用几何校正的扩散采样方法，提升图像重建速度与质量。
Geometry-Correct Diffusion Posterior Sampling with Denoiser-Pullback Curvature Guidance and Manifold-Aligned Damping
- 通过扩散状态坐标计算阻尼高斯-牛顿修正，替代人工调参的引导权重。
- 在FFHQ和ImageNet上达到竞争性指标，加速MRI重建时性能最优。
- 适用于需要快速高精度图像重建的科研与医疗场景。
扩散后验采样将扩散先验与观测数据结合，但传统数据一致性更新依赖手动调节的引导权重，在高曲率条件下易失稳。本文提出一种基于每噪声水平的阻尼高斯-牛顿修正，该修正在扩散状态坐标中计算，通过去噪器回传似然梯度，采用单侧曲率模型避免前向去噪器雅可比矩阵计算，并应用与去噪残差对齐的扩散校准秩一阻尼。每次修正使用自动微分实现的无矩阵GMRES求解，采样过程采用保持方差的Langevin转移，具有闭式漂移/噪声分解。在FFHQ与ImageNet的各类逆问题中，性能达到竞争性PSNR/SSIM/LPIPS，且显著快于多数对比基线；在加速MRI重建任务中，达到所比较方法中的最高PSNR与SSIM。
原文摘要 · Abstract (English)
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.
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