Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework

Rajesh Shrestha; Xiao Fu

cs.LGMar 10, 2026

Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework

Authors: Rajesh Shrestha, Xiao Fu

Organizations: School of EECS, Oregon State University

Abstract

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 $\textit{ball convergence}$ 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

{\widetilde{\bm{z}}}^{(k)}

using score functions could lead to unnatural recovered signals with artifacts. Right: AC-DC denoising brings

{\widetilde{\bm{z}}}^{(k)}

closer to

\mathcal{M}_{{\sigma}^{(k)}}

, and then uses the score function to bring

{\widetilde{\bm{z}}}^{(k)}

to the data manifold

\mathcal{M}_{\rm data}

Figure 2: Inpainting under random missings.

		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
${\bm{x}}\in\mathbb{R}^{d}$	The unknown signal or image to be recovered
${\bm{y}}\in\mathbb{R}^{n}$	Measurements, with $n\leq d$
$y_{i}$	$i$ th element of measurement ${\bm{y}}$
$\mathcal{A}:\mathbb{R}^{d}\to\mathbb{R}^{n}$	Measurement operator
$\mathcal{X}$	Support of ${\bm{x}}$
$\mathcal{X}_{t}$	Support of ${\bm{x}}_{t}$

Appendix

Table 2: Summary of notation

Task	$\rho$	$W$	lr of Adam in ( 7a )
Superresolution ( $4\times$ )	$100$	$100$	$3\times 10^{-2}$
Gaussian Deblur	$100$	$100$	$5\times 10^{-2}$
HDR	$500$	$100$	$3\times 10^{-2}$
Inpainting (Random)	$500$	$100$	$1\times 10^{-1}$
Inpainting (Box)	$500$	$100$	$1\times 10^{-1}$
Motion Deblur	$100$	$100$	$1\times 10^{-1}$

Appendix

Table 3: Hyperparameter settings for each task

Figure 6: Illustration of correction and denoising step in proposed method.

Figure 7: Histogram of score difference norm ratio: $\|\nabla\log p_{\mathrm{data}}({\bm{x}}_{2})-\nabla\log p_{\mathrm{data}}({\bm{x}}_{1})\|_{2}/\|{\bm{x}}_{1}-{\bm{x}}_{2}\|_{2}$ , illustrating empirical smoothness (Assumption 2).

Figure 8: Empirical coercivity test: relationship between $\langle{\bm{x}},-\nabla\log p_{\mathrm{data}}({\bm{x}})\rangle$ and $\|{\bm{x}}\|_{2}^{2}$ . The strong positive correlation indicates coercive energy behavior (Assumption 3 ).

Figure 9: Demonstration of incorporating additional perceptual regularization.

		FFHQ			ImageNet
Task	Method	PSNR↑	SSIM↑	LPIPS↓	PSNR↑	SSIM↑	LPIPS↓
HDR	Ours–tweedie	27.425	0.853	0.164	26.515	0.817	0.182
	DAPS	26.94	0.852	0.154	26.848	0.816	0.172
	RED-diff	26.815	0.836	0.241	20.794	0.771	0.232
	PMC	21.582	0.707	0.291	22.745	0.707	0.290
Nonlinear Deblur	Ours–tweedie	29.326	0.823	0.185	27.837	0.725	0.212

Appendix

Table 4: Reconstruction metrics (100 images) on FFHQ / ImageNet for additional tasks. Bold : best, blue : 2nd best.

	Ours-tweedie without correction			Ours-tweedie with correction
Tasks	PSNR↑	SSIM↑	LPIPS↓	PSNR↑	SSIM↑	LPIPS↓
Superresolution (4x)	26.915	0.730	0.314	30.439	0.857	0.178
Gaussian Blur	28.896	0.788	0.275	30.402	0.853	0.175
Inpainting (Box)	15.604	0.617	0.361	24.025	0.859	0.131
Motion Deblur	25.123	0.538	0.370	30.003	0.854	0.179
Nonlinear Deblur	21.731	0.561	0.375	29.326	0.823	0.185

Appendix

Table 5: Comparison of our method with and without correction on FFHQ. Best results are highlighted in bold.

Figure 10: Performance with respect to NFE for Superresolution task (FFHQ)

Figure 11: Performance with respect to NFE for Gaussian deblurring task (FFHQ)

Figure 12: Performance with respect to NFE for Inpainting with random missings (FFHQ)

Figure 13: Performance with respect to NFE for Inpainting with box missing (FFHQ)

Figure 14: Performance with respect to NFE for Motion blur (FFHQ)

Figure 15: Performance with respect to NFE for Phase retrieval (FFHQ)

Figure 16: Recovery under $4\times$ superresolution task on FFHQ

Figure 17: Recovery under inpainting with random missings on FFHQ

Figure 18: Recovery under motion blur task on FFHQ

Diffusion-Based Inverse Problems

Diffusion-based inverse problems use generative priors to recover images and physical fields from incomplete, noisy, or indirect measurements.

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FlowADMM: Plug-and-play ADMM with Flow-based Renoise-Denoise Priors

Hendrik Sommerhoff, Michael Moeller

Computer Vision Group, University of Siegen Hölderlinstraße 3, 57076 Siegen, Germany

Alternating Direction Method of Multipliers Image Restoration Constrained Optimization Inverse Problems

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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.

Abstract

Diffusion-Based Inverse Problems

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