  We show, both heuristically and numerically, that three-dimensional periodic
Lorentz gases -- clouds of particles scattering off crystalline arrays of hard
spheres -- often exhibit normal diffusion, even when there are gaps through
which particles can travel without ever colliding, i.e., when the system has an
infinite horizon. This is the case provided that these gaps are not "too big",
as measured by their dimension. The results are illustrated with simulations of
a simple three-dimensional model having different types of diffusive regime,
and are then extended to higher-dimensional billiard models, which include
hard-sphere fluids.
