  We study the diffusion process in a Heisenberg chain with correlated spatial
disorder, with a power spectrum in the momentum space behaving as $k^{-\beta}$,
using a stochastic description. It establishes a direct connection between the
fluctuation in the spin-wave density of states and the noise density of states.
For continuous ranges of the exponent $\beta $, we find superdiffusive and
ballistic spin-wave motions. Both diffusion exponents predicted by the
stochastic procedure agree with the ones calculated using the Hamiltonian
dynamics.
