WaveDiST: A Wavelet Diffusion Transformer for Spatio-Temporal Estimation on Unobserved Locations

Spatio-temporal estimation plays a vital role in numerous scientific and engineering tasks, particularly for novel or unobserved locations lacking historical references. Many areas remain unobserved by sensors due to their non-core location or pending development status. The states of these areas can only be estimated through similar nodes in the geospace, rather than through historical data with temporal trends. Estimating these unobserved node states is crucial for city-wide spatio-temporal sensing and urban development, extending beyond simple point or block data imputation. In this study, we introduce a diffusion point process in high-frequency space to develop a robust spatio-temporal diffusion transformer for urban estimation where partial historical reference data is lacking. Our approach decomposes spatio-temporal data into high and low-frequency components through wavelet transform, and trains a diffusion model of spatial temporal data with a transformer that operates on high frequency signals. We incorporate low-frequency signals as diffusion conditions in the transformer architecture to capture overall spatio-temporal profiles and gradual trends. To enhance the learning of each step, we design an diffusion model featuring a spatio-temporal attention module that adaptively captures interdependencies between time and space. Extensive experiments across diverse domains including traffic, economics, and environment demonstrate that our method significantly outperforms state-of-the-art baselines.