  Generative neural networks have a well recognized ability to estimate
underlying manifold structure of high dimensional data. However, if a single
latent space is used, it is not possible to faithfully represent a manifold
with topology different from Euclidean space. In this work we define the
general class of Atlas Generative Models (AGMs), models with hybrid
discrete-continuous latent space that estimate an atlas on the underlying data
manifold together with a partition of unity on the data space. We identify
existing examples of models from various popular generative paradigms that fit
into this class. Due to the atlas interpretation, ideas from non-linear latent
space analysis and statistics, e.g. geodesic interpolation, which has
previously only been investigated for models with simply connected latent
spaces, may be extended to the entire class of AGMs in a natural way. We
exemplify this by generalizing an algorithm for graph based geodesic
interpolation to the setting of AGMs, and verify its performance
experimentally.
