<p>Propagation on temporal networks exhibits richer characteristics in comparison with static networks due to the existence of temporal properties, such as burstiness and causality. In this paper, we focus on the causality between adjacent edges and illustrate its influence on propagation speed. Based on stochastic process theory, we discuss propagation in the local path and derive the distribution of propagation time. In combination with the assumption of the fastest propagation, we extend local results to global network and propose the metric of causality-driven temporal distance (CTD). Incorporating temporal network topology with propagation parameters, CTD approximates the speed of propagation in temporal networks with high accuracy. In addition, its calculation can be accelerated by exploiting Dijkstra’s algorithm on the weighted second-order aggregated network. As validation, we perform numerical simulations on both synthetic and empirical temporal networks. Results demonstrate that CTD provides a superior characterization of propagation patterns, which confirms the influence of causality on propagation speed. In addition, CTD has profound applications in identifying superspreaders and reconstructing the origin of propagation on temporal networks. This work advances our understanding of propagation on temporal networks and has great potential in a variety of real-world scenarios, including social network analysis and traffic control.</p>