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

Seunghyeok Shin, Minwoo Kim, Dabin Kim, Hongki Lim

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. Code is available at https://github.com/Seunghyeok0715/CLAMP

Lay Summary:

Many imaging tasks start from imperfect measurements: a photo may be blurry, or an MRI scan may collect fewer measurements to reduce scanning time. The goal is to recover an image that looks realistic while still agreeing with the measurements that were actually collected.

AI image-generation models can help because they learn what realistic images tend to look like, but existing methods often depend on task-specific choices about how strongly to force agreement with the data. If this force is too weak, important details may not match the measurements; if it is too strong, the recovery process can become unstable.

We propose a method that adjusts the correction during recovery and limits updates that are likely to be too aggressive. On standard natural-image recovery tasks, it achieves quality comparable to strong existing methods while often running faster. On accelerated MRI reconstruction, it gives the best recovered-image quality among the methods we compared, suggesting a stable and efficient way to use image-generation models when measurements are limited or noisy.

Link To Code: https://github.com/Seunghyeok0715/CLAMP

Primary Area: Deep Learning->Generative Models and Autoencoders

Keywords: inverse problem, diffusion models, posterior sampling

Submission Number: 32428