Abstract: Quantum corrections to holographic entanglement entropy are well-understood for ordinary quantum matter in a classical gravitational background. These famously lead to a unitary Page curve for evaporating black holes in AdS (coupled to a bath). However, the correct treatment of quantum fluctuations of the metric, including graviton excitations, is a longstanding problem. I will provide a gauge-invariant prescription for the generalized entropy of gravitons in anti-de Sitter space in terms of areas and bulk entanglement entropy, generalizing the quantum extremal surface prescription to accommodate fluctuations in the semiclassical spacetime geometry. I will give some justification for the prescription using covariant phase techniques and explicitly check it in a non-trivial example. Along the way, I will identify a class of perturbative graviton states that have parametrically larger generalized entropy, in the small G_N expansion, any low-energy excitations of an ordinary quantum field.