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Listening to the noise: Blind Denoising with Gibbs Diffusion
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Introduces Gibbs Diffusion (GDiff), which alternates a noise-parameter-conditional diffusion posterior sampler with HMC over Gaussian noise parameters to perform blind denoising of images with colored noise and CMB component separation.
Problem
Blind denoising requires sampling the joint posterior of signal and noise parameters, but diffusion-based posterior sampling assumes the noise level and covariance are known.
Approach
Combine a noise-parameter-conditional diffusion model (trained as a denoiser whose forward SDE maps the signal prior to the family of Gaussian noise distributions) with an HMC sampler for noise parameters inside a Gibbs loop, and analyze the stationary distribution's compatibility and the error introduced by the diffusion approximation.
Key results
- On ImageNet with white noise sigma=0.1, GDiff posterior mean reaches 32.7 dB PSNR vs 31.8 dB for BM3D and 31.8 dB for DnCNN (blind GDiff posterior mean outperforms non-blind BM3D).
- GDiff posterior samples yield lower PSNR than BM3D and DnCNN, while posterior-mean estimates systematically outperform both across tested noise levels and spectral indices.
- Simulation-based calibration shows sigma well calibrated on natural images but spectral index phi shows bias; for CMB, H0 and omega_b are well calibrated while sigma shows slant.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GDiff posterior-mean estimates instead of BM3D | Blind natural-image denoising · ImageNet, pink noise, σ=0.06 | PSNR (dB): 31.0 -> 32.2 | Helped |
| Use GDiff posterior-mean estimates instead of the strongest baseline | Blind natural-image denoising · ImageNet, white noise, σ=0.1 | PSNR (dB): 31.8 -> 32.7 | Helped |
| Use GDiff posterior samples rather than the posterior mean | GDiff · Natural-image denoising | PSNR: posterior mean estimate improves the PSNR of the sample by ~3 dB | Hurt |
| Train DnCNN on white noise only and evaluate at non-white noise levels | DnCNN · Natural-image denoising with φ ≠ 0 | PSNR | Hurt |
| Continue diffusion-model training after the loss plateau | Cosmological GDiff · CMB inference | Posterior calibration | Helped |
| Use Fourier features at lower noise levels | Cosmological GDiff diffusion network · CMB inference | Posterior calibration | Helped |
| Use the diffusion posterior approximation q(x|y,φ) instead of the exact conditional | GDiff · Posterior inference on φ | KL divergence from true posterior | Hurt |
| Use a time-dependent regularization term for Π-GDM | Guidance-based cosmological posterior sampling · CMB inference | Posterior estimation | Hurt |
Surprising findings
- Posterior samples denoise worse in PSNR than BM3D and DnCNN, while posterior means do better, reflecting the tradeoff between realism and PSNR.
- Off-the-shelf guidance-based methods DPS and Pi-GDM produced numerical overflows and failed to sample the posterior in the cosmology application.
Limitations
- Restricted to Gaussian noise assumption.
- Diffusion model approximation error introduces bias in the stationary distribution, detected by SBC for spectral index and CMB amplitude.
- Computationally expensive diffusion sampling within each Gibbs iteration.
Experimental setup
Datasets: ImageNet 2012 CBSD68 CATS dust simulations Planck 2018 fiducial cosmology (simulated CMB via CAMB)
Benchmarks: ImageNet validation subset CBSD68
Metrics: PSNR SSIM R-hat effective sample size simulation-based calibration rank statistics
Baselines: BM3D DnCNN DPS Pi-GDM
Builds on: denoising diffusion probabilistic models Gibbs sampling Hamiltonian Monte Carlo
Closest papers by meaning
- Warm Diffusion: Recipe for Blur-Noise Mixture Diffusion Models (ICLR 2025 · similarity 0.88)
- Divide-and-Conquer Posterior Sampling for Denoising Diffusion priors (NeurIPS 2024 · similarity 0.88)
- Diffusion Priors for Variational Likelihood Estimation and Image Denoising (NeurIPS 2024 · similarity 0.88)
- A Mixture-Based Framework for Guiding Diffusion Models (ICML 2025 · similarity 0.88)
- Provable Posterior Sampling with Denoising Oracles via Tilted Transport (NeurIPS 2024 · similarity 0.88)
- Diffusion Models With Learned Adaptive Noise (NeurIPS 2024 · similarity 0.87)
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