The aim of this talk is to describe how Spin Foam Models can be used to construct normalized Borel measure spaces that carry the action of a group of diffeomorphisms of a manifold Diff(M).These measure spaces can have the interpretation of a path integral for physical theories of connections,and in interesting cases the constructed measure is invariant under Diff(M).We outline the construction,give some easy examples,and comment on how the conditions for cylindrical consistency of measures corresponds to Wilsonian renormalization group flow equations.This construction could provide a framework for background-independent renormalization,which is in particular of interest for constructing a theory of quantum gravity.