# DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models

arXiv: https://arxiv.org/abs/2405.16749 · HTML: https://mlsanity.com/paper/2405.16749/

## Key facts

- Cited by 61 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 61 of its 80 references that are in the map.
- First posted on arXiv 27 May 2024.

## 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 61)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulation](https://mlsanity.com/paper/2110.02711/) (2021)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [DeblurGAN: Blind Motion Deblurring Using Conditional Adversarial Networks](https://mlsanity.com/paper/1711.07064/) (2017)
- [DeblurGAN-v2: Deblurring (Orders-of-Magnitude) Faster and Better](https://mlsanity.com/paper/1908.03826/) (2019)
- [Generative Visual Manipulation on the Natural Image Manifold](https://mlsanity.com/paper/1609.03552/) (2016)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)

## Built on by (most cited first, 30 of 61)

- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints](https://mlsanity.com/paper/2506.04171/) (2025)
- [Gradient-Free Generation for Hard-Constrained Systems](https://mlsanity.com/paper/2412.01786/) (2024)
- [SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems](https://mlsanity.com/paper/2410.04479/) (2024)
- [Variational Control for Guidance in Diffusion Models](https://mlsanity.com/paper/2502.03686/) (2025)
- [Free Hunch: Denoiser Covariance Estimation for Diffusion Models Without Extra Costs](https://mlsanity.com/paper/2410.11149/) (2024)
- [Inverse Problems with Diffusion Models: A MAP Estimation Perspective](https://mlsanity.com/paper/2407.20784/) (2024)
- [A Baseline Method for Removing Invisible Image Watermarks using Deep Image Prior](https://mlsanity.com/paper/2502.13998/) (2025)
- [Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2505.20789/) (2025)
- [Whitened Score Diffusion: A Structured Prior for Imaging Inverse Problems](https://mlsanity.com/paper/2505.10311/) (2025)
- [D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matching](https://mlsanity.com/paper/2602.21469/) (2026)
- [Physics-informed diffusion models in spectral space](https://mlsanity.com/paper/2602.09708/) (2026)
- [Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Learnable Linear Extrapolation](https://mlsanity.com/paper/2503.10103/) (2025)
- [Temporal-Consistent Video Restoration with Pre-trained Diffusion Models](https://mlsanity.com/paper/2503.14863/) (2025)
- [Weak Diffusion Priors Can Still Achieve Strong Inverse-Problem Performance](https://mlsanity.com/paper/2601.22443/) (2026)
- [Provable diffusion-based posterior sampling for linear inverse problems via DDIM](https://mlsanity.com/paper/2607.19333/) (2026)
- [Dual Ascent Diffusion for Inverse Problems](https://mlsanity.com/paper/2505.17353/) (2025)
- [FMPlug: Plug-In Foundation Flow-Matching Priors for Inverse Problems](https://mlsanity.com/paper/2508.00721/) (2025)
- [Multitask Learning with Stochastic Interpolants](https://mlsanity.com/paper/2508.04605/) (2025)
- [Solving Diffusion Inverse Problems with Restart Posterior Sampling](https://mlsanity.com/paper/2511.20705/) (2025)
- [DM4CT: Benchmarking Diffusion Models for Computed Tomography Reconstruction](https://mlsanity.com/paper/2602.18589/) (2026)
- [Local MAP Sampling for Diffusion Models](https://mlsanity.com/paper/2510.07343/) (2025)
- [Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Sampling](https://mlsanity.com/paper/2510.09676/) (2025)
- [Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving](https://mlsanity.com/paper/2511.06138/) (2025)
- [Trajectory Stitching for Solving Inverse Problems with Flow-Based Models](https://mlsanity.com/paper/2602.08538/) (2026)
- [Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework](https://mlsanity.com/paper/2603.10281/) (2026)
- [Conditional flow matching for physics-constrained inverse problems with finite training data](https://mlsanity.com/paper/2603.14135/) (2026)
- [Noise-Adaptive Diffusion Sampling for Inverse Problems Without Task-Specific Tuning](https://mlsanity.com/paper/2604.16919/) (2026)
- [A Stability Benchmark of Generative Regularizers for Inverse Problems](https://mlsanity.com/paper/2605.10076/) (2026)
- [Couple to Control: Joint Initial Noise Design in Diffusion Models](https://mlsanity.com/paper/2605.11311/) (2026)

## Abstract (arXiv)

Pretrained diffusion models (DMs) have recently been popularly used in solving inverse problems (IPs). The existing methods mostly interleave iterative steps in the reverse diffusion process and iterative steps to bring the iterates closer to satisfying the measurement constraint. However, such interleaving methods struggle to produce final results that look like natural objects of interest (i.e., manifold feasibility) and fit the measurement (i.e., measurement feasibility), especially for nonlinear IPs. Moreover, their capabilities to deal with noisy IPs with unknown types and levels of measurement noise are unknown. In this paper, we advocate viewing the reverse process in DMs as a function and propose a novel plug-in method for solving IPs using pretrained DMs, dubbed DMPlug. DMPlug addresses the issues of manifold feasibility and measurement feasibility in a principled manner, and also shows great potential for being robust to unknown types and levels of noise. Through extensive experiments across various IP tasks, including two linear and three nonlinear IPs, we demonstrate that DMPlug consistently outperforms state-of-the-art methods, often by large margins especially for nonlinear IPs. The code is available at https://github.com/sun-umn/DMPlug.