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Diffusion and localization of ultra-cold particles moving along randomly corrugated substrates is analyzed quasianalytically. The particles are either bound to the substrate or pressed to it by the external holding field. The localization length and diffusion coefficient are expressed explicitly via the correlation radius of surface inhomogeneities. This quantum bouncing hall problem with a random rough wall is solved analytically in three limiting cases of longwave particles, large gaps between bound states, and single-state occupancy. Elsewhere, the diffusion coefficient and localization length are evaluated numerically for Gaussian correlation of inhomogeneities. The results are applied to ultra-cold neutrons in the gravitational trap, electrons on helium and hydrogen surfaces, and hydrogen particles bound to helium surface. Experimental observation of weak 2D localization for neutrons and electrons requires further cooling and substrate preparation.