Semantic Editing with Coupled Stochastic Differential Equations

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.

Editing an image with a text request often changes more than intended, such as lighting, texture, faces, or background details. We introduce sync-SDE, a simple way to keep an edited image closely tied to the original. It guides the original and edited versions through the same random steps, so unchanged parts stay aligned while the requested change is made. The method works with existing image-generation systems without retraining or extra networks. Experiments show that it follows edit requests while better preserving the rest of the image.