  Random walks are studied on disordered cellular networks in 2-and
3-dimensional spaces with arbitrary curvature. The coefficients of the
evolution equation are calculated in term of the structural properties of the
cellular system. The effects of disorder and space-curvature on the diffusion
phenomena are investigated. In disordered systems the mean square displacement
displays an enhancement at short time and a lowering at long ones, with respect
to the ordered case. The asymptotic expression for the diffusion equation on
hyperbolic cellular systems relates random walk on curved lattices to
hyperbolic Brownian motion.
