This paper deals with the diffusion limit of a kinetic equation where the
collisions are modeled by a Lorentz type operator. The main aim is to construct a
discrete scheme to approximate this equation which gives for any value of the
Knudsen number, and in particular at the diffusive limit, the right discrete
diffusion equation with the same value of the diffusion coefficient as in the
continuous case. We are also naturally interested with a discretization which
can be used with few velocity discretization points, in order to reduce the cost of
computation.