Positron diffusion in Si(100) and Si(111) has been studied using a variable-energy positron beam. The positron diffusion coefficient is found to be ${D}_{+}$=2.7\ifmmode\pm\else\textpm\fi{}0.3 ${\mathrm{cm}}^{2}$/sec using a Makhov-type positron implantation profile, which is demonstrated to fit the data more reliably than the more commonly applied exponential profile. The diffusion-related parameter, ${E}_{0}$, which results from the exponential profile, is found to be 4.2\ifmmode\pm\else\textpm\fi{}0.2 keV, significantly longer than previously reported values. A drastic reduction in ${E}_{0}$ is found after annealing the sample at 1300 K, showing that previously reported low values of ${E}_{0}$ are probably associated with the thermal history of the sample. Reconstruction of the Si(111) into the 7\ifmmode\times\else\texttimes\fi{}7 (low-energy electron diffraction) structure had no detectable effect on the positron diffusion behavior.