  We investigate the decay rate of a false vacuum state in de Sitter space at
high Hubble rates, using two methods: the Hawking-Moss instanton method which
is fully quantum mechanical but relies on the saddle-point approximation, and
the Starobinsky-Yokoyama stochastic approach which is non-perturbative but does
not include quantum effects. We use the flux-over-population method to compute
the Hawking-Moss decay rate at one-loop order, and demonstrate that in its
domain of validity, it is reproduced by the stochastic calculation using the
one-loop constraint effective potential. This suggests that the stochastic
approach together with the constraint effective potential can be used to
accurately describe vacuum decay beyond the saddle-point approximation.
