  Tightly bound excitons in monolayer semiconductors represent a versatile
platform to study two-dimensional propagation of neutral quasiparticles. Their
intrinsic properties, however, can be severely obscured by spatial energy
fluctuations due to a high sensitivity to the immediate environment. Here, we
take advantage of the encapsulation of individual layers in hexagonal boron
nitride to strongly suppress environmental disorder. Diffusion of excitons is
then directly monitored using time- and spatially-resolved emission microscopy
at ambient conditions. We consistently find very efficient propagation with
linear diffusion coefficients up to 10\,cm$^2$/s, corresponding to room
temperature effective mobilities as high as 400\,cm$^2$/Vs as well as a
correlation between rapid diffusion and short population lifetime. At elevated
densities we detect distinct signatures of many-particle interactions and
consequences of strongly suppressed Auger-like exciton-exciton annihilation. A
combination of analytical and numerical theoretical approaches is employed to
provide pathways towards comprehensive understanding of the observed linear and
non-linear propagation phenomena. We emphasize the role of dark exciton states
and present a mechanism for diffusion facilitated by free electron hole plasma
from entropy-ionized excitons.
