# On Exact Inversion of DPM-Solvers

arXiv: https://arxiv.org/abs/2311.18387 · HTML: https://mlsanity.com/paper/2311.18387/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 41 of its 45 references that are in the map.
- First posted on arXiv 30 Nov 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 41)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (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)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [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)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Image2StyleGAN: How to Embed Images Into the StyleGAN Latent Space?](https://mlsanity.com/paper/1904.03189/) (2019)
- [DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulation](https://mlsanity.com/paper/2110.02711/) (2021)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [In-Domain GAN Inversion for Real Image Editing](https://mlsanity.com/paper/2004.00049/) (2020)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [Image2StyleGAN++: How to Edit the Embedded Images?](https://mlsanity.com/paper/1911.11544/) (2019)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Inversion-Based Style Transfer with Diffusion Models](https://mlsanity.com/paper/2211.13203/) (2022)
- [EDICT: Exact Diffusion Inversion via Coupled Transformations](https://mlsanity.com/paper/2211.12446/) (2022)

## Built on by (most cited first, 30 of 47)

- [Taming Rectified Flow for Inversion and Editing](https://mlsanity.com/paper/2411.04746/) (2024)
- [Improving the Training of Rectified Flows](https://mlsanity.com/paper/2405.20320/) (2024)
- [DiT4Edit: Diffusion Transformer for Image Editing](https://mlsanity.com/paper/2411.03286/) (2024)
- [An Undetectable Watermark for Generative Image Models](https://mlsanity.com/paper/2410.07369/) (2024)
- [Watermark Anything with Localized Messages](https://mlsanity.com/paper/2411.07231/) (2024)
- [Video Seal: Open and Efficient Video Watermarking](https://mlsanity.com/paper/2412.09492/) (2024)
- [ROBIN: Robust and Invisible Watermarks for Diffusion Models with Adversarial Optimization](https://mlsanity.com/paper/2411.03862/) (2024)
- [Lightning-Fast Image Inversion and Editing for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2312.12540/) (2023)
- [Unveil Inversion and Invariance in Flow Transformer for Versatile Image Editing](https://mlsanity.com/paper/2411.15843/) (2024)
- [BELM: Bidirectional Explicit Linear Multi-step Sampler for Exact Inversion in Diffusion Models](https://mlsanity.com/paper/2410.07273/) (2024)
- [DiffuseTrace: A Transparent and Flexible Watermarking Scheme for Latent Diffusion Model](https://mlsanity.com/paper/2405.02696/) (2024)
- [SmoothCache: A Universal Inference Acceleration Technique for Diffusion Transformers](https://mlsanity.com/paper/2411.10510/) (2024)
- [IntrinsicEdit: Precise generative image manipulation in intrinsic space](https://mlsanity.com/paper/2505.08889/) (2025)
- [Pixel Seal: Adversarial-only training for invisible image and video watermarking](https://mlsanity.com/paper/2512.16874/) (2025)
- [Dual-Schedule Inversion: Training- and Tuning-Free Inversion for Real Image Editing](https://mlsanity.com/paper/2412.11152/) (2024)
- [Gradient-free Decoder Inversion in Latent Diffusion Models](https://mlsanity.com/paper/2409.18442/) (2024)
- [MarkDiffusion: An Open-Source Toolkit for Generative Watermarking of Latent Diffusion Models](https://mlsanity.com/paper/2509.10569/) (2025)
- [Secure and Robust Watermarking for AI-generated Images: A Comprehensive Survey](https://mlsanity.com/paper/2510.02384/) (2025)
- [Oscillation Inversion: Understand the structure of Large Flow Model through the Lens of Inversion Method](https://mlsanity.com/paper/2411.11135/) (2024)
- [SuperMark: Robust and Training-free Image Watermarking via Diffusion-based Super-Resolution](https://mlsanity.com/paper/2412.10049/) (2024)
- [HOFAR: High-Order Augmentation of Flow Autoregressive Transformers](https://mlsanity.com/paper/2503.08032/) (2025)
- [Fine-Tuning Diffusion Models via Intermediate Distribution Shaping](https://mlsanity.com/paper/2510.02692/) (2025)
- [SemBind: Binding Diffusion Watermarks to Semantics Against Black-Box Forgery Attacks](https://mlsanity.com/paper/2601.20310/) (2026)
- [MeSS: City Mesh-Guided Outdoor Scene Generation with Cross-View Consistent Diffusion](https://mlsanity.com/paper/2508.15169/) (2025)
- [FlowOpt: Fast Optimization Through Whole Flow Processes for Training-Free Editing](https://mlsanity.com/paper/2510.22010/) (2025)
- [Learning to Watermark in the Latent Space of Generative Models](https://mlsanity.com/paper/2601.16140/) (2026)
- [Learning Single Index Models with Diffusion Priors](https://mlsanity.com/paper/2505.21135/) (2025)
- [Instability in Diffusion ODEs: An Explanation for Inaccurate Image Reconstruction](https://mlsanity.com/paper/2506.18290/) (2025)
- [Zero-Shot Video Deraining with Video Diffusion Models](https://mlsanity.com/paper/2511.18537/) (2025)
- [OSI: One-step Inversion Excels in Extracting Diffusion Watermarks](https://mlsanity.com/paper/2602.09494/) (2026)

## Abstract (arXiv)

Diffusion probabilistic models (DPMs) are a key component in modern generative models. DPM-solvers have achieved reduced latency and enhanced quality significantly, but have posed challenges to find the exact inverse (i.e., finding the initial noise from the given image). Here we investigate the exact inversions for DPM-solvers and propose algorithms to perform them when samples are generated by the first-order as well as higher-order DPM-solvers. For each explicit denoising step in DPM-solvers, we formulated the inversions using implicit methods such as gradient descent or forward step method to ensure the robustness to large classifier-free guidance unlike the prior approach using fixed-point iteration. Experimental results demonstrated that our proposed exact inversion methods significantly reduced the error of both image and noise reconstructions, greatly enhanced the ability to distinguish invisible watermarks and well prevented unintended background changes consistently during image editing. Project page: urlhttps://smhongok.github.io/inv-dpm.html.