Data-driven approaches for modeling human skeletal motion have found various applications in interactive media and social robotics. Challenges remain in these fields for generating high-fidelity samples and robustly reconstructing motion from imperfect input data, due to e.g. missed marker detection. In this paper, we propose a probabilistic generative model to synthesize and reconstruct long horizon motion sequences conditioned on past information and control signals, such as the path along which an individual is moving. Our method adapts the existing work MoGlow by introducing a new graph-based model. The model leverages the spatial-temporal graph convolutional network (ST-GCN) to effectively capture the spatial structure and temporal correlation of skeletal motion data at multiple scales. We evaluate the models on a mixture of motion capture datasets of human locomotion with foot-step and bone-length analysis. The results demonstrate the advantages of our model in reconstructing missing markers and achieving comparable results on generating realistic future poses. When the inputs are imperfect, our model shows improvements on robustness of generation.