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 wavevector range from zero to 6E4 cm-1. We find that the spin polarization lifetime is maximal at nonzero wavevector, in contrast with expectation based on ordinary spin diffusion, but in quantitative agreement with recent theories that treat diffusion in the presence of spin-orbit coupling.