Title: A   RECURRENT NEURAL CASCADE-BASED MODEL FOR CONTINUOUS-TIME DIFFUSION PROCESS. Abstract: Many works have been proposed in the literature to capture the dynamics of diffusion in networks. While some of them define graphical markovian models to extract temporal relationships between node infections in networks, others consider diffusion episodes as sequences of infections via recurrent neural models. In this paper we propose a model at the crossroads of these two extremes, which embeds the history of diffusion in infected nodes as hidden continuous states. Depending on the trajectory followed by the content before reaching a given node, the distribution of influence probabilities may vary. However, content trajectories  are usually hidden in the data, which induces challenging learning problems. We propose a topological recurrent neural model which exhibits good experimental performances for diffusion modelling and prediction. 