**Abstract:**
It is well known that in a generally covariant gravitational theory
the choice of spacetime scalars as coordinates yields phase-space
observables (or "invariants"). However, their relation to the
symmetry group of diffeomorphism transformations has remained
obscure. In a symmetry-inspired approach we construct invariants
(observables) out of canonically induced active gauge
transformations.
We make full contact with the "evolving constants of motion"
program.
All invariants can be obtained as limits of a family of canonical
transformations. This permits a short proof that the invariants
satisfy
Poisson brackets that are equal to the invariants of their
corresponding
Dirac brackets.