Spatiotemporal data analysis is pivotal across various domains, such as transportation, meteorology, and healthcare. The data collected in real-world scenarios are often incomplete due to device malfunctions and network errors. Spatiotemporal imputation aims to predict missing values by exploiting the spatial and temporal dependencies in the observed data. Traditional imputation approaches based on statistical and machine learning techniques require the data to conform to their distributional assumptions, while graph and recurrent neural networks are prone to error accumulation problems due to their recurrent structures. Generative models, especially diffusion models, can potentially circumvent the reliance on inaccurate, previously imputed values for future predictions; However, diffusion models still face challenges in generating stable results. We propose to address these challenges by designing conditional information to guide the generative process and expedite the training process. We introduce a conditional diffusion framework called C$^2$TSD, which incorporates disentangled temporal (trend and seasonality) representations as conditional information and employs contrastive learning to improve generalizability. Our extensive experiments on three real-world datasets demonstrate the superior performance of our approach compared to a number of state-of-the-art baselines.

The presence of multivariate time series data is extensively documented across a variety of sectors including economics, transportation, healthcare, and meteorology, as evidenced in several studies [1, 2, 3, 4]. A range of statistical and machine learning techniques have been shown to perform effectively on complete datasets in several time series tasks, including forecasting [5], classification [6], and anomaly detection [7]. However, it is often observed that multivariate time series data collected from real-world scenarios are prone to missing values due to various factors, such as sensor malfunctions and data transmission errors. These missing values can considerably affect the quality of the data, subsequently impacting the effectiveness of the aforementioned methods in their respective tasks. Extensive research efforts have been dedicated to addressing the challenges in spatiotemporal imputation. A typical approach involves the development of a distinct framework for initially estimating missing values, followed by the application of the completed dataset in another sophisticated framework for subsequent operations like forecasting, classification, and anomaly detection. To fill in missing values, various statistical and machine learning techniques are applied.

Spatiotemporal data mining plays an important role in air quality monitoring, crowd flow modeling, and climate forecasting. However, the originally collected spatiotemporal data in real-world scenarios is usually incomplete due to sensor failures or transmission loss. Spatiotemporal imputation aims to fill the missing values according to the observed values and the underlying spatiotemporal dependence of them. The previous dominant models impute missing values autoregressively and suffer from the problem of error accumulation. As emerging powerful generative models, the diffusion probabilistic models can be adopted to impute missing values conditioned by observations and avoid inferring missing values from inaccurate historical imputation. However, the construction and utilization of conditional information are inevitable challenges when applying diffusion models to spatiotemporal imputation. To address above issues, we propose a conditional diffusion framework for spatiotemporal imputation with enhanced prior modeling, named PriSTI. Our proposed framework provides a conditional feature extraction module first to extract the coarse yet effective spatiotemporal dependencies from conditional information as the global context prior. Then, a noise estimation module transforms random noise to realistic values, with the spatiotemporal attention weights calculated by the conditional feature, as well as the consideration of geographic relationships. PriSTI outperforms existing imputation methods in various missing patterns of different real-world spatiotemporal data, and effectively handles scenarios such as high missing rates and sensor failure. The implementation code is available at https://github.com/LMZZML/PriSTI.