这篇论文提出了 EPS 方法，能更高效准确地求解线性逆问题，在多个基准上表现优异，且计算开销低。
本文提出 Exact Posterior Score (EPS) 方法，针对线性高斯逆问题推导出后验分数的闭式解。该方法在一般高斯插值下，将后验采样转化为特定算子依赖的平移点下的各向异性噪声去噪问题。EPS 可从头训练或从预训练去噪器微调，推理时使用与基础模型相同的采样器，无需似然梯度或投影。在 FFHQ 和 ImageNet 上的五个线性逆问题中，EPS 在保真度、感知和分布指标上优于无训练和基于训练的方法，且去噪器评估次数比基于梯度的后验采样器少约一个数量级。
Diffusion and flow-based models learn powerful data priors by training a denoiser to reverse Gaussian corruption. To use this prior to solve a linear inverse problem, one needs to sample from the posterior, but the score that the prior provides is the unconditional score, not the posterior score. Existing methods either steer a fixed pretrained denoiser with approximate measurement-matching corrections, or train a conditional restoration model that abandons the denoising structure of the prior. We derive the exact posterior score in closed form for linear Gaussian inverse problems under general Gaussian interpolants, and show that posterior sampling reduces to a denoising problem at an operator-dependent shifted pivot under an anisotropic noise covariance. We turn this identity into Exact Posterior Score (EPS), a denoising training objective that preserves the input/output structure of standard pretraining and can therefore be trained from scratch or fine-tuned from a pretrained denoiser. At inference, EPS uses the same sampler as the underlying backbone, with no likelihood gradients or projections. We evaluate EPS on five linear inverse problems across FFHQ and ImageNet, where it outperforms training-free and training-based baselines on fidelity, perceptual, and distributional metrics, while using roughly an order of magnitude fewer denoiser evaluations than gradient-based posterior samplers.