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Diffusion Priors for Variational Likelihood Estimation and Image Denoising
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Proposes variational Bayes adaptive likelihood estimation with a noise-precision prior inside diffusion reverse sampling (plus local Gaussian rectification and low-resolution diffusion priors) for real-world image denoising without training.
Problem
Real-world noise (signal-dependent, spatially correlated) is hard to model in diffusion-prior-based restoration, where existing methods assume i.i.d. Gaussian noise or use hard data-consistency with approximate posterior inference.
Approach
Use an independent non-identically distributed Gaussian likelihood with a Gamma precision prior, infer the per-pixel precision posterior via mean-field variational Bayes at each reverse diffusion step, rectify the noise variance with local Gaussian convolution, and take MAP updates; also exploit local priors of low-resolution diffusion models to denoise high-resolution images directly.
Key results
- Achieves average PSNR/SSIM of 36.16/0.919 across SIDD, FMDD, PolyU and CC, versus 35.68/0.906 for ScoreDVI (second best).
- Ablation shows adaptive likelihood estimation raises SIDD PSNR from 32.12 to 34.63 and CC from 33.10 to 37.82.
- Using 1000 diffusion steps is needed: reducing to 250 steps drops CC PSNR to 22.72.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DiffusionVI instead of the strongest reported baseline | Real-world denoising · SIDD Validation, FMDD, PolyU, and CC | PSNR/SSIM | Mixed |
| Add adaptive likelihood estimation (ALE) (ablation) | DiffusionVI · SIDD Validation | PSNR/SSIM: 32.12/0.741 -> 34.63/0.870 | Helped |
| Add adaptive likelihood estimation (ALE) (ablation) | DiffusionVI · FMDD | PSNR/SSIM: 27.07/0.530 -> 33.11/0.865 | Helped |
| Add adaptive likelihood estimation (ALE) (ablation) | DiffusionVI · PolyU | PSNR/SSIM: 35.40/0.895 -> 38.70/0.969 | Helped |
| Add adaptive likelihood estimation (ALE) (ablation) | DiffusionVI · CC | PSNR/SSIM: 33.10/0.830 -> 37.82/0.956 | Helped |
| Add local Gaussian convolution to rectify estimated noise variance (ablation) | DiffusionVI with ALE · SIDD Validation, FMDD, PolyU, and CC | PSNR/SSIM: 34.63/0.870 -> 34.76/0.887; 33.11/0.865 -> 33.14/0.860; 38.70/0.969 -> 38.71/0.970; 37.82/0.956 -> 38.01/0.959 | Mixed |
| Set temperature γ to 1/5 (ablation) | DiffusionVI · CC | PSNR/SSIM: 37.74/0.955 -> 38.01/0.959 | Helped |
| Reduce temperature γ further to 1/20 (ablation) | DiffusionVI · CC | PSNR/SSIM: 38.01/0.959 -> 35.55/0.913 | Hurt |
| Change β from 1e-2 to 1.5e-2 (ablation) | DiffusionVI · CC | PSNR/SSIM: 38.01/0.959 -> 37.47/0.953 | Hurt |
| Change Gaussian kernel scale s from 1.0 to 0.8 (ablation) | DiffusionVI · CC | PSNR/SSIM: 38.01/0.959 -> 37.876/0.957 | Hurt |
| Change Gaussian kernel scale s from 1.0 to 1.2 (ablation) | DiffusionVI · CC | PSNR/SSIM: 38.01/0.959 -> 38.10/0.959 | Mixed |
| Use a 128×128-trained prior for 256×256 SIDD images (ablation) | DiffusionVI · SIDD Validation | PSNR/SSIM: 34.76/0.887 -> 34.80/0.836 | Mixed |
Surprising findings
- APBSN achieves the best PSNR on SIDD (36.80) but degrades substantially on FMDD, PolyU, and CC where fewer noisy images are available.
- Low-resolution (256x256) diffusion priors applied to 512x512 images outperform 512x512 priors on most datasets, suggesting local priors from medium-resolution models are better for restoration.
Limitations
- Slow inference: about 230 seconds per 256x256 image with 1000 DDPM steps, and performance drops sharply with fewer steps.
- Noise correlation handled only via a heuristic Gaussian convolution rather than a full covariance model.
- No statistical significance or error bars reported.
Experimental setup
Datasets: SIDD validation PolyU CC FMDD CBSD68 Kodak Set14
Benchmarks: SIDD validation FMDD PolyU CC CBSD68 Kodak Set14
Metrics: PSNR SSIM
Baselines: DIP Self2Self PD-denoising ZS-N2N ScoreDVI AP-BSN DDRM GDP DR2
Builds on: DDPM DDNM DPS GDP DR2
Closest papers by meaning
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.92)
- Diffusion Models With Learned Adaptive Noise (NeurIPS 2024 · similarity 0.91)
- Divide-and-Conquer Posterior Sampling for Denoising Diffusion priors (NeurIPS 2024 · similarity 0.91)
- A Mixture-Based Framework for Guiding Diffusion Models (ICML 2025 · similarity 0.91)
- Denoising as Adaptation: Noise-Space Domain Adaptation for Image Restoration (ICLR 2025 · similarity 0.90)
- Residual Denoising Diffusion Models (CVPR 2024 · similarity 0.90)
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