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)
PSNR ↑
SSIM ↑
PSNR ↑
SSIM ↑
PSNR ↑
SSIM ↑
PSNR ↑
SSIM ↑
A†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 )
5×200
30.02
0.891
37.05
0.939
34.89
0.967
27.04
0.910
SITCOM ( Alkhouri et al., 2025 )
50×10
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 ↑
SSIM ↑
LPIPS ↓
✗
✗
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.
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 ( xgt+σtn ). (b) Ours ( Orange ): Our SH module aligns the spectrum perfectly, yielding clean results. (c) Naive Injection ( Red ): Adding noise ( x+u+σtn ) 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)
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
A†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]∘ , 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, “ A†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
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 ↑
SSIM ↑
LPIPS ↓
Gaussian Blur
DAPS
29.609 ± 1.637
0.786 ± 0.031
0.180 ± 0.030
DiffPIR
30.506 ± 1.940
0.858 ± 0.038
0.145 ± 0.029
DC-PnPDP
30.741 ± 2.011
0.861 ± 0.037
0.165 ± 0.031
Motion Blur
DAPS
31.653 ± 1.337
0.836 ± 0.021
0.138 ± 0.027
DiffPIR
31.088 ± 1.451
0.831 ± 0.026
0.129 ± 0.023
DC-PnPDP
33.305 ± 1.622
0.904 ± 0.023
0.116 ± 0.027
Appendix
Table 6: Quantitative natural-image restoration results on Gaussian blur, motion blur, and 4× super-resolution. Results are reported as mean ± 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× super-resolution.
Figure 10: Additional qualitative results on limited-angle CT (LACT) reconstruction with the angular range [0,90]∘ . 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]∘ . 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.
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
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
Solving severely ill-posed imaging inverse problems requires recovering image structures that are unobservable or weakly constrained by the measurements. Diffusion models provide expressive learned priors for inferring such missing information, while posterior sampling incorporates measurement consistency along the reverse process. Standard diffusion posterior samplers, however, rely on instantaneous measurement-aware estimates, without explicitly exploiting information carried by previous posterior corrections. We introduce Consecutive Posterior Fusion Denoising Diffusion Null-Space Models (CPF-DDNM), an inference-time strategy that fuses consecutive measurement-aware estimates to improve the diffusive recovery of unobservable image structures, without requiring retraining or additional denoiser evaluations. We instantiate this principle within DDNM, whose range/null-space decomposition reveals that consecutive fusion preserves the measurement-determined component while acting exclusively on the prior-driven null-space estimate. We thus provide a geometric interpretation of CPF-DDNM and a local error analysis that characterizes the optimal time-dependent fusion coefficient, including the extrapolative regime. Experiments on sparse-view and simulated low-dose computed tomography, as well as medical image super-resolution, show consistent improvements over DDNM and competitive performance against diffusion-based inverse solvers.
Elena Morotti, Davide Evangelista, Elena Loli Piccolomini
Department of Computer Science and Engineerin University of Bologna Bologna, 40126, Italy