The increased popularity of Deep Learning and the growing availability of large volumes of human motion capture data have both contributed to a rise in data-driven statistical approaches to human motion modelling. Among these methods, those that aim to exploit these data collections to generate new plausible and realistic motions can be found at the intersection of graphics and computer vision, with tasks such as motion synthesis and motion prediction being researched and applied in animation, games and robotics, among others. Most methods proposed so far take a deterministic approach to modelling human motion, and, albeit successful, they are limited to outputting a single predicted motion sequence and do not consider the highly stochastic nature of human motion. To overcome this lack of motion diversity, probabilistic methods have lately received a lot of attention as they have the potential to account for the multi-modality of human motion. For these reasons, and based on the successful use of heatmaps to represent 3D human poses and motion trajectories in pose estimation and action recognition, in this research we aim to study the validity and effectiveness of such representation for the tasks of motion prediction and synthesis, and thus propose a novel framework whose goal is to learn both spatial and temporal dependencies of human motion and generate new sequences that are valid, diverse and realistic.