  We investigate spin transport in the anisotropic Heisenberg chain in the
limit of high temperatures ({\beta} \to 0). We particularly focus on diffusion
and the quantitative evaluation of diffusion constants from current
autocorrelations as a function of the anisotropy parameter {\Delta} and the
spin quantum number s. Our approach is essentially based on an application of
the time-convolutionless (TCL) projection operator technique. Within this
perturbative approach the projection onto the current yields the decay of
autocorrelations to lowest order of {\Delta}. The resulting diffusion constants
scale as 1/{\Delta}^2 in the Markovian regime {\Delta}<<1 (s=1/2) and as
1/{\Delta} in the highly non-Markovian regime above {\Delta} \sim 1 (arbitrary
s). In the latter regime the dependence on s appears approximately as an
overall scaling factor \sqrt{s(s+1)} only. These results are in remarkably good
agreement with diffusion constants for {\Delta}>1 which are obtained directly
from the exact diagonalization of autocorrelations or have been obtained from
non-equilibrium bath scenarios.
