  Generative neural networks have a well recognized ability to estimate
underlying manifold structure of high dimensional data. However, if a simply
connected latent space is used, it is not possible to faithfully represent a
manifold with non-trivial homotopy type. 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.
