Scene flow is a challenging task aimed at jointly estimating the 3D structure and motion of the sensed environment. Although deep learning solutions achieve outstanding performance in terms of accuracy, these approaches divide the whole problem into standalone tasks (stereo and optical flow) addressing them with independent networks. Such a strategy dramatically increases the complexity of the training procedure and requires power-hungry GPUs to infer scene flow barely at 1 FPS. Conversely, we propose DWARF, a novel and lightweight architecture able to infer full scene flow jointly reasoning about depth and optical flow easily and elegantly trainable end-to-end from scratch. Moreover, since ground truth images for full scene flow are scarce, we propose to leverage on the knowledge learned by networks specialized in stereo or flow, for which much more data are available, to distill proxy annotations.Exhaustive experiments show that i) DWARF runs at about 10 FPS on a single high-end GPU and about 1 FPS on NVIDIA Jetson TX2 embedded system processing KITTI images, with moderate drop in accuracy compared to 10× deeper models, ii) learning from many distilled samples is more effective than from the few, annotated ones available.