Simultaneous Localization and Mapping (SLAM) research has reached a level of maturity enabling systems to build autonomously an accurate sparse map of the environment while localizing themselves in that map. At the same time, the use of deep learning has recently brought great improvements in Monocular Depth Prediction (MDP). Some applications such as autonomous drone navigation and obstacle avoidance require dense structure information and cannot only rely on sparse SLAM representation. We propose to densify a state-of-theart SLAM algorithm using deep learning-based dense MDP at keyframe rate. Towards this goal, we describe a scale recovery from SLAM landmarks by minimizing a depth error metric combined with a multi-view depth refinement using a volumetric approach. We conclude with experiments that attest the added value of our approach in terms of depth estimation.