  We determine the evolution of a cluster of quantum vortices initially placed
at the centre of a larger vortex-free region. We find that the cluster spreads
out spatially. This spreading motion consists of two effects: the rapid
evaporation of vortex dipoles from the cluster and the slow expansion of the
cluster itself. The latter is akin to a diffusion process controlled by the
quantum of circulation. Numerical simulations of the Gross-Pitaevskii equation
show that this phenomenon is qualitatively unaffected by the presence of sound
waves, vortex annihilations, and boundaries, and it should be possible to
create it in the laboratory.
