# PnP-CM: Consistency Models as Plug-and-Play Priors for Inverse Problems

arXiv: https://arxiv.org/abs/2509.22736 · HTML: https://mlsanity.com/paper/2509.22736/

## Key facts

- Cited by 5 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 53 of its 77 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## 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 53)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [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)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [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)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights](https://mlsanity.com/paper/1503.01243/) (2015)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
- [Deep Learning Methods for Parallel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1904.01112/) (2019)

## Built on by (most cited first, 5 of 5)

- [Stochastic Generative Plug-and-Play Priors](https://mlsanity.com/paper/2604.03603/) (2026)
- [Time-Embedded Algorithm Unrolling for Computational MRI](https://mlsanity.com/paper/2510.16321/) (2025)
- [Harnessing Magnitude-Only and Complex Measurements for Improved Dynamic MRI Reconstruction with Learned Priors](https://mlsanity.com/paper/2608.18036/) (2026)
- [Consistency Models for Fast MRI Reconstruction Using Regularization by Denoising](https://mlsanity.com/paper/2608.20561/) (2026)
- [S3-PnP: Plug-and-Play Denoising for Scientific Imaging with Self-Supervised Score Priors](https://mlsanity.com/paper/2610.18458/) (2026)

## Abstract (arXiv)

Diffusion models have found extensive use in solving inverse problems, by sampling from an approximate posterior distribution of data given the measurements. Recently, consistency models (CMs) have been proposed to directly predict the final output from any point on the diffusion ODE trajectory, enabling high-quality sampling in just a few neural function evaluations (NFEs). CMs have also been utilized for inverse problems, but existing CM-based solvers either require additional task-specific training or utilize data fidelity operations with slow convergence, limiting their applicability to large-scale problems and making them difficult to extend to nonlinear settings. In this work, we reinterpret CMs as proximal operators of a prior, enabling their integration into plug-and-play (PnP) frameworks. Specifically, we propose PnP-CM, an ADMM-based PnP solver that provides a unified framework for solving a wide range of inverse problems, and incorporates noise perturbations and momentum-based updates to improve performance in the low-NFE regime. We evaluate our approach on a diverse set of linear and nonlinear inverse problems. We also train and apply CMs to MRI data for the first time. Our results show that PnP-CM achieves high-quality reconstructions in as few as 4 NFEs, and produces meaningful results in 2 steps, highlighting its effectiveness in real-world inverse problems while outperforming existing CM-based approaches.