Analyzing and modeling the temporal diffusion of information on social media has mainly been treated as a diffusion process on known graphs or proximity structures. The underlying phenomenon results however from the interactions of several actors and media and is more complex than what these models can account for and cannot be explained using such limiting assumptions. We introduce here a new approach to this problem whose goal is to learn a mapping of the observed temporal dynamic onto a continuous space. Nodes participating to diffusion cascades are projected in a latent representation space in such a way that information diffusion can be modeled efficiently using a heat diffusion process. This amounts to learning a diffusion kernel for which the proximity of nodes in the projection space reflects the proximity of their infection time in cascades. The proposed approach possesses several unique characteristics compared to existing ones. Since its parameters are directly learned from cascade samples without requiring any additional information, it does not rely on any pre-existing diffusion structure. Because the solution to the diffusion equation can be expressed in a closed form in the projection space, the inference time for predicting the diffusion of a new piece of information is greatly reduced compared to discrete models. Experiments and comparisons with baselines and alternative models have been performed on both synthetic networks and real datasets. They show the effectiveness of the proposed method both in terms of prediction quality and of inference speed.