Spatiotemporal spin dynamics under spin-orbit interaction is investigated in a (001) GaAs two-dimensional electron gas using magneto-optical Kerr rotation microscopy. Spin-polarized electrons are diffused away from the excited position, resulting in spin precession because of the diffusion-induced spin-orbit field. Near the cancellation between the spin-orbit field and the external magnetic field, the induced spin precession frequency depends nonlinearly on the diffusion velocity, which is unexpected from the conventional linear relation between the spin-orbit field and the electron velocity. This behavior originates from an enhancement of the spin relaxation anisotropy by the electron velocity perpendicular to the diffused direction. We demonstrate that the spin relaxation anisotropy, which has been regarded as a material constant, can be controlled via diffusive electron motion.