  In this paper, we propose a simple yet effective method to represent point
clouds as sets of samples drawn from a cloud-specific probability distribution.
This interpretation matches intrinsic characteristics of point clouds: the
number of points and their ordering within a cloud is not important as all
points are drawn from the proximity of the object boundary. We postulate to
represent each cloud as a parameterized probability distribution defined by a
generative neural network. Once trained, such a model provides a natural
framework for point cloud manipulation operations, such as aligning a new cloud
into a default spatial orientation. To exploit similarities between same-class
objects and to improve model performance, we turn to weight sharing: networks
that model densities of points belonging to objects in the same family share
all parameters with the exception of a small, object-specific embedding vector.
We show that these embedding vectors capture semantic relationships between
objects. Our method leverages generative invertible flow networks to learn
embeddings as well as to generate point clouds. Thanks to this formulation and
contrary to similar approaches, we are able to train our model in an end-to-end
fashion. As a result, our model offers competitive or superior quantitative
results on benchmark datasets, while enabling unprecedented capabilities to
perform cloud manipulation tasks, such as point cloud registration and
regeneration, by a generative network.
