general relativity - Conserved quantity of Spactime Diffeomorphism Group

So it's my understanding that the underlying symmetry of GR is the Diffeomorphism Group of 3+1 spacetime.

It's also my understanding that a symmetry implies a corresponding conserved quantity in a physical theory.

Then, if my understanding is correct, there should be a conserved quantity associated with the Diffeomorphism Group of 3+1 spacetime. What is it?