Urban air pollutants have obvious diffusion phenomena between air monitoring stations, i.e., the pollutant concentration at one station is often influenced by neighboring stations. Therefore, the task of inter-site diffusion path prediction is of great significance for the advance prevention of pollution and the prevention and control of emergencies. In this paper, based on the PM \(_{2.5}\) concentration data from 456 air monitoring stations in Lanzhou City, the graph structure reflecting the inter-site diffusion paths is calculated, and in this way, a dataset of PM \(_{2.5}\) diffusion paths in Lanzhou is constructed. Then this paper proposes a spatio-temporal graph attention network model PM \(_{2.5}\) -STAN, which contains a temporal attention module and a spatial attention module. The temporal attention module utilizes the self-attention mechanism to weight the information of historical moments so as to accurately capture the temporal changes, while the spatial attention module introduces geographic distance information on the basis of the graph attention network to realize the adaptive portrayal of dynamic dependencies between monitoring stations. Finally, the proposed model is evaluated through a series of experiments, and the results show that PM \(_{2.5}\) -STAN has high accuracy in the diffusion path prediction task.