Accurate imputation is essential for the reliability and success of downstream tasks. Recently, diffusion models have attracted great attention in this field. However, these models neglect the latent distribution in a lower-dimensional space derived from the observed data, which limits the generative capacity of the diffusion model. Additionally, dealing with the original missing data without labels becomes particularly problematic. To address these issues, we propose the Latent Space Score-Based Diffusion Model (LSSDM) for probabilistic multivariate time series imputation. Observed values are projected onto low-dimensional latent space and coarse values of the missing data are reconstructed without knowing their ground truth values by this unsupervised learning approach. Finally, the reconstructed values are fed into a conditional diffusion model to obtain the precise imputed values of the time series. In this way, LSSDM not only possesses the power to identify the latent distribution but also seamlessly integrates the diffusion model to obtain the high-fidelity imputed values and assess the uncertainty of the dataset. Experimental results demonstrate that LSSDM achieves superior imputation performance while also providing a better explanation and uncertainty analysis of the imputation mechanism. The website of the code is \textit{https://github.com/gorgen2020/LSSDM\_imputation}.

翻译：精确插补对于下游任务的可靠性和成功至关重要。近年来，扩散模型在该领域引起了极大关注。然而，这些模型忽略了从观测数据导出的低维空间中的潜在分布，这限制了扩散模型的生成能力。此外，处理无标签的原始缺失数据变得尤为棘手。为解决这些问题，我们提出了用于概率多元时间序列插补的潜在空间基于分数的扩散模型（LSSDM）。观测值被投影到低维潜在空间，并通过这种无监督学习方法在不知道其真实值的情况下重建缺失数据的粗略值。最后，将重建值输入条件扩散模型以获得时间序列的精确插补值。通过这种方式，LSSDM不仅具备识别潜在分布的能力，还能无缝集成扩散模型以获得高保真插补值并评估数据集的不确定性。实验结果表明，LSSDM实现了优越的插补性能，同时为插补机制提供了更好的解释和不确定性分析。代码网站为 \textit{https://github.com/gorgen2020/LSSDM\_imputation}。