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PnP-Flow: Plug-and-Play Image Restoration with Flow Matching
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Proposes PnP-Flow, a plug-and-play forward-backward algorithm that uses a time-dependent denoiser built from a pre-trained optimal-transport flow matching velocity field, with an interpolation (reprojection) step, for imaging inverse problems.
Problem
Solving imaging inverse problems (denoising, deblurring, super-resolution, inpainting) with priors from pre-trained Flow Matching models, which is hard because backpropagating through the ODE is numerically and computationally expensive, and PnP denoisers struggle on generative tasks like inpainting
Approach
Define a time-dependent denoiser D_t = Id + (1-t) v_t from a pre-trained straight-line (OT) flow matching velocity field and plug it into a forward-backward splitting loop, adding a linear interpolation reprojection step with fresh noise before each denoising, avoiding backpropagation through the ODE.
Key results
- On CelebA, PnP-Flow reaches 33.54 dB PSNR on random inpainting (70%) vs 33.07 for D-Flow and 30.59 dB on box inpainting vs 29.70 for D-Flow.
- On AFHQ-Cat super-resolution (x4), PnP-Flow achieves 26.75 dB / 0.774 SSIM, ahead of OT-ODE at 25.17 dB.
- Computation: PnP-Flow takes 3.40 s and 0.10 GB peak GPU memory per deblurring image on CelebA, versus 32.19 s and 5.91 GB for D-Flow.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PnP-Flow instead of the strongest listed baseline | CelebA denoising · CelebA denoising | PSNR: 32.45 -> 32.45 | No clear effect |
| Use PnP-Flow instead of the strongest listed baseline | CelebA deblurring · CelebA deblurring | PSNR: 33.65 -> 34.51 | Helped |
| Use PnP-Flow instead of the strongest listed baseline | CelebA super-resolution · CelebA super-resolution | PSNR: 31.20 -> 31.49 | Helped |
| Use PnP-Flow instead of the strongest listed baseline | CelebA random inpainting · CelebA random inpainting | PSNR: 33.07 -> 33.54 | Helped |
| Use PnP-Flow instead of the strongest listed baseline | CelebA box inpainting · CelebA box inpainting | PSNR: 29.70 -> 30.59 | Helped |
| Use PnP-Flow instead of the strongest listed baseline | AFHQ-Cat denoising · AFHQ-Cat denoising | PSNR: 32.34 -> 31.65 | Hurt |
| Use PnP-Flow instead of the strongest listed baseline | AFHQ-Cat deblurring · AFHQ-Cat deblurring | PSNR: 27.97 -> 27.62 | Hurt |
| Use PnP-Flow instead of the strongest listed baseline | AFHQ-Cat super-resolution · AFHQ-Cat super-resolution | PSNR: 25.17 -> 26.75 | Helped |
| Use PnP-Flow instead of the strongest listed baseline | AFHQ-Cat random inpainting · AFHQ-Cat random inpainting | PSNR: 31.76 -> 32.98 | Helped |
| Use PnP-Flow instead of the strongest listed baseline | AFHQ-Cat box inpainting · AFHQ-Cat box inpainting | PSNR: 26.69 -> 26.87 | Helped |
| Use PnP-Flow instead of Flow-Priors | CelebA deblurring restoration · CelebA deblurring | GPU peak memory load: 2.96GB -> 0.10GB | Helped |
| Use PnP-Flow instead of D-Flow | CelebA deblurring restoration · CelebA deblurring | GPU peak memory load: 5.91GB -> 0.10GB | Helped |
Surprising findings
- Averaging the denoising step over several interpolation noise draws is said to slightly help, and the method is independent of initialization (e.g., zero-image start), unlike the baselines.
- PnP-Flow is not the best on LPIPS; the authors note PSNR-optimal reconstructions do not yield optimal perceptual scores.
Limitations
- Reconstructions are somewhat over-smoothed because the denoiser is a mean-square estimator.
- Baselines were reimplemented by the authors since no official implementations were available, and PnP-Diff uses a diffusion model trained on FFHQ rather than the test dataset.
- Algorithm is a point estimator rather than a posterior sampler.
Experimental setup
Datasets: CelebA AFHQ-Cat CelebA-HQ FFHQ MNIST
Benchmarks: CelebA AFHQ-Cat CelebA-HQ
Metrics: PSNR SSIM LPIPS
Baselines: PnP-Diff PnP-GS OT-ODE D-Flow Flow-Priors
Builds on: Plug-and-Play priors Flow Matching Mini-batch OT flow matching Flow-Priors D-Flow
Closest papers by meaning
- Plug-and-Play image restoration with Stochastic deNOising REgularization (ICML 2024 · similarity 0.90)
- Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving (NeurIPS 2025 · similarity 0.88)
- Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction (NeurIPS 2024 · similarity 0.88)
- Reconciling Stochastic and Deterministic Strategies for Zero-shot Image Restoration using Diffusion Model in Dual (CVPR 2025 · similarity 0.88)
- Fast samplers for Inverse Problems in Iterative Refinement models (NeurIPS 2024 · similarity 0.88)
- Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching (NeurIPS 2024 · similarity 0.88)
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