  We present a technique for efficiently synthesizing images of atmospheric
clouds using a combination of Monte Carlo integration and neural networks. The
intricacies of Lorenz-Mie scattering and the high albedo of cloud-forming
aerosols make rendering of clouds---e.g. the characteristic silverlining and
the "whiteness" of the inner body---challenging for methods based solely on
Monte Carlo integration or diffusion theory. We approach the problem
differently. Instead of simulating all light transport during rendering, we
pre-learn the spatial and directional distribution of radiant flux from tens of
cloud exemplars. To render a new scene, we sample visible points of the cloud
and, for each, extract a hierarchical 3D descriptor of the cloud geometry with
respect to the shading location and the light source. The descriptor is input
to a deep neural network that predicts the radiance function for each shading
configuration. We make the key observation that progressively feeding the
hierarchical descriptor into the network enhances the network's ability to
learn faster and predict with high accuracy while using few coefficients. We
also employ a block design with residual connections to further improve
performance. A GPU implementation of our method synthesizes images of clouds
that are nearly indistinguishable from the reference solution within seconds
interactively. Our method thus represents a viable solution for applications
such as cloud design and, thanks to its temporal stability, also for
high-quality production of animated content.
