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Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance
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Proposes DDPG, a diffusion-based restoration sampler whose data-fidelity guidance is an iteration-dependent preconditioned gradient that moves from back-projection to least-squares guidance, using pretrained DDPM denoisers for deblurring and super-resolution.
Problem
Zero-shot linear image restoration (deblurring, super-resolution) with pretrained denoisers/diffusion models: back-projection guidance is strong in low noise but amplifies noise when observations are noisy and A has small singular values.
Approach
Interprets back-projection as a preconditioned least-squares gradient step and uses an iteration-dependent preconditioner W_t that interpolates from regularized BP (early iterations) to plain LS (late iterations), applied within both a PnP optimizer (IDPG) and a DDIM-style sampler (DDPG) with effective-noise rescaling.
Key results
- On CelebA-HQ Gaussian deblurring with sigma_e=0.1, DDPG reaches 29.18 dB vs 27.59 dB for DiffPIR.
- On CelebA-HQ bicubic SRx4 with sigma_e=0.05, IDPG improves PSNR to 29.89 dB vs 28.95 dB for IDBP and 28.91 dB for PGM-LS.
- DDPG gives better LPIPS than IDPG on noisy tasks, e.g., motion deblurring sigma_e=0.05 LPIPS 0.082 vs 0.134 for IDPG.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use iteratively preconditioned guidance instead of pure least-squares guidance (ablation) | IDPG · CelebA-HQ 1K, bicubic SRx4, σe=0.05 | PSNR [dB]: 28.91 -> 29.89 | Helped |
| Use iteratively preconditioned guidance instead of pure back-projection guidance (ablation) | IDPG · CelebA-HQ 1K, Gaussian deblurring, σe=0.1 | PSNR [dB]: 28.29 -> 29.28 | Helped |
| Use iteratively preconditioned guidance instead of pure least-squares guidance (ablation) | IDPG · CelebA-HQ 1K, Gaussian deblurring, σe=0.1 | PSNR [dB]: 27.89 -> 29.28 | Helped |
| Add sampling-based noise injection and the DDPG sampling scheme to IDPG | IDPG · Image restoration benchmarks in Tables 2–3 | LPIPS | Helped |
| Add sampling-based noise injection and the DDPG sampling scheme to IDPG | IDPG · Image restoration benchmarks in Tables 2–3 | PSNR [dB] | Mixed |
| Use iteratively preconditioned guidance instead of pure back-projection guidance (ablation) | IDPG · CelebA-HQ 1K, bicubic SRx4, σe=0 | PSNR [dB]: 32.66 -> 32.66 | No clear effect |
Surprising findings
- DPS requires 1000 NFEs and takes about a dozen minutes per image, and limiting it to 100 iterations fails to produce meaningful recoveries.
Limitations
- Preconditioner schedule delta_t is an engineered rule rather than learned
- Hyperparameters (eta, gamma, zeta) must be tuned per setting
- Evaluated only on deblurring and super-resolution with CelebA-HQ and ImageNet; noisy SR shows PSNR gap versus some baselines
Experimental setup
Datasets: CelebA-HQ ImageNet
Benchmarks: CelebA-HQ 1K ImageNet 1K
Metrics: PSNR LPIPS
Baselines: DDRM DPS DDNM DiffPIR IDBP PGM-LS
Builds on: DDIM DDNM IDBP DiffPIR DPS
Closest papers by meaning
- A Restoration Network as an Implicit Prior (ICLR 2024 · similarity 0.90)
- Improving Diffusion-Based Image Restoration with Error Contraction and Error Correction (AAAI 2024 · similarity 0.89)
- Zero-Shot Image Restoration Using Few-Step Guidance of Consistency Models (and Beyond) (CVPR 2025 · similarity 0.88)
- Denoising as Adaptation: Noise-Space Domain Adaptation for Image Restoration (ICLR 2025 · similarity 0.88)
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.87)
- Resfusion: Denoising Diffusion Probabilistic Models for Image Restoration Based on Prior Residual Noise (NeurIPS 2024 · similarity 0.87)
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