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FiRe: Fixed-points of Restoration Priors for Solving Inverse Problems
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Proposes FiRe priors, which treat restoration models composed with their training degradation as projections whose fixed points define an implicit prior, and combines multiple such priors in a PnP-style HQS algorithm for inverse problems.
Problem
Plug-and-Play methods rely on denoisers as implicit priors; using general pretrained restoration models (super-resolution, deblurring, JPEG, inpainting) naively as priors yields poor reconstructions because smooth images are not fixed points of R alone.
Approach
Smooth images are fixed points of the composition of the training degradation with the restoration model; this yields an explicit distance-to-fixed-point prior (gradient 1/2 grad d^2 = x - R(D(x))), and an ensemble over multiple degradation-restoration pairs plus measurement-conditioned degradations are unified in one HQS-style algorithm.
Key results
- On Imnet100 Motion Blur, FiRe-HQS (denoising+SR+deblur ensemble) reaches 30.49 dB PSNR vs 30.39 for DPIR and 25.38 for DRP-style SR priors, at 30 iterations.
- A single Restormer Gaussian-deblurring prior within FiRe achieves 27.14 dB on Gaussian blur in Set3C, matching or beating the DRUNet PnP baseline (25.93 dB).
- FiRe reaches comparable quality to ShaRP in 30 iterations versus the 200 iterations ShaRP needs.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use FiRe-HQS with denoising, SR, and deblurring priors instead of DRP | inverse-problem reconstruction · Imnet100 test, Gaussian Blur | PSNR: 25.48 -> 25.80 | Helped |
| use FiRe-HQS with denoising, SR, and deblurring priors instead of DRP | inverse-problem reconstruction · Imnet100 test, Motion Blur | PSNR: 25.38 -> 30.49 | Helped |
| use FiRe-HQS with denoising, SR, and deblurring priors instead of DRP | inverse-problem reconstruction · Imnet100 test, SRx4 | PSNR: 23.23 -> 23.92 | Helped |
| use FiRe-HQS with denoising, SR, and deblurring priors instead of DRP | inverse-problem reconstruction · BSD20 subset, Gaussian Blur | PSNR: 26.18 -> 27.00 | Helped |
| use FiRe-HQS with denoising, SR, and deblurring priors instead of DRP | inverse-problem reconstruction · BSD20 subset, Motion Blur | PSNR: 26.05 -> 31.67 | Helped |
| use FiRe-HQS with denoising, SR, and deblurring priors instead of DRP | inverse-problem reconstruction · BSD20 subset, SRx4 | PSNR: 23.65 -> 25.15 | Hurt |
| use FiRe with SCUNet blind denoising prior instead of PnP (ablation) | SCUNet restoration · Set3C, Gaussian Blur | PSNR: 23.91 -> 28.03 | Helped |
| use FiRe with a JPEG-restoration SCUNet prior instead of PnP with SCUNet blind denoising (ablation) | SCUNet restoration · Set3C, Motion Blur | PSNR: 30.19 -> 31.23 | Helped |
| use an ensemble of denoising, SR, and deblurring models instead of DRP | FiRe-HQS · BSD20 subset, SRx4 | PSNR: 26.18 -> 25.15 | Hurt |
| combine multiple restoration priors and tune their weights (ablation) | FiRe · Gaussian deblurring and SRx4 | PSNR | Helped |
| combine an inpainting-specific LAMA prior with a general denoising prior (ablation) | FiRe · noisy image inpainting | PSNR | Helped |
| use the LAMA random-inpainting prior as the sole restoration prior (ablation) | FiRe · Set3C, SRx4 | PSNR: 21.69 -> 21.80 | Hurt |
Surprising findings
- A LAMA inpainting model trained only on binary masks, without noise, still provides a meaningful prior for SR and deblurring despite being off-task.
- Naively iterating a restoration model without degradation (fixed-point R alone) yields strong artifacts, while composing with the training degradation stabilizes the iterations.
Limitations
- Hyperparameters (step sizes, degradation strength, ensemble weights gamma) significantly affect performance and require tuning.
- Restoration priors can fail when the restoration model is not suited to the target task, e.g. LAMA inpainting cannot remove noise.
Experimental setup
Datasets: Imnet100 BSD20 Set3C
Benchmarks: Imnet100 BSD20 Set3C
Metrics: PSNR SSIM LPIPS
Baselines: DRP DPIR DiffPIR ShaRP PnP with DRUNet
Builds on: Plug-and-Play (PnP) DRP ShaRP DPIR Tweedie's formula
Closest papers by meaning
- A Restoration Network as an Implicit Prior (ICLR 2024 · similarity 0.91)
- Stochastic Deep Restoration Priors for Imaging Inverse Problems (ICML 2025 · similarity 0.89)
- Exact Posterior Score Estimation for Solving Linear Inverse Problems (NeurIPS 2026 · similarity 0.89)
- Unleashing the Denoising Capability of Diffusion Prior for Solving Inverse Problems (NeurIPS 2024 · similarity 0.88)
- Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction (NeurIPS 2024 · similarity 0.88)
- Improving Diffusion Posterior Samplers with Lagged Temporal Corrections for Image Restoration (NeurIPS 2026 · similarity 0.88)
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