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

Researchers present a new diffusion posterior sampling method that improves inverse problem solving by replacing hand-tuned guidance weights with a mathematically principled damped Gauss-Newton correction. The approach demonstrates competitive or superior performance on image reconstruction tasks including accelerated MRI while reducing computational overhead compared to existing methods.

This research addresses a fundamental challenge in diffusion model-based inverse problems: balancing data consistency with sampling stability. Traditional diffusion posterior sampling relies on scalar guidance weights that require manual tuning and can destabilize under complex operator geometries. The proposed method introduces per-noise-level damping that adapts to the problem's inherent curvature, eliminating manual hyperparameter selection.

The technical innovation centers on computing corrections in diffusion-state coordinates using a one-sided curvature model that avoids expensive forward denoiser Jacobian computations. By pulling likelihood gradients back through the denoiser and applying diffusion-calibrated rank-one damping aligned with denoiser residuals, the method achieves theoretical robustness while maintaining computational efficiency. Matrix-free GMRES solvers with automatic differentiation enable practical implementation.

For practitioners, the results suggest meaningful improvements in inverse problem applications spanning natural image reconstruction on FFHQ and ImageNet to medical imaging. The approach achieves competitive perceptual metrics while demonstrating faster runtimes than comparable baselines. Accelerated MRI reconstruction shows particular promise, achieving superior PSNR and SSIM scores—clinically relevant metrics for medical imaging quality.

The broader implication extends to generative model deployment in domains requiring precise geometric handling. As diffusion models expand into scientific computing and inverse problem solving, principled guidance mechanisms replace ad-hoc tuning. This work establishes a foundation for geometry-aware sampling that could influence how generative models integrate into computational imaging pipelines across research and commercial applications.

• →Replaces manual guidance weights with adaptive per-noise-level damped Gauss-Newton corrections for stable diffusion posterior sampling
• →Achieves competitive or superior image quality metrics while running faster than most baseline methods on FFHQ and ImageNet inverse problems
• →Demonstrates best-in-class PSNR/SSIM performance for accelerated MRI reconstruction compared to evaluated baselines
• →Eliminates expensive denoiser Jacobian computations through one-sided curvature modeling, reducing computational burden
• →Enables practical deployment via matrix-free GMRES solvers with automatic differentiation for large-scale inverse problems