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 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).

翻译：我们考虑普遍存在的含加性高斯噪声的线性逆问题，并提出一种无监督采样方法——基于扩散模型的后验采样（DMPS），用于从含噪线性测量中重建未知信号。具体而言，使用一个扩散模型（DM）作为隐式先验，进行后验采样的根本困难在于噪声扰动下的似然得分（即退火似然函数的梯度）难以处理。为解决此问题，我们引入一种简单而有效的闭式近似，其基于无信息先验假设。我们在多种含噪线性逆问题（如含噪超分辨率、去噪、去模糊和着色）上进行了大量实验。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，同时比当前最先进的竞争方法扩散后验采样（DPS）快3倍。