Quote by Ben Niehoff
It should be noted that the group of diffeomorphisms is a local gauge symmetry, so it is not the sort of symmetry one can use to construct Noether charges. Noether charges result from continuous, global symmetries. For example, the continuous global symmetries of Minkowski spacetime lead to conservation of momentum, energy, and angular momentum. And in electrodynamics, global gauge symmetry leads to the conservation of electric charge.

But what about the Wald prescription of black hole entropy, in which the entropy is constructed with the Noether charge associated to diffeomorphism invariance?