We study spatiotemporal forecasting of high-dimensional rectangular grid graph structured data, which exhibits both complex spatial and temporal dependencies. In most high-dimensional spatiotemporal forecasting scenarios, deep learningbased methods are widely used. However, deep learning algorithms are overconfident in their predictions, and this overconfidence causes problems in the human-in-the-loop domains such as medical diagnosis and many applications of 5 th generation wireless networks. We propose spatiotemporal extensions to variational autoencoders for regularization, robustness against out-of data distribution, and incorporating uncertainty in predictions to resolve overconfident predictions. However, variational inference methods are prone to biased posterior approximations due to using explicit exponential family densities and mean-field assumption in their posterior factorizations. To mitigate these problems, we utilize variational inference & learning with semi-implicit distributions and apply this inference scheme into convolutional long-short term memory networks(ConvLSTM) for the first time in the literature. In chapter 3, we propose variational autoencoders with convolutional long-short term memory networks, called VarConvLSTM. In chapter 4, we improve our algorithm via semi-implicit & doubly semi-implicit variational inference to model multi-modalities in the data distribution . In chapter 5, we demonstrate that proposed algorithms are applicable for spatiotemporal forecasting tasks, including space-time mobile traffic forecasting over Turkcell base station networks.