  Generating point clouds, e.g., molecular structures, in arbitrary rotations,
translations, and enumerations remains a challenging task. Meanwhile, neural
networks utilizing symmetry invariant layers have been shown to be able to
optimize their training objective in a data-efficient way. In this spirit, we
present an architecture which allows to produce valid Euclidean distance
matrices, which by construction are already invariant under rotation and
translation of the described object. Motivated by the goal to generate
molecular structures in Cartesian space, we use this architecture to construct
a Wasserstein GAN utilizing a permutation invariant critic network. This makes
it possible to generate molecular structures in a one-shot fashion by producing
Euclidean distance matrices which have a three-dimensional embedding.
