With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative models. However, while remarkable reconstruction performances have been achieved, their inference time is typically too slow since most of them rely on the seminal diffusion posterior sampling (DPS) framework and thus to approximate the intractable likelihood score, time-consuming gradient calculation through back-propagation is needed. To address this issue, this paper provides a fast and effective solution by proposing a simple closed-form approximation to the likelihood score. For both diffusion and flow-based models, extensive experiments are conducted on various noisy linear inverse problems such as noisy super-resolution, denoising, deblurring, and colorization. In all these tasks, our method (namely DMPS) demonstrates highly competitive or even better reconstruction performances while being significantly faster than all the baseline methods.

翻译：随着扩散模型和基于流的生成模型的快速发展，利用生成模型解决噪声线性逆问题（如超分辨率、去模糊、去噪、着色等）的研究兴趣激增。然而，尽管这些方法已取得显著的重建性能，其推理时间通常过于缓慢，因为大多数方法依赖于开创性的扩散后验采样（DPS）框架，需要通过耗时的反向传播梯度计算来近似难以处理的似然分数。为解决这一问题，本文提出了一种简单闭式似然分数近似方法，提供了一种快速有效的解决方案。针对扩散模型和基于流的模型，我们在多种噪声线性逆问题（如噪声超分辨率、去噪、去模糊和着色）上进行了大量实验。在所有任务中，我们的方法（称为DMPS）展现出高度竞争力甚至更优的重建性能，同时显著快于所有基线方法。