We consider the ubiquitous linear inverse problems with additive Gaussian noise and propose an unsupervised sampling approach called diffusion model based posterior sampling (DMPS) to reconstruct the unknown signal from noisy linear measurements. Specifically, using one diffusion model (DM) as an implicit prior, the fundamental difficulty in performing posterior sampling is that the noise-perturbed likelihood score, i.e., gradient of an annealed likelihood function, is intractable. To circumvent this problem, we introduce a simple yet effective closed-form approximation of it using an uninformative prior assumption. Extensive experiments are conducted on a variety of noisy linear inverse problems such as noisy super-resolution, denoising, deblurring, and colorization. In all tasks, the proposed DMPS demonstrates highly competitive or even better performances on various tasks while being 3 times faster than the state-of-the-art competitor diffusion posterior sampling (DPS). The code to reproduce the results is available at https://github.com/mengxiangming/dmps.

翻译：我们考虑具有加性高斯噪声的普遍线性逆问题，并提出一种名为基于扩散模型的后验采样（DMPS）的无监督采样方法，用于从含噪线性测量中重构未知信号。具体而言，使用一个扩散模型（DM）作为隐式先验时，进行后验采样的根本困难在于噪声扰动下的似然分数（即退火似然函数的梯度）是难以处理的。为解决该问题，我们引入一种基于无信息先验假设的简洁有效闭式近似。针对含噪超分辨率、去噪、去模糊及着色等多种含噪线性逆问题开展了广泛实验。在所有任务中，所提出的DMPS均展现出极具竞争力甚至更优的性能，同时其速度比当前最优的竞争者扩散后验采样（DPS）快3倍。复现结果的代码见 https://github.com/mengxiangming/dmps。