We consider a scalar quantum field φ with arbitrary polynomial self-interaction in perturbation theory. If the field variable φ is repaced by a local diffeomorphism φ(x) = ρ(x) + a1ρ 2 (x) + . . ., this field ρ obtains infinitely many additional interaction vertices. We show that the S-matrix of ρ coincides with the one of φ without using path-integral arguments. This result holds even if the underlying field has a propagator of higher than quadratic order in the momentum.If tadpole diagrams vanish, the diffeomorphism can be tuned to cancel all contributions of an underlying φ s -type self interaction at one fixed external offshell momentum, rendering ρ a free theory at this momentum.Finally, we propose one way to extend the diffeomorphism to a non-local transformation involving derivatives without spoiling the combinatoric structure of the local diffeomorphism.