The guiding idea of this work is that classical diffusion theory, being nonrelativistic, should be associated with nonrelativistic quantum mechanics. A study of classical diffusion leads to a generalization which should correspond to the relativistic domain. Actually, with a convenient choice of the basic constants, one sees the relativistic features (Lorentz contraction and covariant diffusion equation) emerge in the generalized process. This leads first to a derivation of the nonrelativistic and relativistic wave equations (and to a model of the Dirac (...) fluid); then to a better understanding of several relativistic aspects of quantum mechanics (spin connection with relativity and link of relativity with nonlocalization). No quantum mechanical forces are postulated: they arise as pseudo-forces in the course of the calculations. The physical significance of the stochastic model is examined and shown to give a pictorial description only in certain ideal situations, but to remove several conceptual difficulties. Remarks are presented on the role of idealization in microphysics. (shrink)