In this work, we present LaserFlow, an efficient method for 3D object detection and motion forecasting from LiDAR. Unlike the previous work, our approach utilizes the native range view representation of the LiDAR, which enables our method to operate at the full range of the sensor in real-time without voxelization or compression of the data. We propose a new multi-sweep fusion architecture, which extracts and merges temporal features directly from the range images. Furthermore, we propose a novel technique for learning a probability distribution over future trajectories inspired by curriculum learning. We evaluate LaserFlow on two autonomous driving datasets and demonstrate competitive results when compared to the existing state-of-the-art methods.