  Hilbert-Noether theorem states that a current associated to diffeomorphism
invariance of a Lagrangian vanishes on shell modulo a divergence of an
arbitrary superpotential. Application of the Noether procedure to physical
Lagrangians yields, however, meaningful (and measurable) currents. The well
known solution to this ``paradox'' is to involve the variation of the metric
tensor. Such procedure, for the field considered on a fixed (flat) background,
is sophisticated logically (one need to introduce the variation of a fixed
field) and formal.
  We analyze the Noether procedure for a generic diffeomorphism invariant
$p$-form field model. We show that the Noether current of the field considered
on a variable background coincides with the current treated in a fixed
geometry. Consistent description of the canonical energy-momentum current is
possible only if the dynamics of the geometry (gravitation) is taken into
account. However, even the ``truncated'' consideration yields the proper
expression. We examine the examples of the free $p$-form gauge field theory,
the GR in the coframe representation and the metric-free electrodynamics.
Although, the variation of a metric tensor is not acceptable in the latter
case, the Noether procedure yields the proper result.
