Despite the success of Generative Adversarial Networks (GANs), their training suffers from several well-known problems, including mode collapse and difficulties learning a disconnected set of manifolds. In this paper, we break down the challenging task of learning complex high dimensional distributions, supporting diverse data samples, to simpler sub-tasks. Our solution relies on designing a partitioner that breaks the space into smaller regions, each having a simpler distribution, and training a different generator for each partition. This is done in an unsupervised manner without requiring any labels. We formulate two desired criteria for the space partitioner that aid the training of our mixture of generators: 1) to produce connected partitions and 2) provide a proxy of distance between partitions and data samples, along with a direction for reducing that distance. These criteria are developed to avoid producing samples from places with non-existent data density, and also facilitate training by providing additional direction to the generators. We develop theoretical constraints for a space partitioner to satisfy the above criteria. Guided by our theoretical analysis, we design an effective neural architecture for the space partitioner that empirically assures these conditions. Experimental results on various standard benchmarks show that the proposed unsupervised model outperforms several recent methods.
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