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This paper introduces a geometry-correct diffusion posterior sampling method that replaces hand-tuned guidance weights with a per-noise-level damped Gauss-Newton correction computed in diffusion-state coordinates. The method uses a one-sided curvature model and diffusion-calibrated rank-one damping aligned with the denoiser residual, solved efficiently with matrix-free GMRES and automatic differentiation. Experiments on FFHQ, ImageNet, and accelerated MRI reconstruction demonstrate competitive or superior performance in terms of PSNR/SSIM/LPIPS while also achieving faster sampling speeds compared to existing baselines.
Ditch the hand-tuning: this new diffusion sampling method uses a learned, geometry-aware correction that's faster and more accurate.
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.
