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Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors
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Proposes PnP-DM, an MCMC posterior sampler that runs split Gibbs sampling with a likelihood Langevin/Gaussian step and a prior step solved exactly via EDM-formulated diffusion models, applied to linear, nonlinear, and black hole imaging inverse problems.
Problem
Existing diffusion-model inverse solvers approximate the intractable likelihood score, so their samples deviate from the true Bayesian posterior for general (linear and nonlinear) imaging inverse problems.
Approach
Reduce posterior sampling to a Gaussian denoising posterior sampling problem solved by split Gibbs sampling, and solve the denoising step rigorously by running the reverse SDE of any diffusion model converted to the unified EDM formulation, with an annealed coupling parameter rho.
Key results
- On linear problems PnP-DM (EDM) reaches 29.66 dB PSNR on Gaussian deblur and 29.60 dB on 4x super-resolution, the best or near-best among compared methods.
- On Fourier phase retrieval PnP-DM (EDM) achieves 31.14 dB PSNR versus 23.60 dB for DPS and 29.28 dB for DPnP.
- In the uncertainty analysis for motion deblur, PnP-DM covers 97.46% of ground-truth pixels within the 3-sigma credible interval versus 96.20% and 88.77% for baselines.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PnP-DM (EDM) instead of DPnP | Gaussian deblurring · FFHQ validation, Gaussian deblur | PSNR: 29.24 -> 29.66 | Helped |
| Use PnP-DM (VE) instead of DPnP | Motion deblurring · FFHQ validation, motion deblur | PSNR: 30.21 -> 30.38 | Helped |
| Use PnP-DM (EDM) instead of DPnP | Super-resolution · FFHQ validation, super-resolution (4×) | PSNR: 29.32 -> 29.60 | Helped |
| Use PnP-DM (iDDPM) instead of DPS | Coded diffraction patterns · FFHQ test, coded diffraction patterns | PSNR: 33.43 -> 33.35 | Hurt |
| Use PnP-DM (EDM) instead of DPnP | Fourier phase retrieval · FFHQ test, Fourier phase retrieval | PSNR: 29.28 -> 31.14 | Helped |
| Replace the VP diffusion prior with the VE diffusion prior (ablation) | PnP-DM · FFHQ validation, Gaussian deblur | PSNR: 29.46 -> 29.65 | Helped |
| Replace the VP diffusion prior with the EDM diffusion prior (ablation) | PnP-DM · FFHQ validation, motion deblur | PSNR: 30.06 -> 30.35 | Helped |
| Replace the VP diffusion prior with the EDM diffusion prior (ablation) | PnP-DM · FFHQ validation, super-resolution (4×) | PSNR: 29.40 -> 29.60 | Helped |
| Replace the VP diffusion prior with the iDDPM diffusion prior (ablation) | PnP-DM · FFHQ test, coded diffraction patterns | PSNR: 32.91 -> 33.35 | Helped |
| Replace the VP diffusion prior with the EDM diffusion prior (ablation) | PnP-DM · FFHQ test, Fourier phase retrieval | PSNR: 30.36 -> 31.14 | Helped |
Surprising findings
- PnP-SGS collapses on Fourier phase retrieval (15.36 dB PSNR), showing heuristic prior steps fail on hard nonlinear problems.
- DPS gives a higher PSNR than PnP-DM on coded diffraction patterns (33.43 vs 33.25 for EDM), so PnP-DM does not win everywhere.
Limitations
- Processes the entire image at once, which may be computationally challenging for large-scale (e.g. 3D) or expensive-likelihood problems.
- Theory ignores the finite-iteration Langevin approximation error in the likelihood step for nonlinear problems.
Experimental setup
Datasets: FFHQ CelebA EHT 2017 M87 observations GRMHD black hole simulations
Benchmarks: FFHQ 100 validation images (Gaussian deblur, motion deblur, super-resolution, CDP, Fourier phase retrieval) black hole imaging (simulated Sgr A* and real M87 data) synthetic Gaussian prior with known posterior
Metrics: PSNR SSIM LPIPS uncertainty calibration (3-sigma coverage) data mismatch chi-squared
Baselines: PnP-ADMM DPIR DDRM DPS PnP-SGS DPnP HIO
Builds on: Split Gibbs Sampler EDM DPS DPnP PnP-SGS
Closest papers by meaning
- Divide-and-Conquer Posterior Sampling for Denoising Diffusion priors (NeurIPS 2024 · similarity 0.92)
- Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction (NeurIPS 2024 · similarity 0.90)
- A Mixture-Based Framework for Guiding Diffusion Models (ICML 2025 · similarity 0.90)
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.90)
- Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing (CVPR 2025 · similarity 0.90)
- Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo (ICML 2025 · similarity 0.89)
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