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arxiv: 2509.22736 · v2 · submitted 2025-09-25 · 📡 eess.IV · cs.AI· cs.CV· cs.LG· physics.med-ph· stat.ML

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

Merve G\"ulle , Junno Yun , Ya\c{s}ar Utku Al\c{c}alar , Mehmet Ak\c{c}akaya This is my paper

Pith reviewed 2026-05-18 13:36 UTC · model grok-4.3

classification 📡 eess.IV cs.AIcs.CVcs.LGphysics.med-phstat.ML
keywords consistency modelsplug and playinverse problemsADMMproximal operatorsMRIdiffusion modelsimage reconstruction
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The pith

Consistency models can be reinterpreted as proximal operators to serve as plug-and-play priors in ADMM for solving inverse problems.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper reinterprets consistency models as proximal operators of a data prior. It integrates them into a plug-and-play ADMM framework called PnP-CM to solve various inverse problems without task-specific training. The solver includes noise perturbations and momentum updates to perform well with very few neural function evaluations. Readers would care if this makes high-quality image reconstruction faster and more flexible for applications like MRI.

Core claim

By treating consistency models as proximal operators, PnP-CM provides a unified ADMM-based solver that handles linear and nonlinear inverse problems, achieving high-quality results in as few as four neural function evaluations and meaningful outputs in two steps, while outperforming other consistency model approaches and being applied to MRI data for the first time.

What carries the argument

The PnP-ADMM iteration where the consistency model acts as the proximal operator for the prior, augmented with noise perturbation and momentum-based updates to handle the low number of function evaluations.

Load-bearing premise

That a consistency model trained on one dataset can function effectively as a proximal operator for the prior in a different inverse problem without any fine-tuning.

What would settle it

Reconstructing images from measurements in a new nonlinear inverse problem where PnP-CM produces artifacts or lower quality than traditional methods even after 4 steps would falsify the effectiveness claim.

Figures

Figures reproduced from arXiv: 2509.22736 by Junno Yun, Mehmet Ak\c{c}akaya, Merve G\"ulle, Ya\c{s}ar Utku Al\c{c}alar.

Figure 1
Figure 1. Figure 1: Representative results of our method (PnP-CM) on four distinct noisy inverse problems: [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Representative results for Gaussian deblurring, inpainting (70%), and super-resolution [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Qualitative comparisons of DPS, DDS, and PnP-CM. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Representative Gaussian deblurring results on LSUN Bedroom with [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Illustrative inpainting results on LSUN Bedroom with [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Demonstration of super resolution (×4) results on LSUN Bedroom with σy = 0.05. Reconstructions are compared against all baseline methods, with PnP-CM producing sharper details and closer resemblance to the ground truth. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Qualitative comparisons for R = 4 and R = 8 on the Coronal PD and Coronal PD￾FS datasets across different methods. The proposed method, PnP-CM, consistently demonstrates superior performance by effectively reducing artifacts. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes PnP-CM, a plug-and-play ADMM framework that reinterprets pre-trained consistency models as proximal operators of an implicit data prior for solving linear and nonlinear inverse problems. It incorporates noise perturbations to the CM input and momentum-based updates to the iterates specifically to stabilize performance in the low-NFE regime. The approach is evaluated on diverse inverse problems including MRI reconstruction (claimed as the first application of CMs to MRI), with the central claim that it achieves high-quality results in as few as 4 NFEs (and meaningful results in 2 steps) while outperforming existing CM-based solvers without task-specific training.

Significance. If the performance claims and the proximal reinterpretation hold under scrutiny, the work would provide a training-free, unified PnP route for deploying fast consistency models on large-scale and nonlinear inverse problems, addressing a practical gap where prior CM solvers either require fine-tuning or exhibit slow convergence.

major comments (2)
  1. [Proposed PnP-CM algorithm and low-NFE stabilization] The central construction treats the CM output as the proximal map of an implicit prior inside ADMM. However, the method description explicitly adds noise perturbations to the input of the CM and momentum-based updates to the ADMM iterates specifically to stabilize the low-NFE regime. This indicates that the bare proximal reinterpretation (i.e., feeding the current ADMM variable directly into a fixed pre-trained CM) does not by itself produce the reported 2- and 4-NFE results. If the unmodified proximal step already satisfies the necessary fixed-point or contraction properties for ADMM, the extra mechanisms would be superfluous; their inclusion therefore suggests an unstated mismatch between the CM consistency function and the proximal operator required by the splitting.
  2. [Experimental results and evaluation] The abstract states that the method was evaluated on diverse linear and nonlinear problems including MRI and that it outperforms prior CM approaches, but provides no quantitative metrics, baseline details, or ablation results on the contribution of the added noise schedule and momentum coefficient. Without these, the central performance claims cannot be verified and the load-bearing role of the proposed adaptations remains unclear.
minor comments (1)
  1. [Method] Notation for the momentum coefficient and noise perturbation schedule should be introduced with explicit definitions and ranges early in the method section to improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. We address each major comment below, clarifying the algorithmic foundations and committing to expanded experimental documentation in the revision.

read point-by-point responses

  1. Referee: [Proposed PnP-CM algorithm and low-NFE stabilization] The central construction treats the CM output as the proximal map of an implicit prior inside ADMM. However, the method description explicitly adds noise perturbations to the input of the CM and momentum-based updates to the ADMM iterates specifically to stabilize the low-NFE regime. This indicates that the bare proximal reinterpretation (i.e., feeding the current ADMM variable directly into a fixed pre-trained CM) does not by itself produce the reported 2- and 4-NFE results. If the unmodified proximal step already satisfies the necessary fixed-point or contraction properties for ADMM, the extra mechanisms would be superfluous; their inclusion therefore suggests an unstated mismatch between the CM consistency function and the proximal operator required by the splitting.

    Authors: We appreciate the referee's careful reading. The proximal-operator reinterpretation of consistency models remains the theoretical foundation of PnP-CM and is valid for the ADMM splitting; the consistency function is treated as an (approximate) proximal map of an implicit prior. In practice, however, pre-trained consistency models are finite approximations to the underlying diffusion process and therefore yield inexact proximal steps. When the number of ADMM iterations is restricted to the 2-4 NFE regime, these approximations can destabilize the iterates. The added noise perturbations restore consistency with the model's training distribution at each step, while the momentum updates provide acceleration for the inexact splitting scheme. Such stabilization techniques are standard in the PnP literature when proximal operators are only approximate. We will revise the manuscript to include a dedicated subsection that (i) states the proximal interpretation formally, (ii) explains why the bare step alone is insufficient for few-NFE convergence, and (iii) justifies the noise and momentum terms as practical enhancements that preserve the overall PnP framework rather than indicating a fundamental mismatch. revision: partial

  2. Referee: [Experimental results and evaluation] The abstract states that the method was evaluated on diverse linear and nonlinear problems including MRI and that it outperforms prior CM approaches, but provides no quantitative metrics, baseline details, or ablation results on the contribution of the added noise schedule and momentum coefficient. Without these, the central performance claims cannot be verified and the load-bearing role of the proposed adaptations remains unclear.

    Authors: We agree that the current presentation would benefit from greater transparency. The full manuscript contains quantitative comparisons on the reported tasks, but we acknowledge that the abstract and experimental section do not sufficiently highlight the numerical metrics, the precise baseline implementations, or ablations isolating the noise schedule and momentum coefficient. In the revised version we will (i) add a table summarizing PSNR/SSIM values across all tasks and baselines, (ii) provide explicit implementation details for each competing CM-based solver, and (iii) include a dedicated ablation study that quantifies the contribution of the noise perturbation schedule and the momentum parameter to the observed low-NFE performance. These additions will make the performance claims verifiable and will clarify the practical importance of the proposed stabilizations. revision: yes

Circularity Check

0 steps flagged

Standard reinterpretation of pre-trained CMs inside ADMM with minor self-citation; no load-bearing reduction to fitted inputs or definitions

full rationale

The paper's core step reinterprets consistency models as proximal operators for PnP-ADMM integration, drawing on existing ADMM splitting and pre-trained CMs without defining the proximal map in terms of the target reconstruction or fitting parameters to the reported low-NFE results. Noise perturbations and momentum updates are explicitly added as stabilizers rather than being derived from the proximal claim itself. Any self-citations to prior CM or PnP work are not load-bearing for the central performance claims, which remain independently testable against external inverse-problem benchmarks. This yields only a minor circularity score with no equations reducing predictions to inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that consistency models act as effective proximal operators for arbitrary inverse problems and that the added noise and momentum terms improve convergence in the low-NFE regime; these are domain assumptions rather than derived quantities.

free parameters (2)
  • momentum coefficient
    Introduced to stabilize updates in the low-NFE regime; value is chosen to improve performance but not derived from first principles.
  • noise perturbation schedule
    Added at each step; specific levels are design choices that affect stability and quality.
axioms (1)
  • domain assumption Consistency models trained on clean data can be treated as proximal operators of an implicit image prior without further adaptation.
    This reinterpretation is the foundational step that allows integration into the PnP-ADMM framework.

pith-pipeline@v0.9.0 · 5804 in / 1301 out tokens · 40954 ms · 2026-05-18T13:36:51.041785+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

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  2. Plug-and-Play Consistency Models for MIMO Channel Estimation

    eess.SP 2026-04 unverdicted novelty 4.0

    Plug-and-play consistency models recover angular-domain MIMO channels from pilot observations in a small number of iterations.

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    \@ifxundefined[1] #1\@undefined \@firstoftwo \@secondoftwo \@ifnum[1] #1 \@firstoftwo \@secondoftwo \@ifx[1] #1 \@firstoftwo \@secondoftwo [2] @ #1 \@temptokena #2 #1 @ \@temptokena \@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later remove the command n...

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