Diffusion models provide powerful generative priors for solving inverse problems by sampling from a posterior distribution conditioned on corrupted measurements. Existing methods primarily follow two paradigms: direct methods, which approximate the likelihood term, and proximal methods, which incorporate intermediate solutions satisfying measurement constraints into the sampling process. We demonstrate that these approaches differ fundamentally in their treatment of the diffusion denoiser's Jacobian within the likelihood term. While this Jacobian encodes critical prior knowledge of the data distribution, training-induced non-idealities can degrade performance in zero-shot settings. In this work, we bridge direct and proximal approaches by proposing a principled Jacobian-Aware Posterior Sampler (JAPS). JAPS leverages the Jacobian's prior knowledge while mitigating its detrimental effects through a corresponding proximal solution, requiring no additional computational cost. Our method enhances reconstruction quality across diverse linear and nonlinear noisy imaging tasks, outperforming existing diffusion-based baselines in perceptual quality while maintaining or improving distortion metrics.

翻译：扩散模型通过从基于损坏观测量的后验分布中采样，为求解逆问题提供了强大的生成式先验。现有方法主要遵循两种范式：近似似然项的免训练方法，以及将满足观测约束的中间解融入采样过程的近端方法。我们证明这两种方法在似然项中对扩散去噪器雅可比矩阵的处理存在根本性差异。尽管该雅可比矩阵编码了数据分布的关键先验知识，但训练导致的非理想性会在零样本场景中降低性能。本文通过提出一种原理性的雅可比感知后验采样器（JAPS）来桥接免训练与近端方法。JAPS在利用雅可比矩阵先验知识的同时，通过对应的近端解缓解其不利影响，且无需额外计算成本。该方法在多种线性和非线性噪声成像任务中提升了重建质量，在感知质量上超越了现有基于扩散的基线方法，同时保持或改进了失真指标。