  The spin-diffusion constant of the 2D $t-J$ model is calculated for the first
time using an analytical approach at high temperatures and a recently-developed
numerical method based on the Lanczos technique combined with random sampling
in the intermediate temperature regime. A simple relation, $\sigma = D_s\chi$,
between spin conductivity and spin diffusion is established and used to
calculate the latter. In the high-temperature and low-doping limit the
calculated diffusion constant agrees with known results for the Heisenberg
model. At small hole doping, $D_s$ increases approximately linearly with
doping, which leads us to an important conclusion that hopping processes
enhance spin diffusion at high temperatures. At modest hole doping, $\delta\sim
0.25$, diffusion exhibits a nonmonotonic temperature dependence, which
indicates anomalous spin dynamics at small frequencies.
