.com/paper/2411.04746/) (2024)
- [Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations](https://mlsanity.com/paper/2410.10792/) (2024)
- [LEDITS++: Limitless Image Editing using Text-to-Image Models](https://mlsanity.com/paper/2311.16711/) (2023)
- [Direct Inversion: Boosting Diffusion-based Editing with 3 Lines of Code](https://mlsanity.com/paper/2310.01506/) (2023)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)

## Built on by (most cited first, 5 of 5)

- [ManipShield: A Unified Framework for Image Manipulation Detection, Localization and Explanation](https://mlsanity.com/paper/2511.14259/) (2025)
- [EditHF-1M: A Million-Scale Rich Human Preference Feedback for Image Editing](https://mlsanity.com/paper/2603.14916/) (2026)
- [EditRefiner: A Human-Aligned Agentic Framework for Image Editing Refinement](https://mlsanity.com/paper/2605.07457/) (2026)
- [Encoder-Decoder Manifold Alignment for Idempotent Generation](https://mlsanity.com/paper/2606.22304/) (2026)
- [Variance Reduction on the Camera Axis: Multi-View Score Distillation for 3D](https://mlsanity.com/paper/2606.29964/) (2026)

## Abstract (arXiv)

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