  In view synthesis, a neural radiance field approximates underlying density
and radiance fields based on a sparse set of scene pictures. To generate a
pixel of a novel view, it marches a ray through the pixel and computes a
weighted sum of radiance emitted from a dense set of ray points. This rendering
algorithm is fully differentiable and facilitates gradient-based optimization
of the fields. However, in practice, only a tiny opaque portion of the ray
contributes most of the radiance to the sum. We propose a simple end-to-end
differentiable sampling algorithm based on inverse transform sampling. It
generates samples according to the probability distribution induced by the
density field and picks non-transparent points on the ray. We utilize the
algorithm in two ways. First, we propose a novel rendering approach based on
Monte Carlo estimates. This approach allows for evaluating and optimizing a
neural radiance field with just a few radiance field calls per ray. Second, we
use the sampling algorithm to modify the hierarchical scheme proposed in the
original NeRF work. We show that our modification improves reconstruction
quality of hierarchical models, at the same time simplifying the training
procedure by removing the need for auxiliary proposal network losses.
