# Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations

arXiv: https://arxiv.org/abs/2410.10792 · HTML: https://mlsanity.com/paper/2410.10792/

## Key facts

- Cited by 165 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 55 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## 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)
- [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)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (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)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation](https://mlsanity.com/paper/2211.12572/) (2022)
- [DiffEdit: Diffusion-based semantic image editing with mask guidance](https://mlsanity.com/paper/2210.11427/) (2022)
- [DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulation](https://mlsanity.com/paper/2110.02711/) (2021)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [An Edit Friendly DDPM Noise Space: Inversion and Manipulations](https://mlsanity.com/paper/2304.06140/) (2023)
- [HyperDreamBooth: HyperNetworks for Fast Personalization of Text-to-Image Models](https://mlsanity.com/paper/2307.06949/) (2023)
- [Style Aligned Image Generation via Shared Attention](https://mlsanity.com/paper/2312.02133/) (2023)

## Built on by (most cited first, 30 of 165)

- [OminiControl: Minimal and Universal Control for Diffusion Transformer](https://mlsanity.com/paper/2411.15098/) (2024)
- [FlowEdit: Inversion-Free Text-Based Editing Using Pre-Trained Flow Models](https://mlsanity.com/paper/2412.08629/) (2024)
- [Taming Rectified Flow for Inversion and Editing](https://mlsanity.com/paper/2411.04746/) (2024)
- [ReCapture: Generative Video Camera Controls for User-Provided Videos using Masked Video Fine-Tuning](https://mlsanity.com/paper/2411.05003/) (2024)
- [FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing](https://mlsanity.com/paper/2412.07517/) (2024)
- [KV-Edit: Training-Free Image Editing for Precise Background Preservation](https://mlsanity.com/paper/2502.17363/) (2025)
- [EEdit: Rethinking the Spatial and Temporal Redundancy for Efficient Image Editing](https://mlsanity.com/paper/2503.10270/) (2025)
- [VoxHammer: Training-Free Precise and Coherent 3D Editing in Native 3D Space](https://mlsanity.com/paper/2508.19247/) (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)
- [LumiNet: Latent Intrinsics Meets Diffusion Models for Indoor Scene Relighting](https://mlsanity.com/paper/2412.00177/) (2024)
- [AnimateAnything: Consistent and Controllable Animation for Video Generation](https://mlsanity.com/paper/2411.10836/) (2024)
- [Unveil Inversion and Invariance in Flow Transformer for Versatile Image Editing](https://mlsanity.com/paper/2411.15843/) (2024)
- [FlowAlign: Trajectory-Regularized, Inversion-Free Flow-based Image Editing](https://mlsanity.com/paper/2505.23145/) (2025)
- [DragFlow: Unleashing DiT Priors with Region Based Supervision for Drag Editing](https://mlsanity.com/paper/2510.02253/) (2025)
- [Follow-Your-Shape: Shape-Aware Image Editing via Trajectory-Guided Region Control](https://mlsanity.com/paper/2508.08134/) (2025)
- [UniCombine: Unified Multi-Conditional Combination with Diffusion Transformer](https://mlsanity.com/paper/2503.09277/) (2025)
- [DNAEdit: Direct Noise Alignment for Text-Guided Rectified Flow Editing](https://mlsanity.com/paper/2506.01430/) (2025)
- [Personalize Anything for Free with Diffusion Transformer](https://mlsanity.com/paper/2503.12590/) (2025)
- [Edit Away and My Face Will not Stay: Personal Biometric Defense against Malicious Generative Editing](https://mlsanity.com/paper/2411.16832/) (2024)
- [Training-Free Text-Guided Image Editing with Visual Autoregressive Model](https://mlsanity.com/paper/2503.23897/) (2025)
- [Personalized Image Generation with Deep Generative Models: A Decade Survey](https://mlsanity.com/paper/2502.13081/) (2025)
- [Multi-turn Consistent Image Editing](https://mlsanity.com/paper/2505.04320/) (2025)
- [Exploring Multimodal Diffusion Transformers for Enhanced Prompt-based Image Editing](https://mlsanity.com/paper/2508.07519/) (2025)
- [FiVE: A Fine-grained Video Editing Benchmark for Evaluating Emerging Diffusion and Rectified Flow Models](https://mlsanity.com/paper/2503.13684/) (2025)
- [ReFlex: Text-Guided Editing of Real Images in Rectified Flow via Mid-Step Feature Extraction and Attention Adaptation](https://mlsanity.com/paper/2507.01496/) (2025)
- [SplitFlow: Flow Decomposition for Inversion-Free Text-to-Image Editing](https://mlsanity.com/paper/2510.25970/) (2025)
- [EditMGT: Unleashing Potentials of Masked Generative Transformers in Image Editing](https://mlsanity.com/paper/2512.11715/) (2025)
- [Flux Already Knows -- Activating Subject-Driven Image Generation without Training](https://mlsanity.com/paper/2504.11478/) (2025)
- [Memories of Forgotten Concepts](https://mlsanity.com/paper/2412.00782/) (2024)

## Abstract (arXiv)

Generative models transform random noise into images; their inversion aims to transform images back to structured noise for recovery and editing. This paper addresses two key tasks: (i) inversion and (ii) editing of a real image using stochastic equivalents of rectified flow models (such as Flux). Although Diffusion Models (DMs) have recently dominated the field of generative modeling for images, their inversion presents faithfulness and editability challenges due to nonlinearities in drift and diffusion. Existing state-of-the-art DM inversion approaches rely on training of additional parameters or test-time optimization of latent variables; both are expensive in practice. Rectified Flows (RFs) offer a promising alternative to diffusion models, yet their inversion has been underexplored. We propose RF inversion using dynamic optimal control derived via a linear quadratic regulator. We prove that the resulting vector field is equivalent to a rectified stochastic differential equation. Additionally, we extend our framework to design a stochastic sampler for Flux. Our inversion method allows for state-of-the-art performance in zero-shot inversion and editing, outperforming prior works in stroke-to-image synthesis and semantic image editing, with large-scale human evaluations confirming user preference.