This work presents a generative adversarial architecture for generating three-dimensional shapes based on signed distance representations. While the deep generation of shapes has been mostly tackled by voxel and surface point cloud approaches, our generator learns to approximate the signed distance for any point in space given prior latent information. Although structurally similar to generative point cloud approaches, this formulation can be evaluated with arbitrary point density during inference, leading to fine-grained details in generated outputs. Furthermore, we study the effects of using either progressively growing voxel- or point-processing networks as discriminators, and propose a refinement scheme to strengthen the generator's capabilities in modeling the zero iso-surface decision boundary of shapes. We train our approach on the ShapeNet benchmark dataset and validate, both quantitatively and qualitatively, its performance in generating realistic 3D shapes.