  We show that Vassiliev invariants of knots, appropriately generalized to the
spin network context, are loop differentiable in spite of being diffeomorphism
invariant. This opens the possibility of defining rigorously the constraints of
quantum gravity as geometrical operators acting on the space of Vassiliev
invariants of spin nets. We show how to explicitly realize the diffeomorphism
constraint on this space and present proposals for the construction of
Hamiltonian constraints.
