  Coleman-de Luccia processes for AdS to AdS decays in Einstein-scalar theories
are studied. Such tunnelling processes are interpreted as vev-driven
holographic RG flows of a quantum field theory on de Sitter space-time. These
flows do not exist for generic scalar potentials, which is the holographic
formulation of the fact that gravity can act to stabilise false AdS vacua. The
existence of Coleman-de Luccia tunnelling solutions in a potential with a false
AdS vacuum is found to be tied to the existence of exotic RG flows in the same
potential. Such flows are solutions where the flow skips possible fixed points
or reverses direction in the coupling. This connection is employed to construct
explicit potentials that admit Coleman-de Luccia instantons in AdS and to study
the associated tunnelling solutions. Thin-walled instantons are observed to
correspond to dual field theories with a parametrically large value of the
dimension $\Delta$ for the operator dual to the scalar field, casting doubt on
the attainability of this regime in holography. From the boundary perspective,
maximally symmetric instantons describe the probability of symmetry breaking of
the dual QFT in de Sitter. It is argued that, even when such instantons exist,
they do not imply an instability of the same theory on flat space or on
$R\times S^3$.
