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

2026-05-27

AI Summary

This work addresses the instability of traditional scalar guidance weights in diffusion posterior sampling under high curvature regimes. To overcome this, the authors propose a geometrically corrected diffusion posterior sampling method that achieves stable and efficient data consistency through noise-level-specific damped Gauss–Newton updates in the diffusion coordinate system. Key innovations include implicitly pulling back likelihood gradients via the denoiser, employing a one-sided curvature model to circumvent explicit Jacobian computation, and introducing a rank-one damping mechanism aligned with denoising residuals. The framework further integrates a matrix-free GMRES solver, variance-preserving Langevin transitions, and closed-form drift/noise decompositions. Evaluated on inverse problems for FFHQ and ImageNet, the method achieves state-of-the-art PSNR, SSIM, and LPIPS scores with significantly faster runtime than baselines, and attains optimal performance in accelerated MRI reconstruction.

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.

Problem

• diffusion posterior sampling
• data consistency
• curvature guidance
• damping
• inverse problems

Innovation

• diffusion posterior sampling
• denoiser-pullback curvature
• manifold-aligned damping
• matrix-free GMRES
• variance-preserving Langevin