  We study diffusion of particles in large-scale simulations of one-dimensional
stochastic sandpiles, in both the restricted and unrestricted versions. The
results indicate that the diffusion constant scales in the same manner as the
activity density, so that it represents an alternative definition of an order
parameter. The critical behavior of the unrestricted sandpile is very similar
to that of its restricted counterpart, including the fact that a data collapse
of the order parameter as a function of the particle density is only possible
over a very narrow interval near the critical point. We also develop a series
expansion, in inverse powers of the density. for the collective diffusion
coefficient in a variant of the stochastic sandpile in which the toppling rate
at a site with $n$ particles is $n(n-1)$, and compare the theoretical
prediction with simulation results.
