  Scheme independence of exact renormalization group equations, including
independence of the choice of cutoff function, is shown to follow from general
field redefinitions, which remains an inherent redundancy in quantum field
theories. Renormalization group equations and their solutions are amenable to a
simple formulation which is manifestly covariant under such a symmetry group.
Notably, the kernel of the exact equations which controls the integration of
modes acts as a field connection along the flow.
