  We use a simple model to study the long time fluctuations induced by random
pinning on the motion of driven non--interacting vortices. We find that vortex
motion seen from the co--moving frame is diffusive and anisotropic, with
velocity dependent diffusion constants. Longitudinal and transverse diffusion
constants cross at a characteristic velocity where diffusion is isotropic. The
diffusion front is elongated in the direction of the drive at low velocities
and elongated in the transverse direction at large velocities. We find that the
mobility in the driven direction is always larger than the transverse mobility,
and becomes isotropic only in the large velocity limit.
