Self-driving vehicles plan around both static and dynamic objects, applying predictive models of behavior to estimate future locations of the objects in the environment. However, future behavior is inherently uncertain, and models of motion that produce deterministic outputs are limited to short timescales. Particularly difficult is the prediction of human behavior. In this work, we propose the discrete residual flow network (DRF-Net), a convolutional neural network for human motion prediction that captures the uncertainty inherent in long-range motion forecasting. In particular, our learned network effectively captures multimodal posteriors over future human motion by predicting and updating a discretized distribution over spatial locations. We compare our model against several strong competitors and show that our model outperforms all baselines.