For autonomous vehicles to proactively plan safe trajectories and make informed decisions, they must be able to predict the future occupancy states of the local environment. However, common issues with occupancy prediction include predictions where moving objects vanish or become blurred, particularly at longer time horizons. We propose an environment prediction framework that incorporates environment semantics for future occupancy prediction. Our method first semantically segments the environment and uses this information along with the occupancy information to predict the spatiotemporal evolution of the environment. We validate our approach on the real-world Waymo Open Dataset. Compared to baseline methods, our model has higher prediction accuracy and is capable of maintaining moving object appearances in the predictions for longer prediction time horizons.