HP-PnP-Flow: Hybrid Time Scheduling and Projection for Plug-and-Play Image Restoration via Flow Matching

Yong Li; Xiaojie Wang; Xiaoyan Zhang

cs.CVOct 19, 2026

HP-PnP-Flow: Hybrid Time Scheduling and Projection for Plug-and-Play Image Restoration via Flow Matching

Authors: Yong Li, Xiaojie Wang, Xiaoyan Zhang

Organizations: School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha 410083, Hunan, China

Abstract

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 $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
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 $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
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).

Panel of Figure 2 — 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).

Panel of Figure 3 — 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 $t_{0}$ .

	PnP-Flow ( $t_{0}=0.0$ )	$t_{0}=0.2$	$t_{0}=0.5$	$t_{0}=0.7$	$t_{0}=0.9$	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

t_{0}

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
$\gamma$ (step size)	—	2.0	2.0	—	—
$\alpha$ (momentum)	1.0	0.3	1.0	—	—
$\sigma_{f}$ (noise factor)	1.0	1.8	3.0	—	—
$n_{\text{iter}}$ (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
$\gamma$ (step size)	—	2.0	2.0	—	—
$\alpha$ (momentum)	1.0	0.3	1.0	—	—
$\sigma_{f}$ (noise factor)	1.0	1.8	5.0	—	—
$n_{\text{iter}}$ (iterations)	1	60	50	23	—
OT-ODE

Appendix

Table 6: Optimal hyperparameter settings on AFHQ-Cat.

Panel of Figure 6 — Figure 6: Denoising on CelebA ( $\sigma=0.2$ ).

Panel of Figure 7 — Figure 7: Denoising on AFHQ-Cat ( $\sigma=0.2$ ).

Panel of Figure 8 — Figure 8: Deblurring on CelebA ( $\sigma=0.05$ , $b=1.0$ ).

Panel of Figure 9 — Figure 9: Deblurring on AFHQ-Cat ( $\sigma=0.05$ , $b=3.0$ ).

Panel of Figure 10 — Figure 10: Super-resolution on CelebA ( $\times 2$ , $\sigma=0.05$ ).

Panel of Figure 11 — Figure 11: Super-resolution on AFHQ-Cat ( $\times 4$ , $\sigma=0.05$ ).

Panel of Figure 12 — Figure 12: Random inpainting on CelebA (70% masked, $\sigma=0.01$ ).

Panel of Figure 13 — Figure 13: Random inpainting on AFHQ-Cat (70% masked, $\sigma=0.01$ ).

Panel of Figure 14 — Figure 14: Box inpainting on CelebA ( $40\times 40$ , $\sigma=0.05$ ).

Panel of Figure 15 — Figure 15: Box inpainting on AFHQ-Cat ( $80\times 80$ , $\sigma=0.05$ ).

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Hendrik Sommerhoff, Michael Moeller

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

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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

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