Constructing high-quality generative models for 3D shapes is a fundamental task in computer vision with diverse applications in geometry processing, engineering, and design. Despite the recent progress in deep generative modelling, synthesis of finely detailed 3D surfaces, such as high-resolution point clouds, from scratch has not been achieved with existing learning-based approaches. In this work, we propose to employ the latent-space Laplacian pyramid representation within a hierarchical generative model for 3D point clouds. We combine the latent-space GAN and Laplacian GAN architectures proposed in the recent years to form a multi-scale model capable of generating 3D point clouds at increasing levels of detail. Our initial evaluation demonstrates that our model outperforms the existing generative models for 3D point clouds, emphasizing the need for an in-depth comparative study on the topic of multi-stage generative learning with point clouds.