There are many real-world knowledge based networked systems with multi-type interacting entities that can be regarded as heterogeneous networks including human connections and biological evolutions. One of the main issues in such networks is to predict information diffusion such as shape, growth and size of social events and evolutions in the future. While there exist a variety of works on this topic mainly using a threshold-based approach, they suffer from the local viewpoint on the network and sensitivity to the threshold parameters. In this paper, information diffusion is considered through a latent representation learning of the heterogeneous networks to encode in a deep learning model. To this end, we propose a novel meta-path representation learning approach, Heterogeneous Deep Diffusion(HDD), to exploit meta-paths as main entities in networks. At first, the functional heterogeneous structures of the network are learned by a continuous latent representation through traversing meta-paths with the aim of global end-to-end viewpoint. Then, the well-known deep learning architectures are employed on our generated features to predict diffusion processes in the network. The proposed approach enables us to apply it on different information diffusion tasks such as topic diffusion and cascade prediction. We demonstrate the proposed approach on benchmark network datasets through the well-known evaluation measures. The experimental results show that our approach outperforms the earlier state-of-the-art methods.