# EDICT: Exact Diffusion Inversion via Coupled Transformations

arXiv: https://arxiv.org/abs/2211.12446 · HTML: https://mlsanity.com/paper/2211.12446/

## Key facts

- Cited by 258 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 30 of its 34 references that are in the map.
- First posted on arXiv 22 Nov 2022.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 30 of 30)

- [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)
- [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)
- [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)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [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)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Imagic: Text-Based Real Image Editing with Diffusion Models](https://mlsanity.com/paper/2210.09276/) (2022)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers](https://mlsanity.com/paper/2211.01324/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [DiffEdit: Diffusion-based semantic image editing with mask guidance](https://mlsanity.com/paper/2210.11427/) (2022)
- [Dual Diffusion Implicit Bridges for Image-to-Image Translation](https://mlsanity.com/paper/2203.08382/) (2022)
- [On Fast Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.00132/) (2021)
- [Diffusion-based Image Translation using Disentangled Style and Content Representation](https://mlsanity.com/paper/2209.15264/) (2022)
- [Unifying Diffusion Models' Latent Space, with Applications to CycleDiffusion and Guidance](https://mlsanity.com/paper/2210.05559/) (2022)

## Built on by (most cited first, 30 of 258)

- [BLIP-Diffusion: Pre-trained Subject Representation for Controllable Text-to-Image Generation and Editing](https://mlsanity.com/paper/2305.14720/) (2023)
- [SVDiff: Compact Parameter Space for Diffusion Fine-Tuning](https://mlsanity.com/paper/2303.11305/) (2023)
- [Emu Edit: Precise Image Editing via Recognition and Generation Tasks](https://mlsanity.com/paper/2311.10089/) (2023)
- [Video-P2P: Video Editing with Cross-attention Control](https://mlsanity.com/paper/2303.04761/) (2023)
- [Composer: Creative and Controllable Image Synthesis with Composable Conditions](https://mlsanity.com/paper/2302.09778/) (2023)
- [Text-to-image Diffusion Models in Generative AI: A Survey](https://mlsanity.com/paper/2303.07909/) (2023)
- [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)
- [Diffusion Model-Based Image Editing: A Survey](https://mlsanity.com/paper/2402.17525/) (2024)
- [Taming Rectified Flow for Inversion and Editing](https://mlsanity.com/paper/2411.04746/) (2024)
- [UniControl: A Unified Diffusion Model for Controllable Visual Generation In the Wild](https://mlsanity.com/paper/2305.11147/) (2023)
- [HQ-Edit: A High-Quality Dataset for Instruction-based Image Editing](https://mlsanity.com/paper/2404.09990/) (2024)
- [Tree-Ring Watermarks: Fingerprints for Diffusion Images that are Invisible and Robust](https://mlsanity.com/paper/2305.20030/) (2023)
- [TF-ICON: Diffusion-Based Training-Free Cross-Domain Image Composition](https://mlsanity.com/paper/2307.12493/) (2023)
- [HIVE: Harnessing Human Feedback for Instructional Visual Editing](https://mlsanity.com/paper/2303.09618/) (2023)
- [InstructDiffusion: A Generalist Modeling Interface for Vision Tasks](https://mlsanity.com/paper/2309.03895/) (2023)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)
- [Direct Inversion: Boosting Diffusion-based Editing with 3 Lines of Code](https://mlsanity.com/paper/2310.01506/) (2023)
- [Editing Implicit Assumptions in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.08084/) (2023)
- [ReNoise: Real Image Inversion Through Iterative Noising](https://mlsanity.com/paper/2403.14602/) (2024)
- [State of the Art on Diffusion Models for Visual Computing](https://mlsanity.com/paper/2310.07204/) (2023)
- [One-Step Image Translation with Text-to-Image Models](https://mlsanity.com/paper/2403.12036/) (2024)
- [Stable Flow: Vital Layers for Training-Free Image Editing](https://mlsanity.com/paper/2411.14430/) (2024)
- [Robust Watermarking Using Generative Priors Against Image Editing: From Benchmarking to Advances](https://mlsanity.com/paper/2410.18775/) (2024)
- [End-to-End Diffusion Latent Optimization Improves Classifier Guidance](https://mlsanity.com/paper/2303.13703/) (2023)
- [Improving the Training of Rectified Flows](https://mlsanity.com/paper/2405.20320/) (2024)
- [Optimizing Diffusion Noise Can Serve As Universal Motion Priors](https://mlsanity.com/paper/2312.11994/) (2023)
- [FreeControl: Training-Free Spatial Control of Any Text-to-Image Diffusion Model with Any Condition](https://mlsanity.com/paper/2312.07536/) (2023)
- [Arbitrary-steps Image Super-resolution via Diffusion Inversion](https://mlsanity.com/paper/2412.09013/) (2024)
- [A Complete Survey on Generative AI (AIGC): Is ChatGPT from GPT-4 to GPT-5 All You Need?](https://mlsanity.com/paper/2303.11717/) (2023)

## Abstract (arXiv)

Finding an initial noise vector that produces an input image when fed into the diffusion process (known as inversion) is an important problem in denoising diffusion models (DDMs), with applications for real image editing. The state-of-the-art approach for real image editing with inversion uses denoising diffusion implicit models (DDIMs) to deterministically noise the image to the intermediate state along the path that the denoising would follow given the original conditioning. However, DDIM inversion for real images is unstable as it relies on local linearization assumptions, which result in the propagation of errors, leading to incorrect image reconstruction and loss of content. To alleviate these problems, we propose Exact Diffusion Inversion via Coupled Transformations (EDICT), an inversion method that draws inspiration from affine coupling layers. EDICT enables mathematically exact inversion of real and model-generated images by maintaining two coupled noise vectors which are used to invert each other in an alternating fashion. Using Stable Diffusion, a state-of-the-art latent diffusion model, we demonstrate that EDICT successfully reconstructs real images with high fidelity. On complex image datasets like MS-COCO, EDICT reconstruction significantly outperforms DDIM, improving the mean square error of reconstruction by a factor of two. Using noise vectors inverted from real images, EDICT enables a wide range of image edits--from local and global semantic edits to image stylization--while maintaining fidelity to the original image structure. EDICT requires no model training/finetuning, prompt tuning, or extra data and can be combined with any pretrained DDM. Code is available at https://github.com/salesforce/EDICT.