  Density estimation plays a crucial role in many data analysis tasks, as it
infers a continuous probability density function (PDF) from discrete samples.
Thus, it is used in tasks as diverse as analyzing population data, spatial
locations in 2D sensor readings, or reconstructing scenes from 3D scans. In
this paper, we introduce a learned, data-driven deep density estimation (DDE)
to infer PDFs in an accurate and efficient manner, while being independent of
domain dimensionality or sample size. Furthermore, we do not require access to
the original PDF during estimation, neither in parametric form, nor as priors,
or in the form of many samples. This is enabled by training an unstructured
convolutional neural network on an infinite stream of synthetic PDFs, as
unbound amounts of synthetic training data generalize better across a deck of
natural PDFs than any natural finite training data will do. Thus, we hope that
our publicly available DDE method will be beneficial in many areas of data
analysis, where continuous models are to be estimated from discrete
observations.
