  We show that position space correlators of a Poincare invariant quantum field
theory can be recast in terms of conformally invariant correlators, in other
words, as functions of conformal cross ratios. In particular, we show that
correlators of massless fields in flat spacetimes with $n-$point interactions
can be expressed as position space soft limits of conformally invariant
correlators with $(n+1)-$point interactions. We show that this correspondence
applies at the level of every Feynman diagram that appears in the perturbative
expansion of the correlators in the respective coupling constants. We apply
this method to find exact answers for some Feynman diagrams including several
loop examples. We also show that the analogous correlators for massive fields
can be expressed as infinite sums of conformal correlators.
