Synthesis of high-quality 3D shapes with smooth surfaces has various creative and practical use cases, such as 3D content creation and CAD modeling. A vector field decoder neural network is trained to predict a generative vector field (GVF) representation of a 3D shape from a latent representation (latent code or feature volume) of the 3D shape. The GVF representation is agnostic to surface orientation, all dimensions of the vector field vary smoothly, the GVF can represent both watertight and non-watertight 3D shapes, and there is a one-to-one mapping between a predicted 3D shape and the ground truth 3D shape (i.e., the mapping is bijective). The vector field decoder can synthesize 3D shapes in multiple categories and can also synthesize 3D shapes for objects that were not included in the training dataset. In other words, the vector field decoder is also capable of zero-shot generation.