  It has been recently shown that a certain non-topological spin foam model can
be obtained from the Feynman expansion of a field theory over a group. The
field theory defines a natural ``sum over triangulations'', which removes the
cut off on the number of degrees of freedom and restores full covariance. The
resulting formulation is completely background independent: spacetime emerges
as a Feynman diagram, as it did in the old two-dimensional matrix models. We
show here that any spin foam model can be obtained from a field theory in this
manner. We give the explicit form of the field theory action for an arbitrary
spin foam model. In this way, any model can be naturally extended to a sum over
triangulations. More precisely, it is extended to a sum over 2-complexes.
