Diffusion models (DMs) are a class of generative models that allow sampling from a distribution learned over a training set. When applied to solving inverse imaging problems (IPs), the reverse sampling steps of DMs are typically modified to approximately sample from a measurement-conditioned distribution in the image space. However, these modifications may be unsuitable for certain settings (such as in the presence of measurement noise) and non-linear tasks, as they often struggle to correct errors from earlier sampling steps and generally require a large number of optimization and/or sampling steps. To address these challenges, we state three conditions for achieving measurement-consistent diffusion trajectories. Building on these conditions, we propose a new optimization-based sampling method that not only enforces the standard data manifold measurement consistency and forward diffusion consistency, as seen in previous studies, but also incorporates backward diffusion consistency that maintains a diffusion trajectory by optimizing over the input of the pre-trained model at every sampling step. By enforcing these conditions, either implicitly or explicitly, our sampler requires significantly fewer reverse steps. Therefore, we refer to our accelerated method as Step-wise Triple-Consistent Sampling (SITCOM). Compared to existing state-of-the-art baseline methods, under different levels of measurement noise, our extensive experiments across five linear and three non-linear image restoration tasks demonstrate that SITCOM achieves competitive or superior results in terms of standard image similarity metrics while requiring a significantly reduced run-time across all considered tasks.

本研究旨在解决传统扩散模型在逆成像问题中由于测量噪声或非线性任务带来的采样困难。提出了一种新的优化基础采样方法——步进三重一致采样（SITCOM），该方法不仅确保数据流形测量一致性，还引入了反向扩散一致性，以减少所需的反向步骤。实验结果显示，SITCOM在五个线性和三个非线性图像恢复任务中，在图像相似度指标上表现出竞争力或优越性，同时显著减少了运行时间。

步进三重一致扩散采样用于逆问题