Data-driven generative modeling has made remarkable progress by leveraging\nthe power of deep neural networks. A reoccurring challenge is how to enable a\nmodel to generate a rich variety of samples from the entire target\ndistribution, rather than only from a distribution confined to the training\ndata. In other words, we would like the generative model to go beyond the\nobserved samples and learn to generate ``unseen'', yet still plausible, data.\nIn our work, we present CompoNet, a generative neural network for 2D or 3D\nshapes that is based on a part-based prior, where the key idea is for the\nnetwork to synthesize shapes by varying both the shape parts and their\ncompositions. Treating a shape not as an unstructured whole, but as a\n(re-)composable set of deformable parts, adds a combinatorial dimension to the\ngenerative process to enrich the diversity of the output, encouraging the\ngenerator to venture more into the ``unseen''. We show that our part-based\nmodel generates richer variety of plausible shapes compared with baseline\ngenerative models. To this end, we introduce two quantitative metrics to\nevaluate the diversity of a generative model and assess how well the generated\ndata covers both the training data and unseen data from the same target\ndistribution. Code is available at https://github.com/nschor/CompoNet.\n