Online social networks play a major role in the spread of information at very large scale and it becomes essential to provide means to analyse this phenomenon. In this paper we address the issue of predicting the temporal dynamics of the information diffusion process. We develop a graph-based approach built on the assumption that the macroscopic dynamics of the spreading process are explained by the topology of the network and the interactions that occur through it, between pairs of users, on the basis of properties at the microscopic level. We introduce a generic model, called T-BaSIC, and describe how to estimate its parameters from users behaviours using machine learning techniques. Contrary to classical approaches where the parameters are fixed in advance, T-BaSIC's parameters are functions depending of time, which permit to better approximate and adapt to the diffusion phenomenon observed in online social networks. Our proposal has been validated on real Twitter datasets. Experiments show that our approach is able to capture the particular patterns of diffusion depending of the studied sub-networks of users and topics. The results corroborate the "two-step" theory (1955) that states that information flows from media to a few "opinion leaders" who then transfer it to the mass population via social networks and show that it applies in the online context. This work also highlights interesting recommendations for future investigations.