# Free Lunch for Stabilizing Rectified Flow Inversion arXiv: https://arxiv.org/abs/2602.11850 ยท HTML: https://mlsanity.com/paper/2602.11850/ ## Key facts - Cited by 2 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 44 of its 51 references that are in the map. - First posted on arXiv 12 Feb 2026. ## 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 44) - [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (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) - [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022) - [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) - [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022) - [FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space](https://mlsanity.com/paper/2506.15742/) (2025) - [EDICT: Exact Diffusion Inversion via Coupled Transformations](https://mlsanity.com/paper/2211.12446/) (2022) - [An Edit Friendly DDPM Noise Space: Inversion and Manipulations](https://mlsanity.com/paper/2304.06140/) (2023) - [FlowEdit: Inversion-Free Text-Based Editing Using Pre-Trained Flow Models](https://mlsanity.com/paper/2412.08629/) (2024) - [TripoSG: High-Fidelity 3D Shape Synthesis using Large-Scale Rectified Flow Models](https://mlsanity.com/paper/2502.06608/) (2025) - [Taming Rectified Flow for Inversion and Editing](https://mlsanity.com/paper/2411.04746/) (2024) - [Negative-prompt Inversion: Fast Image Inversion for Editing with Text-guided Diffusion Models](https://mlsanity.com/paper/2305.16807/) (2023) - [Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations](https://mlsanity.com/paper/2410.10792/) (2024) - [ReNoise: Real Image Inversion Through Iterative Noising](https://mlsanity.com/paper/2403.14602/) (2024) - [Inversion-Free Image Editing with Natural Language](https://mlsanity.com/paper/2312.04965/) (2023) - [Prompt Tuning Inversion for Text-Driven Image Editing Using Diffusion Models](https://mlsanity.com/paper/2305.04441/) (2023) - [Improving Tuning-Free Real Image Editing with Proximal Guidance](https://mlsanity.com/paper/2306.05414/) (2023) - [Effective Real Image Editing with Accelerated Iterative Diffusion Inversion](https://mlsanity.com/paper/2309.04907/) (2023) - [Guidance with Spherical Gaussian Constraint for Conditional Diffusion](https://mlsanity.com/paper/2402.03201/) (2024) - [FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing](https://mlsanity.com/paper/2412.07517/) (2024) - [Frieren: Efficient Video-to-Audio Generation Network with Rectified Flow Matching](https://mlsanity.com/paper/2406.00320/) (2024) - [CFG-Zero*: Improved Classifier-Free Guidance for Flow Matching Models](https://mlsanity.com/paper/2503.18886/) (2025) - [Steering Rectified Flow Models in the Vector Field for Controlled Image Generation](https://mlsanity.com/paper/2412.00100/) (2024) - [UniEdit-Flow: Unleashing Inversion and Editing in the Era of Flow Models](https://mlsanity.com/paper/2504.13109/) (2025) - [Lightning-Fast Image Inversion and Editing for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2312.12540/) (2023) - [Unveil Inversion and Invariance in Flow Transformer for Versatile Image Editing](https://mlsanity.com/paper/2411.15843/) (2024) - [SplatFlow: Multi-View Rectified Flow Model for 3D Gaussian Splatting Synthesis](https://mlsanity.com/paper/2411.16443/) (2024) - [TurboEdit: Instant text-based image editing](https://mlsanity.com/paper/2408.08332/) (2024) ## Built on by (most cited first, 2 of 2) - [IMS3: Breaking Distributional Aggregation in Diffusion-Based Dataset Distillation](https://mlsanity.com/paper/2603.13960/) (2026) - [Root-Selecting Fixed-Point Inversion for Rectified Flows via Trajectory Straightness](https://mlsanity.com/paper/2606.17584/) (2026) ## Abstract (arXiv) Rectified-Flow (RF)-based generative models have recently emerged as strong alternatives to traditional diffusion models, demonstrating state-of-the-art performance across various tasks. By learning a continuous velocity field that transforms simple noise into complex data, RF-based models not only enable high-quality generation, but also support training-free inversion, which facilitates downstream tasks such as reconstruction and editing. However, existing inversion methods, such as vanilla RF-based inversion, suffer from approximation errors that accumulate across timesteps, leading to unstable velocity fields and degraded reconstruction and editing quality. To address this challenge, we propose Proximal-Mean Inversion (PMI), a training-free gradient correction method that stabilizes the velocity field by guiding it toward a running average of past velocities, constrained within a theoretically derived spherical Gaussian. Furthermore, we introduce mimic-CFG, a lightweight velocity correction scheme for editing tasks, which interpolates between the current velocity and its projection onto the historical average, balancing editing effectiveness and structural consistency. Extensive experiments on PIE-Bench demonstrate that our methods significantly improve inversion stability, image reconstruction quality, and editing fidelity, while reducing the required number of neural function evaluations. Our approach achieves state-of-the-art performance on the PIE-Bench with enhanced efficiency and theoretical soundness.