Dense point cloud generation from a sparse or incomplete point cloud is a crucial and challenging problem in 3D computer vision and computer graphics. So far, the existing methods are either computationally too expensive, suffer from limited resolution, or both. In addition, some methods are strictly limited to watertight surfaces -- another major obstacle for a number of applications. To address these issues, we propose a lightweight Convolutional Neural Network that learns and predicts the unsigned distance field for arbitrary 3D shapes for dense point cloud generation using the recently emerged concept of implicit function learning. Experiments demonstrate that the proposed architecture achieves slightly better quality results than the state of the art with 87% less model parameters and 40% less GPU memory usage.