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Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysis

ICML 2024 · Image generation › Fast diffusion sampling · approach: Diffusion posterior sampling · 1 citations (OpenAlex)

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Analyzes PnP-ADMM convergence when the denoiser is a mismatched MMSE denoiser (trained on a shifted distribution), giving an explicit error bound for nonconvex data-fidelity and expansive denoisers, and shows that few-shot denoiser adaptation closes the super-resolution performance gap.

Problem

PnP-ADMM is typically analyzed assuming the denoiser matches the test distribution, and existing convergence theory requires convex data-fidelity and nonexpansive denoisers; the effect of prior distribution mismatch between training and testing data is largely unstudied.

Approach

Models a mismatched denoiser as an MMSE estimator for a shifted prior, bounds its output distance to the target denoiser by delta_k, and derives a nonconvex convergence bound for PnP-ADMM whose error term depends on these delta_k; domain adaptation with few target images is then used to shrink the mismatch.

Key results

• Target MMSE denoiser (MetFaces) gives the best PnP-ADMM super-resolution result (avg 32.61 dB / 0.8404 SSIM at kernels averaged), while BreCaHAD, the most dissimilar prior, is worst (avg 30.18 dB / 0.7522 SSIM).
• Adapting the BreCaHAD denoiser with 64 MetFaces images raises the average PSNR from 30.18 to 32.21 dB, nearly closing the gap to the target's 32.61 dB.
• The theory gives a convergence bound for mismatched PnP-ADMM with an averaged error term that vanishes when the denoiser distances delta_k are summable.

Measured effects reported in the paper

Surprising findings

• PnP-ADMM is relatively robust to prior mismatch, with most mismatched denoisers reaching within about 1 dB of the target denoiser on average.
• Denoisers are trained without any nonexpansiveness constraint (no spectral normalization), unlike many PnP methods.

Limitations

• Analysis assumes denoisers exactly compute the MMSE estimator, which holds only for MSE-trained denoisers, not for l1 or SSIM losses.
• Theory assumes bounded iterates (Assumption on R) and Lipschitz gradients of the implicit regularizers, which are assumptions rather than verified properties.
• Numerical validation is limited to image super-resolution with l2 data fidelity.

Experimental setup

Datasets: MetFaces AFHQ CelebA BreCaHAD RxRx1

Benchmarks: MetFaces test set (super-resolution)

Metrics: PSNR SSIM

Baselines: PnP-ADMM with target denoiser (MetFaces) PnP-ADMM with mismatched denoisers (BreCaHAD, RxRx1, AFHQ, CelebA)

Builds on: PnP-ADMM DRUNet

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