  The spontaneous breaking of the $SU(3)^5$ quark/lepton flavor symmetry by
means of three multiplets of scalar `Yukawa fields' admits vacua with one O(1)
and two vanishing vacuum expectation values (vevs) for each multiplet. If the
number of generations is equal to three, and only in this case, the vanishing
vevs are lifted to exponentially suppressed entries by the inclusion of
symmetry invariant logarithmic terms. A strong hierarchy for the Yukawa
couplings and a quark mixing matrix that approaches a diagonal form are
obtained in a natural way from O(1) parameters. This scenario provides a
concrete realization of the minimal flavor violation hypothesis.
