With the rapid advancement of sensing and remote sensing technologies, data collected in transportation, meteorology, and environmental monitoring have become increasingly characterized by high-frequency observations and cross-regional spatiotemporal dependencies. However, missing observations, irregular sampling, and prediction at unobserved locations remain major challenges for spatiotemporal forecasting. To address these issues, this study proposes a spatiotemporal forecasting framework, $\text{SSSD}^{\text{S4+MRTS}}$ + AFRK, which integrates Structured State Space Diffusion Model with S4 Layers ($\text{SSSD}^{\text{S4}}$) and Multi-Resolution Thin-Plate Spline (MRTS) basis functions to jointly model long-range temporal dependencies and spatial structural patterns. MRTS is incorporated into the S4 layers as additional spatial conditioning information, enabling $\text{SSSD}^{\text{S4+MRTS}}$ to learn spatiotemporal dynamics conditioned on observed locations. During inference, the framework further integrates MRTS-based Resolution Adaptive Fixed Rank Kriging (AFRK), which preserves the spatial consistency of the predicted field while enabling interpolation at unobserved locations. Experiments conducted on the Weather2K, MERRA-2, and the dataset from The Second Competition on Spatial Statistics for Large Datasets are used to compare the proposed framework with Temporal Fusion Transformers (TFT), Vector Autoregression (VAR), Stochastic Variational Gaussian Process (SVGP), and Spatio-temporal DeepKriging (STDK). The results demonstrate that $\text{SSSD}^{\text{S4+MRTS}}$ generally improves Mean Squared Prediction Error (MSPE) under most experimental settings, with particularly notable gains in future forecasting at unobserved locations. Overall, the findings indicate that integrating temporal dynamic modeling with spatial statistical methods effectively enhances spatiotemporal forecasting performance under missing-data and spatial extrapolation scenarios.
Keywords: Structured State Space Diffusion Model, Multi-Resolution Thin-Plate Spline Basis Functions, Resolution Adaptive Fixed Rank Kriging, spatiotemporal forecasting, spatial interpolation, missing data imputation
