Image restoration is a fundamental inverse problem that seeks to recover high-quality images from degraded observations. Plug-and-Play (PnP) methods provide a flexible framework for integrating pretrained denoisers into iterative reconstruction, whereas flow matching offers an efficient generative modeling approach based on continuous-time ODE dynamics. Very recently, Martin et al.\ (ICLR, 2025) developed a PnP-Flow method, which integrates the PnP framework with flow matching through a time-dependent denoiser constructed from a pretrained flow matching model.By incorporating a different time schedule and an additional pixel-space projection operator, this paper proposes a novel efficient PnP-Flow algorithm (HP-PnP-Flow) that enjoys rigorous convergence guarantees under mild assumptions, without imposing restrictive conditions on iterates required by the aforementioned work. Numerical experiments on CelebA and AFHQ-Cat demonstrate that the newly proposed HP-PnP-Flow algorithm significantly outperforms PnP-Flow on several restoration tasks such as denoising, deblurring, super-resolution, random inpainting, and box inpainting. Notably, our algorithm achieves comparable or better reconstruction quality with substantially fewer iterations, reducing the iteration count from 500 to 100 for deblurring and super-resolution on AFHQ-Cat.
Figures & tables
Figure 1: Evolution of samples along the learned flow matching trajectories on CelebA at different time points. The ODE ( 2.4 ) is integrated using the forward Euler method with a step size of 0.01 .
Denoise
Deblur
Super-res.
Rand. inp.
Box inp.
Method
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
Degraded
20.01
0.349
0.365
27.79
0.739
0.126
10.51
0.184
0.824
12.26
0.197
1.024
22.42
0.745
0.209
PnP-GS
32.59
0.910
0.035
33.84
0.922
0.040
30.35
0.902
0.056
28.42
0.845
0.087
N/A
OT-ODE
30.49
0.858
0.032
32.87
0.918
0.028
31.56
0.910
0.020
28.82
0.874
0.050
29.92
0.923
0.033
D-Flow
25.99
0.604
0.090
31.16
0.852
0.037
30.39
0.847
0.025
33.65
0.944
0.015
30.93
0.901
0.024
Flow-Priors
29.30
0.769
0.129
31.47
0.858
0.055
28.31
0.716
0.099
32.95
0.943
0.019
30.42
0.862
0.046
Table 1: Quantitative results on CelebA (100 test images).
Denoise
Deblur
Super-res.
Rand. inp.
Box inp.
Method
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
Degraded
20.00
0.294
0.531
24.39
0.530
0.436
11.59
0.212
0.867
13.24
0.214
1.082
21.53
0.727
0.215
PnP-GS
33.03
0.896
0.078
28.38
0.771
0.331
24.26
0.642
0.350
29.80
0.838
0.127
N/A
OT-ODE
30.51
0.819
0.080
26.50
0.680
0.149
26.73
0.738
0.108
30.01
0.850
0.086
24.51
0.874
0.095
D-Flow
26.42
0.570
0.182
28.58
0.745
0.168
25.19
0.616
0.190
32.83
0.900
0.044
27.02
0.841
0.081
Flow-Priors
29.68
0.757
0.164
27.28
0.727
0.188
24.01
0.572
0.271
32.98
0.910
0.051
26.13
0.809
0.130
Table 2: Quantitative results on AFHQ-Cat (100 test images).
Figure 2: PSNR comparison of all methods on CelebA across five restoration tasks (from top to bottom: denoising, deblurring, super-resolution, random inpainting, and box inpainting).
Figure 3: PSNR comparison of all methods on AFHQ-Cat across five restoration tasks (from top to bottom: denoising, deblurring, super-resolution, random inpainting, and box inpainting).
Figure 4: PSNR convergence for different initial offsets t0 .
PnP-Flow ( t0=0.0 )
t0=0.2
t0=0.5
t0=0.7
t0=0.9
HP-PnP-Flow
Mean PSNR
33.73
33.96
34.47
33.95
21.21
34.75
Std. dev.
1.07
1.12
1.19
2.61
1.56
1.34
Table 3: PSNR (dB) for different initial offsets t0 .
Figure 5: PSNR convergence for different transition coefficients K .
PnP-Flow ( K=0 )
K=0.2
K=0.5
K=0.7
K=1.0
HP-PnP-Flow
Mean PSNR
33.73
34.20
34.66
34.65
34.12
34.75
Std. dev.
1.07
1.17
1.24
1.18
1.07
1.34
Table 4: PSNR (dB) for different transition coefficients K .
Appendix figures & tables12 assets
Supplementary material from the paper’s appendix.
Appendix
Method
Denoising
Deblurring
Super-res.
Rand. inp.
Box inp.
PnP-GS
γ (step size)
—
2.0
2.0
—
—
α (momentum)
1.0
0.3
1.0
—
—
σf (noise factor)
1.0
1.8
3.0
—
—
niter (iterations)
1
35
20
23
—
OT-ODE
Appendix
Table 5: Optimal hyperparameter settings on CelebA.
Method
Denoising
Deblurring
Super-res.
Rand. inp.
Box inp.
PnP-GS
γ (step size)
—
2.0
2.0
—
—
α (momentum)
1.0
0.3
1.0
—
—
σf (noise factor)
1.0
1.8
5.0
—
—
niter (iterations)
1
60
50
23
—
OT-ODE
Appendix
Table 6: Optimal hyperparameter settings on AFHQ-Cat.
Figure 6: Denoising on CelebA ( σ=0.2 ).
Figure 7: Denoising on AFHQ-Cat ( σ=0.2 ).
Figure 8: Deblurring on CelebA ( σ=0.05 , b=1.0 ).
Figure 9: Deblurring on AFHQ-Cat ( σ=0.05 , b=3.0 ).
Figure 10: Super-resolution on CelebA ( ×2 , σ=0.05 ).
Figure 11: Super-resolution on AFHQ-Cat ( ×4 , σ=0.05 ).
Figure 12: Random inpainting on CelebA (70% masked, σ=0.01 ).
Figure 13: Random inpainting on AFHQ-Cat (70% masked, σ=0.01 ).
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
Plug-and-Play (PnP) methods solve imaging inverse problems by incorporating deep denoisers into iterative optimization algorithms. Although practical implementations often decrease the denoiser noise level σ along iterations, most existing convergence analyses assume a fixed denoiser. In this work, we establish convergence guarantees for a broad family of Plug-and-Play algorithms with annealed noise level, spanning deterministic methods (RED--GD and PnP--PGD) and stochastic methods (SNORE, equivariant RED, and a variant of PnP--Flow). For each method, we identify an explicit, nonconvex objective associated with the terminal denoising level and prove asymptotic stationarity of the iterates with respect to this objective. Our analysis does not prescribe any decay rate for the noise schedule, and our assumptions cover both learned gradient-step denoisers and exact MMSE denoisers. Overall, our theoretical results bridge the gap between existing PnP convergence theory and the decreasing-denoising practices used by state-of-the-art image restoration methods. We empirically demonstrate the benefits of such schedules and illustrate the predicted convergence behavior on several imaging inverse problems, including inpainting, super-resolution, demosaicing and tomography.
Image restoration is fundamentally constrained by the tradeoff between distortion and perception: minimizing pixel-wise error yields over-smoothed results, whereas optimizing for perceptual realism often introduces structural deviations. Recent approaches attempt to balance this tradeoff via posterior sampling or multi-stage generative pipelines, yet remain computationally expensive and architecturally complex. To overcome these limitations, we propose PCFlow (Perceptually Consistent Flow Matching), a unified framework that directly parameterizes a continuous transport from degraded observations to clean targets, jointly optimizing distortion and perceptual quality. While its latent consistency flow objective drives stable and efficient few-step inference, a Latent Consistency Perceptual Loss (LCPL) imposes semantic constraints directly on the guiding velocity field, steering the dynamics toward visually sharp data manifolds. Furthermore, recognizing the inherent conflict between structural and perceptual consistencies, we integrate a conflict-free gradient projection strategy to stabilize the multi-objective optimization landscape. Combined with lightweight, convolution-only backbone, PCFlow achieves competitive performance across diverse restoration tasks at a fraction of traditional computational costs.
Sangwoo Jo, Donggeun Ko, Jayeon Kang +3
Korea University, Seoul, South Korea · Aim Future, Seoul, South Korea