Transfer of excitation energy is a key step in light harvesting and hence of
technological relevance for solar energy conversion. In bare organic materials
energy transfer proceeds via incoherent hops, which restrict propagation
lengths to nanometers. In contrast, energy transport over several micrometers
has been observed in the strong coupling regime where excitations hybridise
with confined light modes to form polaritons. Because polaritons have group
velocity, their propagation should be ballistic and long-ranged. However,
experiments indicate that organic polaritons propagate in a diffusive manner
and more slowly than their group velocity. Here, we resolve this controversy by
means of molecular dynamics simulations of Rhodamine molecules in a
Fabry-P\'erot cavity. Our results suggest that polariton propagation is limited
by the cavity lifetime and appears diffusive due to reversible population
transfers between bright polaritonic states that propagate ballistically at
their group velocity, and dark states that are stationary. Furthermore, because
long-lived dark states transiently trap the excitation, propagation is observed
on timescales beyond the intrinsic polariton lifetime. These atomistic insights
not only help to better understand and interpret experimental observations, but
also pave the way towards rational design of molecule-cavity systems for
achieving coherent long-range energy transport