We use optical transient-grating spectroscopy to measure the spin diffusion of optically oriented electrons in bulk, semi-insulating GaAs(100). Trapping and recombination do not quickly deplete the photoexcited population. The spin diffusion coefficient of 88±12 cm2/s is roughly constant at temperatures from 15 K to 150 K, and the spin diffusion length is at least 450 nm. We show that it is possible to use spin diffusion to estimate the electron diffusion coefficient. Due to electron-electron interactions, the electron diffusion is 1.4 times larger than the spin diffusion.