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Analyzing and Guiding Zero-Shot Posterior Sampling in Diffusion Models

NeurIPS 2026 · Image generation › Fast diffusion sampling · approach: Diffusion posterior sampling · 0 citations (OpenAlex)

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Analyzes zero-shot diffusion posterior samplers (DPS, ΠGDM, DiffPIR) under a Gaussian prior, derives closed-form spectral transfer functions, and uses them to design guidance weights that outperform heuristics.

Problem

Guidance/weighting hyperparameters in zero-shot diffusion posterior samplers for linear inverse problems are chosen heuristically, with no principled account of prior, observation, and diffusion dynamics.

Approach

Under a Gaussian, shift-invariant prior and linear degradation, the DDIM-based DPS update and the ideal posterior sampler reduce to per-frequency scalar transfer functions; guidance weights are then chosen by minimizing a Wasserstein-2 distance to the true Gaussian posterior, in a method-agnostic way.

Key results

• On FFHQ with LPF (V=0.1, sigma_y=0.1), spectral weights for DPS at 100 steps reach PSNR 27.82 and FID 41.31 versus DPS heuristic PSNR 18.31 and FID 62.68.
• On fastMRI LPF degradation at 50 steps, spectral weights give PSNR 23.20 versus 17.98 for DPS heuristic.
• On the synthetic Gaussian setting, the spectral recommendation consistently yields lower Wasserstein-2 distance than hand-crafted DPS weights across step counts.

Surprising findings

• Optimal spectral guidance weights increase toward the end of the reverse process, opposite to the DPS heuristic which grows as the measurement error shrinks.
• DiffPIR recommendations for small step counts slightly surpass the exact Gaussian posterior denoiser in Wasserstein-2 distance.

Limitations

• Analysis relies on Gaussian prior and shift-invariant covariance and degradation operators.
• Neural denoisers used on real datasets introduce approximation error beyond the closed-form analysis.
• Realization-specific optimization requires solving a separate problem per observation.

Experimental setup

Datasets: FFHQ 256x256 ImageNet 256x256 fastMRI single-coil knee

Benchmarks: FFHQ 256x256 ImageNet 256x256 fastMRI

Metrics: PSNR SSIM LPIPS FID Wasserstein-2 distance

Baselines: DPS heuristic weights ΠGDM DiffPIR DAPS

Builds on: DPS DDIM ΠGDM DiffPIR DAPS

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