  We propose a novel method to reconstruct volumetric flows from sparse views
via a global transport formulation. Instead of obtaining the space-time
function of the observations, we reconstruct its motion based on a single
initial state. In addition we introduce a learned self-supervision that
constrains observations from unseen angles. These visual constraints are
coupled via the transport constraints and a differentiable rendering step to
arrive at a robust end-to-end reconstruction algorithm. This makes the
reconstruction of highly realistic flow motions possible, even from only a
single input view. We show with a variety of synthetic and real flows that the
proposed global reconstruction of the transport process yields an improved
reconstruction of the fluid motion.
