Diffusion Posterior Sampling with Geometry-Correct Guidance
A novel approach to diffusion posterior sampling substitutes scalar guidance with a damped Gauss-Newton correction tailored for each noise level, calculated in diffusion-state coordinates. This correction effectively retracts likelihood gradients through the denoiser, employs a one-sided curvature model that bypasses the need for forward denoiser Jacobians, and integrates diffusion-calibrated rank-one damping that corresponds with the denoiser residual. Each correction is addressed using matrix-free GMRES alongside automatic differentiation, while sampling is executed through a variance-preserving Langevin transition featuring a closed-form drift/noise separation. It demonstrates competitive PSNR/SSIM/LPIPS on FFHQ and ImageNet across inverse problems, running significantly faster than most baselines, and exhibits robust performance in accelerated MRI reconstruction.
Key facts
- Method replaces scalar guidance with per-noise-level damped Gauss-Newton correction.
- Correction pulls likelihood gradients back through the denoiser.
- Uses one-sided curvature model to avoid forward denoiser Jacobians.
- Applies diffusion-calibrated rank-one damping aligned with denoiser residual.
- Each correction solved with matrix-free GMRES using automatic differentiation.
- Sampling uses variance-preserving Langevin transition with closed-form drift/noise split.
- Tested on FFHQ and ImageNet across inverse problems.
- Achieves competitive PSNR/SSIM/LPIPS while running faster than most baselines.
Entities
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