Magnetotransport experiments on antidot lattices show a rich variety of physical phenomena. Depending on the value of the particle mean-free path l in relation to the period λ of regular scatterers, two very different regimes can be distinguished: the strongly diffusive ( l ⪡ λ ) and the weakly diffusive ( l ≳ λ ) . We study particle transport in two-dimensional periodic landscapes based on a classical Langevin equation. The model covers both regimes and exhibits many of the features found experimentally at low magnetic fields. The most interesting observation is the presence of anomalous peaks in the magnetoresistance as a function of the magnetic field in the weakly diffusive regime. The roles of finite temperatures and of the electric field are also discussed.