One of the most successful techniques in generative models has been decomposing a complicated generation task into a series of simpler generation tasks.   For example, generating an image at a low resolution and then learning to refine that into a high resolution image often improves results substantially.   Here we explore a novel strategy for decomposing generation for complicated objects in which we first generate latent variables which describe a subset of the observed variables, and then map from these latent variables to the observed space.   We show that this allows us to achieve decoupled training of complicated generative models and present both theoretical and experimental results supporting the benefit of such an approach.  
Decompose the task of learning a generative model into learning disentangled latent factors for subsets of the data and then learning the joint over those latent factors.   Locally Disentangled Factors for hierarchical latent variable generative model, which can be seen as a hierarchical variant of Adversarially Learned Inference The paper investigates the potential of hierarchical latent variable models for generating images and image sequences and proposes to train several ALI models stacked on top of each other to create a hierarchical representation of the data. The paper aims to learn the hierarchies for training GAN in a hierarchical optimization schedule directly instead of being designed by a human