  We discuss the conditions under which classically conformally invariant
models in four dimensions can arise out of non-conformal (Einstein) gravity. As
an `existence proof' that this is indeed possible we show how to derive N=4
super Yang Mills theory with any compact gauge group G from non-conformal
gauged N=4 supergravity as a special flat space limit. We stress the role that
the anticipated UV finiteness of the (so far unknown) underlying theory of
quantum gravity would have to play in such a scheme, as well as the fact that
the masses of elementary particles would have to arise via quantum
gravitational effects which mimic the conformal anomalies of standard (flat
space) UV divergent quantum field theory.
