  We consider the effect of a magnetic field $B$ on the transport of neutral
composite particles, excitons, in weakly disordered 2D systems. In the case of
classical transport, when the interference of different paths is neglected, the
magnetic field suppresses exciton transport, and the static diffusion constant
$D(B)$ monotonically drops with $B$. When quantum-mechanical corrections due to
weak localization are taken into account, $D(B)$ becomes a nonmonotonic
function of $B$. In weak magnetic fields, where the magnetic length is much
larger than the exciton Bohr radius, $l_B >> a_B$, a positive magnetodiffusion
effect is predicted, i.e., the exciton mobility should increase with $B$.
