This paper focuses on a novel generative approach for 3D point clouds that makes use of invertible flow-based models. The main idea of the method is to treat a point cloud as a probability density in 3D space that is modeled using a cloud-specific neural network. To capture the similarity between point clouds we rely on parameter sharing among networks, with each cloud having only a small embedding vector that defines it. We use invertible flows networks to generate the individual point clouds, and to regularize the embedding vectors. We evaluate the generative capabilities of the model both in qualitative and quantitative manner.