Understanding the dynamics of spreading and diffusion on networks is of critical importance for a variety of processes in real life. However, predicting the temporal evolution of diffusion on networks remains challenging as the process is shaped by network topology, spreading non-linearities, and heterogeneous adaptation behavior. In this study, we propose the ‘spindle vector’, a new network topological feature, which characterizes the hierarchical organization of nodes. The spindle vector shapes nodes according to the distance from the root node, capturing the essence of diffusion propagation, thus allowing us to approximate the spatiotemporal evolution of diffusion dynamics on networks. Through experiments on various networks, we show that our method outperforms the state-of-the-art, such that the prediction error of RMSE and MAE is 100% superior on WS and BA networks, and that the prediction is better than the counterpart model in 36 out of 40 empirical networks. The new metric provides a general and computationally efficient approach to predict network diffusion problems and is of potential for a large range of network applications.