# The Blessing of Randomness: SDE Beats ODE in General Diffusion-based Image Editing

arXiv: https://arxiv.org/abs/2311.01410 · HTML: https://mlsanity.com/paper/2311.01410/

## Key facts

- Cited by 62 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 70 of its 80 references that are in the map.
- First posted on arXiv 2 Nov 2023.

## 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 70)

- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (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)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversion](https://mlsanity.com/paper/2208.01618/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)

## Built on by (most cited first, 30 of 62)

- [Diffusion Model-Based Image Editing: A Survey](https://mlsanity.com/paper/2402.17525/) (2024)
- [GaussCtrl: Multi-View Consistent Text-Driven 3D Gaussian Splatting Editing](https://mlsanity.com/paper/2403.08733/) (2024)
- [MotionStream: Real-Time Video Generation with Interactive Motion Controls](https://mlsanity.com/paper/2511.01266/) (2025)
- [Relightful Harmonization: Lighting-aware Portrait Background Replacement](https://mlsanity.com/paper/2312.06886/) (2023)
- [Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances](https://mlsanity.com/paper/2401.17958/) (2024)
- [SeedEdit 3.0: Fast and High-Quality Generative Image Editing](https://mlsanity.com/paper/2506.05083/) (2025)
- [EEdit: Rethinking the Spatial and Temporal Redundancy for Efficient Image Editing](https://mlsanity.com/paper/2503.10270/) (2025)
- [Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity](https://mlsanity.com/paper/2405.15986/) (2024)
- [Efficient Diffusion Models: A Comprehensive Survey from Principles to Practices](https://mlsanity.com/paper/2410.11795/) (2024)
- [CleanDiffuser: An Easy-to-use Modularized Library for Diffusion Models in Decision Making](https://mlsanity.com/paper/2406.09509/) (2024)
- [Efficient Diffusion Models: A Survey](https://mlsanity.com/paper/2502.06805/) (2025)
- [GoodDrag: Towards Good Practices for Drag Editing with Diffusion Models](https://mlsanity.com/paper/2404.07206/) (2024)
- [RegionDrag: Fast Region-Based Image Editing with Diffusion Models](https://mlsanity.com/paper/2407.18247/) (2024)
- [MagicQuill: An Intelligent Interactive Image Editing System](https://mlsanity.com/paper/2411.09703/) (2024)
- [Conditional Image Synthesis with Diffusion Models: A Survey](https://mlsanity.com/paper/2409.19365/) (2024)
- [DragFlow: Unleashing DiT Priors with Region Based Supervision for Drag Editing](https://mlsanity.com/paper/2510.02253/) (2025)
- [Unifying Bayesian Flow Networks and Diffusion Models through Stochastic Differential Equations](https://mlsanity.com/paper/2404.15766/) (2024)
- [Drag Your Gaussian: Effective Drag-Based Editing with Score Distillation for 3D Gaussian Splatting](https://mlsanity.com/paper/2501.18672/) (2025)
- [FastDrag: Manipulate Anything in One Step](https://mlsanity.com/paper/2405.15769/) (2024)
- [LightningDrag: Lightning Fast and Accurate Drag-based Image Editing Emerging from Videos](https://mlsanity.com/paper/2405.13722/) (2024)
- [VINCIE: Unlocking In-context Image Editing from Video](https://mlsanity.com/paper/2506.10941/) (2025)
- [GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Models](https://mlsanity.com/paper/2509.25170/) (2025)
- [DragText: Rethinking Text Embedding in Point-based Image Editing](https://mlsanity.com/paper/2407.17843/) (2024)
- [MvDrag3D: Drag-based Creative 3D Editing via Multi-view Generation-Reconstruction Priors](https://mlsanity.com/paper/2410.16272/) (2024)
- [FramePainter: Endowing Interactive Image Editing with Video Diffusion Priors](https://mlsanity.com/paper/2501.08225/) (2025)
- [Eta Inversion: Designing an Optimal Eta Function for Diffusion-based Real Image Editing](https://mlsanity.com/paper/2403.09468/) (2024)
- [PoseCrafter: One-Shot Personalized Video Synthesis Following Flexible Pose Control](https://mlsanity.com/paper/2405.14582/) (2024)
- [Consistent Image Layout Editing with Diffusion Models](https://mlsanity.com/paper/2503.06419/) (2025)
- [DragLoRA: Online Optimization of LoRA Adapters for Drag-based Image Editing in Diffusion Model](https://mlsanity.com/paper/2505.12427/) (2025)
- [EgoEdit: Dataset, Real-Time Streaming Model, and Benchmark for Egocentric Video Editing](https://mlsanity.com/paper/2512.06065/) (2025)

## Abstract (arXiv)

We present a unified probabilistic formulation for diffusion-based image editing, where a latent variable is edited in a task-specific manner and generally deviates from the corresponding marginal distribution induced by the original stochastic or ordinary differential equation (SDE or ODE). Instead, it defines a corresponding SDE or ODE for editing. In the formulation, we prove that the Kullback-Leibler divergence between the marginal distributions of the two SDEs gradually decreases while that for the ODEs remains as the time approaches zero, which shows the promise of SDE in image editing. Inspired by it, we provide the SDE counterparts for widely used ODE baselines in various tasks including inpainting and image-to-image translation, where SDE shows a consistent and substantial improvement. Moreover, we propose SDE-Drag -- a simple yet effective method built upon the SDE formulation for point-based content dragging. We build a challenging benchmark (termed DragBench) with open-set natural, art, and AI-generated images for evaluation. A user study on DragBench indicates that SDE-Drag significantly outperforms our ODE baseline, existing diffusion-based methods, and the renowned DragGAN. Our results demonstrate the superiority and versatility of SDE in image editing and push the boundary of diffusion-based editing methods.