Geometry-Correct Diffusion Posterior Sampling with Denoiser-Pullback Curvature Guidance and Manifold-Aligned Damping

• URL: http://arxiv.org/abs/2605.27990v1
• Date: Wed, 27 May 2026 05:29:35 GMT
• Title: Geometry-Correct Diffusion Posterior Sampling with Denoiser-Pullback Curvature Guidance and Manifold-Aligned Damping
• Abstract summary: We replace scalar guidance with a per-noise-level damped Gauss--Newton correction computed in diffusion-state coordinates.<n>It achieves competitive PSNR/SSIM/LPIPS while running markedly faster than most of the compared baselines.
• Score: 2.9985000712079426
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Diffusion posterior sampling conditions diffusion priors on measurements, but data-consistency updates are typically scaled by hand-tuned guidance weights and can destabilize sampling under stiff, operator-dependent curvature. We replace scalar guidance with a per-noise-level damped Gauss--Newton correction computed in diffusion-state coordinates. The correction pulls likelihood gradients back through the denoiser, uses a one-sided curvature model that avoids forward denoiser Jacobians, and applies diffusion-calibrated rank-one damping aligned with the denoiser residual. Each correction is solved with matrix-free GMRES using automatic differentiation, and sampling proceeds with a variance-preserving Langevin transition with a closed-form drift/noise split. On FFHQ and ImageNet across inverse problems, it achieves competitive PSNR/SSIM/LPIPS while running markedly faster than most of the compared baselines; on accelerated MRI reconstruction, it achieves the best PSNR/SSIM among the compared baselines.

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