# Semantic Editing with Coupled Stochastic Differential Equations

arXiv: https://arxiv.org/abs/2509.24223 · HTML: https://mlsanity.com/paper/2509.24223/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 53 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 26 of 26)

- [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)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [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)
- [Taming Rectified Flow for Inversion and Editing](https://mlsanity.com/paper/2411.04746/) (2024)
- [DragonDiffusion: Enabling Drag-style Manipulation on Diffusion Models](https://mlsanity.com/paper/2307.02421/) (2023)
- [EGSDE: Unpaired Image-to-Image Translation via Energy-Guided Stochastic Differential Equations](https://mlsanity.com/paper/2207.06635/) (2022)
- [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)
- [Maximum Principle Based Algorithms for Deep Learning](https://mlsanity.com/paper/1710.09513/) (2017)
- [FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing](https://mlsanity.com/paper/2412.07517/) (2024)
- [The Blessing of Randomness: SDE Beats ODE in General Diffusion-based Image Editing](https://mlsanity.com/paper/2311.01410/) (2023)
- [Unveil Inversion and Invariance in Flow Transformer for Versatile Image Editing](https://mlsanity.com/paper/2411.15843/) (2024)
- [Training Free Guided Flow Matching with Optimal Control](https://mlsanity.com/paper/2410.18070/) (2024)
- [DNAEdit: Direct Noise Alignment for Text-Guided Rectified Flow Editing](https://mlsanity.com/paper/2506.01430/) (2025)

## Abstract (arXiv)

Editing the content of an image with a pretrained text-to-image model remains challenging. Existing methods often distort fine details or introduce unintended artifacts. We propose using coupled stochastic differential equations (coupled SDEs) to guide the sampling process of any pre-trained generative model that can be sampled by solving an SDE, including diffusion and rectified flow models. By driving both the source image and the edited image with the same correlated noise, our approach steers new samples toward the desired semantics while preserving visual similarity to the source. The method works out-of-the-box, without retraining or auxiliary networks, and achieves high prompt fidelity along with near-pixel-level consistency. These results position coupled SDEs as a simple yet powerful tool for controlled generative AI. Project page: https://z-jianxin.github.io/syncSDE-release/. Code: https://github.com/Z-Jianxin/syncSDE-release.