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Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction
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Proposes DPnP, a plug-and-play posterior sampler that alternates a likelihood-based proximal consistency sampler (MALA-style) with a denoising diffusion sampler (DDPM/DDIM-type) using unconditional score functions, with asymptotic and non-asymptotic guarantees for nonlinear inverse problems.
Problem
Posterior sampling for general (including nonlinear) image inverse problems using an unconditional score-based diffusion prior, with provable consistency and robustness.
Approach
Alternate a proximal consistency sampler (Langevin/MALA on likelihood plus Gaussian proximal term) with a denoising diffusion sampler derived from heat-flow/OU reversal (DDS-DDPM and DDS-DDIM) that uses the same unconditional score functions, yielding a modular plug-and-play scheme with TV-error guarantees.
Key results
- On FFHQ, DPnP-DDIM reaches LPIPS 0.376 and PSNR 22.4 on phase retrieval versus DPS 0.490/17.4 and LGD-MC 0.522/16.4.
- On FFHQ 4x super-resolution, DPnP-DDIM achieves LPIPS 0.301 and PSNR 24.2, versus DPS 0.331/23.1.
- On ImageNet, DPnP-DDIM is best on super-resolution (LPIPS 0.416, PSNR 21.6 tied with LGD-MC LPIPS) and quantized sensing (LPIPS 0.363, PSNR 23.0), but on phase retrieval PSNR 13.4 ties DPS while LPIPS is 0.562 vs DPS 0.677.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use DPnP-DDIM instead of LGD-MC | FFHQ super-resolution (4x) · FFHQ validation, super-resolution (4x) | LPIPS: 0.318 -> 0.301 | Helped |
| use DPnP-DDIM instead of LGD-MC | FFHQ super-resolution (4x) · FFHQ validation, super-resolution (4x) | PSNR: 23.9 -> 24.2 | Helped |
| use DPnP-DDIM instead of DPS | FFHQ phase retrieval · FFHQ validation, phase retrieval | LPIPS: 0.490 -> 0.376 | Helped |
| use DPnP-DDIM instead of DPS | FFHQ phase retrieval · FFHQ validation, phase retrieval | PSNR: 17.4 -> 22.4 | Helped |
| use DPnP-DDIM instead of LGD-MC | FFHQ quantized sensing · FFHQ validation, quantized sensing | LPIPS: 0.317 -> 0.293 | Helped |
| use DPnP-DDIM instead of LGD-MC | FFHQ quantized sensing · FFHQ validation, quantized sensing | PSNR: 23.9 -> 24.2 | Helped |
| use DPnP-DDIM instead of LGD-MC | ImageNet super-resolution (4x) · ImageNet validation, super-resolution (4x) | LPIPS: 0.416 -> 0.416 | No clear effect |
| use DPnP-DDIM instead of LGD-MC | ImageNet super-resolution (4x) · ImageNet validation, super-resolution (4x) | PSNR: 20.9 -> 21.6 | Helped |
| use DPnP-DDIM instead of LGD-MC | ImageNet phase retrieval · ImageNet validation, phase retrieval | LPIPS: 0.592 -> 0.562 | Helped |
| use DPnP-DDIM instead of DPS | ImageNet phase retrieval · ImageNet validation, phase retrieval | PSNR: 13.4 -> 13.4 | No clear effect |
| use DPnP-DDIM instead of LGD-MC | ImageNet quantized sensing · ImageNet validation, quantized sensing | LPIPS: 0.384 -> 0.363 | Helped |
| use DPnP-DDIM instead of LGD-MC | ImageNet quantized sensing · ImageNet validation, quantized sensing | PSNR: 22.3 -> 23.0 | Helped |
Surprising findings
- On ImageNet phase retrieval, DPnP-DDIM matches DPS PSNR (13.4) and is far below FFHQ performance, indicating difficulty on diverse data.
Limitations
- Non-asymptotic guarantee assumes black-box bounded total-variation errors for the samplers; spectral gap can be exponentially small in worst case.
- Requires known noise level and differentiable likelihood for MALA-based proximal consistency sampler.
- Compute is about 1.5x that of DPS and LGD-MC baselines.
Experimental setup
Datasets: FFHQ validation set ImageNet validation set
Benchmarks: FFHQ 256x256 validation (1k samples) ImageNet 256x256 validation (1k samples)
Metrics: LPIPS PSNR time per sample
Baselines: DPS LGD-MC
Builds on: Diffusion posterior sampling (DPS) plug-and-play priors Metropolis-adjusted Langevin algorithm exponential integrator DDPM DDIM
Closest papers by meaning
- Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posterior (ICLR 2025 · similarity 0.91)
- Exact Posterior Score Estimation for Solving Linear Inverse Problems (NeurIPS 2026 · similarity 0.91)
- Divide-and-Conquer Posterior Sampling for Denoising Diffusion priors (NeurIPS 2024 · similarity 0.91)
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.91)
- Provable Posterior Sampling with Denoising Oracles via Tilted Transport (NeurIPS 2024 · similarity 0.91)
- Whitened Score Diffusion: A Structured Prior for Imaging Inverse Problems (NeurIPS 2025 · similarity 0.91)
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