A spatiotemporal diffusion framework for state estimation in low-observability distribution systems

State estimation is critical for ensuring the safe, reliable, and efficient operation of modern distribution networks. Its objective is to accurately infer the operating states, such as voltage magnitudes and phase angles, based on limited and sparse measurement data. However, existing methods still face significant challenges in modeling the spatiotemporal coupling characteristics of power systems, primarily limited by insufficient representation capabilities for complex grid topological structures and inadequate robustness to low observability. To address these issues, this paper proposes a novel Spatio-Temporal Diffusion Model (STDM) that reformulates the state estimation problem as a spatiotemporal diffusion process guided by existing measurements as conditional information. The model iteratively denoises and completes potential states through a diffusion mechanism while embedding a graph Transformer structure to explicitly capture the topological and spatial dependencies between nodes in the distribution network, thereby achieving high-precision and robust state estimation. Experimental results on IEEE 33-bus and 37-bus test systems demonstrate that STDM reduces the mean absolute error (p.u.) for voltage magnitude and phase angle estimation by over 80% compared to traditional data-driven methods. Furthermore, under colored noise conditions commonly encountered in real-world scenarios, the method maintains excellent robustness. On the larger-scale IEEE 123-bus system, STDM also exhibits state-of-the-art estimation accuracy, validating its scalability and practical application potential. • A novel spatiotemporal diffusion model for state estimation. • Graph Transformer captures complex spatiotemporal dynamics. • Achieves high-precision estimation in low-observability systems. • Reduces estimation error by over 80% with sparse data.