We describe measurements of spin dynamics in the two-dimensional electron gas in GaAs=GaAlAs quantum wells. Optical techniques, including transient spin-grating spectroscopy, are used to probe the relaxation rates of spin polarization waves in the wave vector range from zero to 6 x 104 cm-1. We find that the spin polarization lifetime is maximal at a nonzero wave vector, in contrast with expectations based on ordinary spin diffusion, but in quantitative agreement with recent theories that treat diffusion in the presence of spin-orbit coupling