The fermion diffusion process, which we recently introduced, is confro
nted with quantum Monte-Carlo calculations for an interacting fermion
system with harmonic interactions. The study of this model illustrates
that fermion diffusion in general leads to either the exact groundsta
te energy or to an exact excited state of the system, whereas a quantu
m Monte-Carlo calculation based on the nodal surface leads to an upper
bound for the groundstate energy. We discovered how a class of totall
y positive determinants relevant for our process allows us to construc
t sample paths with a rejection technique. It is then obvious that the
stochastic implementation of the anti-commutation relations introduce
s no extra noise. Both conceptually and practically are therefore have
developed a methodology which; does not suffer from the so-called sig
n problem for fermions.