We present two learning-based methods for coding point clouds geometry. The two methods target lossy and lossless compression, respectively, and have in common the fact to use a voxel-based representation of geometry. This representation enables us to extend well-known architectures used for 2D image generation and compression to 3D. We show that, when the point cloud density is sufficiently high, the voxel-based approach achieves state-of-the-art performance compared to conventional octree-based methods such as MPEG G-PCC.