Plug-and-Play Diffusion Meets ADMM: Dual-Variable Coupling for Robust Medical Image Reconstruction

Chenhe Du; Xuanyu Tian; Qing Wu; Muyu Liu; Jingyi Yu; Hongjiang Wei; Yuyao Zhang

cs.CVFeb 26, 2026

Plug-and-Play Diffusion Meets ADMM: Dual-Variable Coupling for Robust Medical Image Reconstruction

Authors: Chenhe Du, Xuanyu Tian, Qing Wu, Muyu Liu, Jingyi Yu, Hongjiang Wei, Yuyao Zhang

Organizations: ShanghaiTech University · Shanghai Jiao Tong University

Abstract

Plug-and-Play diffusion prior (PnPDP) frameworks have emerged as a powerful paradigm for solving imaging inverse problems by treating pretrained generative models as modular priors. However, we identify a critical flaw in prevailing PnP solvers (e.g., based on HQS or Proximal Gradient): they function as memoryless operators, updating estimates solely based on instantaneous gradients. This lack of historical tracking inevitably leads to non-vanishing steady-state bias, where the reconstruction fails to strictly satisfy physical measurements under heavy corruption. To resolve this, we propose Dual-Coupled PnP Diffusion (DC-PnPDP), which restores the classical dual variable to provide integral feedback, progressively enforce agreement between the data-consistency and prior. However, this rigorous geometric coupling introduces a secondary challenge: the accumulated dual residuals exhibit spectrally colored, structured artifacts that violate the Additive White Gaussian Noise (AWGN) assumption of diffusion priors, causing severe hallucinations. To bridge this gap, we introduce Spectral Homogenization (SH), a frequency-domain adaptation mechanism that modulates these structured residuals into statistically compliant pseudo-AWGN inputs. This effectively aligns the solver's rigorous optimization trajectory with the denoiser's valid statistical manifold. Extensive experiments on CT and MRI reconstruction demonstrate that our approach resolves the bias-hallucination trade-off, achieving state-of-the-art fidelity with significantly accelerated convergence. The code is available at https://github.com/duchenhe/DC-PnPDP

Figures & tables

Figure 1: Qualitative comparisons on two CT reconstruction tasks. Visualization windows are set to $[-800,800]$ HU for LACT and $[-175,500]$ HU for SVCT, respectively.

Figure 2: Qualitative comparisons of accelerated fastMRI brain reconstruction at AF = 10, including zoomed-in details and error maps.

Method	NFE	LACT-90		SVCT-20		Brain MRI (AF=6)		Brain MRI (AF=10)
Method	NFE	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$
$\mathbf{A}^{\dagger}\mathbf{y}$	–	16.82	0.605	21.82	0.359	23.44	0.680	20.41	0.576
DDNM ( Wang et al., 2023 )	100	27.13	0.800	33.94	0.885	33.23	0.953	26.13	0.889
DDS ( Chung et al., 2024 )	100	26.30	0.806	36.36	0.932	33.26	0.953	26.08	0.889
DAPS ( Zhang et al., 2025a )	$5{\times}200$	30.02	0.891	37.05	0.939	34.89	0.967	27.04	0.910
SITCOM ( Alkhouri et al., 2025 )	$50{\times}10$	32.07	0.911	37.76	0.945	35.58	0.969	28.67	0.927

Table 1: Quantitative comparison under recommended sampling budgets. The table reports PSNR / SSIM on CT and fastMRI brain reconstruction tasks. The best results are highlighted in bold , and the strongest baseline results are underlined . The gray 50-NFE DC-PnPDP row is included as an auxiliary budget reference and is not used for the margin row.

Components		Metrics
DC	SH	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
✗	✗	31.36	0.894	0.023
✗	✓	31.51	0.898	0.022
✓	✗	35.91	0.934	0.012
✓	✓	37.02	0.943	0.011

Table 2: Component ablation results on LACT-90. The first row corresponds to the standard PnP-HQS baseline, i.e., DiffPIR.

Panel of Figure 3 — Figure 3: Mechanism Verification: Why Spectral Homogenization Matters. We analyze the spectral characteristics ( Top ) and the corresponding denoising outputs ( Bottom ) at iteration $k=6$ . (a) Ideal Reference ( Green ): The on-manifold input ( $x_{gt}+\sigma_{t}n$ ). (b) Ours ( Orange ): Our SH module aligns the spectrum perfectly, yielding clean results. (c) Naive Injection ( Red ): Adding noise ( $x+u+\sigma_{t}n$ ) creates an over-energized spectrum, leading to over-smoothing. (d) No Injection ( Blue ): The raw dual input ( $x+u$ ) causes OOD hallucinations.

Figure 4: Inference-efficiency comparison on SVCT-20 and LACT-90. PSNR is plotted as a function of NFE to compare reconstruction quality under different denoiser-evaluation budgets. DC-PnPDP reaches higher fidelity with fewer denoiser calls and maintains a stronger high-budget plateau than DiffPIR.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Method	LACT-90			SVCT-20			Accelerated MRI (AF=6)			Accelerated MRI (AF=10)
Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
$\mathbf{A}^{\dagger}\mathbf{y}$	16.82	0.606	0.140	21.81	0.359	0.249	21.72	0.523	0.194	18.51	0.426	0.237
DDNM ( Wang et al., 2023 )	30.62	0.887	0.025	36.22	0.931	0.021	27.95	0.763	0.043	25.32	0.681	0.065
DDS ( Chung et al., 2024 )	24.86	0.775	0.056	36.71	0.938	0.021	27.12	0.737	0.040	24.01	0.644	0.061
DAPS ( Zhang et al., 2025a )	28.41	0.855	0.032	36.18	0.930	0.020	27.86	0.760	0.042	25.24	0.677	0.062
DiffPIR ( Zhu et al., 2023 )	31.03	0.892	0.023	36.23	0.931	0.021	27.96	0.763	0.043	25.27	0.680	0.065

Appendix

Table 3: Controlled 50-NFE quantitative comparison on medical image reconstruction tasks, including SVCT with 20 views, LACT with angular range

[0,90]^{\circ}

, and accelerated fastMRI knee reconstruction at AF = 6 and AF = 10. The best results are highlighted in bold and the second-best are underlined . Here, “

\mathbf{A}^{\dagger}\mathbf{y}

” denotes the pseudo-inverse reconstruction, i.e., FBP for CT and zero-filling for MRI.

Figure 5: Qualitative results for the controlled 50-NFE fastMRI knee reconstruction setting at AF = 10. The figure shows proton density (PD) and proton density fat-suppressed (PD-FS) scans; red arrows indicate representative improvements and remaining aliasing artifacts.

Method	Time / Iter. (s)	Denoise (s)	DC (s)	SH (s)	VRAM (MB)
SITCOM	7.4618	4.4326	7.4578	–	38009
DAPS	0.3190	0.1856	0.1333	–	3988
DiffPIR	0.1951	0.1856	0.0095	–	3988
DC-PnPDP ( Ours )	0.1958	0.1856	0.0095	0.0007	3988

Appendix

Table 4: Runtime and memory profile on SVCT-20 with batch size 10. Time / Iter. denotes the total wall-clock time per outer iteration; Denoise , DC , and SH denote the time spent on the diffusion prior step, data-consistency step, and Spectral Homogenization module, respectively. All timings are reported in seconds under the same hardware and batch setting, and VRAM denotes peak GPU memory usage.

Figure 6: Residual diagnostics on LACT-90. The curves report the data-fidelity residual and the norm of the accumulated dual state, providing optimization-oriented evidence complementary to PSNR-based evaluation.

Dataset	Method	SVCT				LACT
Dataset	Method	18	36	72	144	90	120	150
AAPM	ProCT	30.2957	33.1703	35.3471	37.2768	31.8320	34.5075	37.0916
	DiffPIR	33.3762	38.9284	43.0297	47.3725	28.8041	34.5525	43.2935
	DC-PnPDP ( Ours )	36.4784	40.5853	43.9589	48.1579	33.8669	39.2974	45.0820
DeepLesion	ProCT	28.8959	30.9438	32.6598	33.8446	31.5145	33.0290	34.0849
	DiffPIR	30.4603	35.8175	40.5997	44.7531	27.8810	34.7194	43.1713

Appendix

Table 5: Quantitative PSNR comparison against the supervised ProCT baseline on AAPM and DeepLesion. Results are grouped by dataset and CT setting; the best results are highlighted in bold and the second-best are underlined .

Figure 7: Additional qualitative comparison with ProCT on LACT-90 and LACT-120. The figure includes reconstruction results, zoomed-in regions, and error maps, with FBP-LV and ground truth shown for reference.

Figure 8: Additional qualitative comparison with ProCT on SVCT-18 and SVCT-36. The figure includes reconstruction results, zoomed-in regions, and error maps, with FBP-LV and ground truth shown for reference.

Task	Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
Gaussian Blur	DAPS	29.609 $\pm$ 1.637	0.786 $\pm$ 0.031	0.180 $\pm$ 0.030
	DiffPIR	30.506 $\pm$ 1.940	0.858 $\pm$ 0.038	0.145 $\pm$ 0.029
	DC-PnPDP	30.741 $\pm$ 2.011	0.861 $\pm$ 0.037	0.165 $\pm$ 0.031
Motion Blur	DAPS	31.653 $\pm$ 1.337	0.836 $\pm$ 0.021	0.138 $\pm$ 0.027
	DiffPIR	31.088 $\pm$ 1.451	0.831 $\pm$ 0.026	0.129 $\pm$ 0.023
	DC-PnPDP	33.305 $\pm$ 1.622	0.904 $\pm$ 0.023	0.116 $\pm$ 0.027

Appendix

Table 6: Quantitative natural-image restoration results on Gaussian blur, motion blur, and

4{\times}

super-resolution. Results are reported as mean

\pm

standard deviation; the best results are highlighted in bold and the second-best are underlined .

Figure 9: Additional qualitative examples for natural-image inverse problems. The figure compares restoration results under Gaussian blur, motion blur, and $4{\times}$ super-resolution.

Figure 10: Additional qualitative results on limited-angle CT (LACT) reconstruction with the angular range $[0,90]^{\circ}$ . The visualization window is set to $[-800,800]$ HU.

Figure 11: Additional qualitative results on limited-angle CT (LACT) reconstruction with the angular range $[0,90]^{\circ}$ . The visualization window is set to $[-800,800]$ HU.

Figure 12: Additional qualitative results on sparse-view CT (SVCT) reconstruction with 20 views. The visualization window is set to $[-800,800]$ HU.

Figure 13: Additional qualitative results on sparse-view CT (SVCT) reconstruction with 20 views. The visualization window is set to $[-800,800]$ HU.

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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.

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