Researchers have been overwhelmed by the explosion of research articles published by various research communities. Many research scholarly websites, search engines, and digital libraries have been created to help researchers identify potential research topics and keep up with recent progress on research of interests. However, it is still difficult for researchers to keep track of the research topic diffusion and evolution without spending a large amount of time reviewing numerous relevant and irrelevant articles. In this paper, we consider a novel topic diffusion discovery technique. Specifically, we propose using a Deep Non-negative Autoencoder with information divergence measurement that monitors evolutionary distance of the topic diffusion to understand how research topics change with time. The experimental results show that the proposed approach is able to identify the evolution of research topics as well as to discover topic diffusions in online fashions.