While score-based generative models have emerged as powerful priors for solving inverse problems, directly integrating them into optimization algorithms such as ADMM remains nontrivial. Two central challenges arise: i) the mismatch between the noisy data manifolds used to train the score functions and the geometry of ADMM iterates, especially due to the influence of dual variables, and ii) the lack of convergence understanding when ADMM is equipped with score-based denoisers. To address the manifold mismatch issue, we propose ADMM plug-and-play (ADMM-PnP) with the AC-DC denoiser, a new framework that embeds a three-stage denoiser into ADMM: (1) auto-correction (AC) via additive Gaussian noise, (2) directional correction (DC) using conditional Langevin dynamics, and (3) score-based denoising. In terms of convergence, we establish two results: first, under proper denoiser parameters, each ADMM iteration is a weakly nonexpansive operator, ensuring high-probability fixed-point ball convergence using a constant step size; second, under more relaxed conditions, the AC-DC denoiser is a bounded denoiser, which leads to convergence under an adaptive step size schedule. Experiments on a range of inverse problems demonstrate that our method consistently improves solution quality over a variety of baselines.
Figures & tables
Figure 1: Left: direct denoising of z(k) using score functions could lead to unnatural recovered signals with artifacts. Right: AC-DC denoising brings z(k) closer to Mσ(k) , and then uses the score function to bring z(k) to the data manifold Mdata .
Figure 2: Inpainting under random missings.
Figure 3: Inpainting under box missing.
Figure 4
FFHQ
ImageNet
Task
Method
PSNR↑
SSIM↑
LPIPS↓
PSNR↑
SSIM↑
LPIPS↓
Superresolution (4×)
Ours–tweedie
30.439
0.857
0.178
27.318
0.717
0.280
Ours–ode
29.991
0.845
0.156
26.919
0.700
0.276
DAPS
29.529
0.814
0.167
26.653
0.680
0.266
DPS
24.828
0.705
0.257
22.785
0.549
0.411
DDRM
27.145
0.782
0.261
26.105
0.683
0.306
Table 1: Reconstruction metrics (100 images) on FFHQ / ImageNet. Bold : best, blue : 2nd best.
Appendix figures & tables17 assets
Supplementary material from the paper’s appendix.
Appendix
Symbol
Description
x∈Rd
The unknown signal or image to be recovered
y∈Rn
Measurements, with n≤d
yi
i th element of measurement y
A:Rd→Rn
Measurement operator
X
Support of x
Xt
Support of xt
Appendix
Table 2: Summary of notation
Task
ρ
W
lr of Adam in ( 7a )
Superresolution ( 4× )
100
100
3×10−2
Gaussian Deblur
100
100
5×10−2
HDR
500
100
3×10−2
Inpainting (Random)
500
100
1×10−1
Inpainting (Box)
500
100
1×10−1
Motion Deblur
100
100
1×10−1
Appendix
Table 3: Hyperparameter settings for each task
Figure 6: Illustration of correction and denoising step in proposed method.
Plug-and-play (PnP) methods for solving inverse problems have recently achieved strong performance by leveraging denoising priors based on powerful generative diffusion and flow models. However, existing diffusion- and flow-based PnP methods typically rely on stochastic renoise-denoise operations, which complicate the analysis of their convergence behavior. In this work, we identify and formalize the deterministic renoise-denoise operator underlying flow-based plug-and-play methods. This perspective reveals that these methods implicitly define a deterministic operator given by the expectation of a denoiser over the latent noise distribution. Building on this insight, we propose FlowADMM, a PnP algorithm that integrates the renoise-denoise operator into the classical alternating direction method of multiplier (ADMM) framework. We establish convergence guarantees for FlowADMM under weak Lipschitz conditions on the underlying flow network, and extend the analysis to non-stationary time schedules. Empirically, FlowADMM achieves state-of-the-art performance among flow-based PnP methods on a range of inverse problems, including denoising, deblurring, super-resolution, and inpainting, while requiring fewer data consistency evaluations than prior approaches.
Hendrik Sommerhoff, Michael Moeller
Computer Vision Group, University of Siegen Hölderlinstraße 3, 57076 Siegen, Germany
Modern image restoration methods increasingly rely on large-scale supervised training, yet clean targets are often prohibitively difficult to obtain in scientific imaging modalities such as hyperspectral imaging (HSI) and magnetic resonance imaging (MRI). Plug-and-play ADMM (PnP-ADMM) with pretrained diffusion priors offers a promising alternative, but the learned prior distribution can mismatch both the target scientific image distribution and the distribution of ADMM denoiser inputs induced by dual feedback. To mitigate these mismatches, we propose S3-PnP, a self-supervised plug-and-play restoration framework that learns a score prior directly from observation-derived ADMM intermediate states, without clean training targets or externally pretrained weights. Specifically, the learned score corrects the input to the analytical prior update, combining observation-driven corrections with analytical regularization. We further analyze the convergence and reconstruction error of the corrected ADMM algorithm assuming an ideal score and quadratic data fidelity. Experiments on reference-guided HSI restoration, single-image HSI denoising, and MRI denoising demonstrate consistent improvements over competing methods.
Yukun Cui, Jiangshe Zhang, Shuang Xu +6
Xi’an Jiaotong University · Northwestern Polytechnical University · Nanyang Technological University +3
Plug-and-play (PnP) methods are widely used for solving imaging inverse problems by incorporating a denoiser into optimization algorithms. Score-based diffusion models (SBDMs) have recently demonstrated strong generative performance through a denoiser trained across a wide range of noise levels. Despite their shared reliance on denoisers, it remains unclear how to systematically use SBDMs as priors within the PnP framework without relying on reverse diffusion sampling. In this paper, we establish a score-based interpretation of PnP that justifies using pretrained SBDMs directly within PnP algorithms. Building on this connection, we introduce a stochastic generative PnP (SGPnP) framework that injects noise to better leverage the expressive generative SBDM priors, thereby improving robustness in severely ill-posed inverse problems. We provide a new theory showing that this noise injection induces optimization on a Gaussian-smoothed objective and promotes escape from strict saddle points. Experiments on challenging inverse tasks, such as multi-coil MRI reconstruction and large-mask natural image inpainting, demonstrate consistent improvement over conventional PnP methods and achieve performance competitive with diffusion-based solvers.
Chicago Y. Park, Edward P. Chandler, Yuyang Hu +4
University of Wisconsin–Madison · Washington University in St. Louis · Los Alamos National Laboratory