SITCOM：用于逆问题的逐步三重一致性扩散采样
SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems
AI总结：
针对逆问题中扩散模型采样误差累积和步骤多的问题，提出SITCOM方法，通过逐步三重一致性约束，减少反向步骤，在多种任务上达到SOTA性能。
摘要：
扩散模型（DMs）是一类生成模型，允许从训练集上学习到的分布中进行采样。当应用于求解逆问题时，反向采样步骤被修改为近似地从测量条件分布中采样。然而，这些修改可能不适用于某些设置（例如，存在测量噪声）和非线性任务，因为它们通常难以纠正早期步骤中的错误，并且通常需要大量的优化和/或采样步骤。为了解决这些挑战，我们提出了实现测量一致扩散轨迹的三个条件。基于这些条件，我们提出了一种新的基于优化的采样方法，该方法不仅强制执行标准的数据流形测量一致性和前向扩散一致性（如先前研究中所见），而且还结合了我们提出的逐步和网络正则化的后向扩散一致性，该一致性通过在每一步采样步骤中优化预训练模型的输入来维持扩散轨迹。通过强制执行这些条件（隐式或显式），我们的采样器需要显著更少的反向步骤。因此，我们将我们的方法称为逐步三重一致性采样（SITCOM）。与SOTA基线相比，我们在多个线性和非线性任务（使用自然图像和医学图像）上的实验表明，SITCOM在标准相似度指标和运行时间方面取得了具有竞争力或更优的结果。
英文摘要：
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 problems, the reverse sampling steps are modified to approximately sample from a measurement-conditioned distribution. However, these modifications may be unsuitable for certain settings (e.g., presence of measurement noise) and non-linear tasks, as they often struggle to correct errors from earlier 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 standard data manifold measurement consistency and forward diffusion consistency, as seen in previous studies, but also incorporates our proposed step-wise and network-regularized 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 (implicitly or explicitly), our sampler requires significantly fewer reverse steps. Therefore, we refer to our method as Step-wise Triple-Consistent Sampling (SITCOM). Compared to SOTA baselines, our experiments across several linear and non-linear tasks (with natural and medical images) demonstrate that SITCOM achieves competitive or superior results in terms of standard similarity metrics and run-time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
