  We describe a one-parameter family of Euclidean wormhole solutions with the
topology of a compact hyperbolic space times an interval in Einstein gravity
minimally coupled to a massless scalar field in AdS$_{d+1}$ commonly referred
to as Einstein-dilaton gravity. These solutions are locally described by the
same metric and dilaton profile as the single-boundary Janus domain wall
solutions in the same theory which are usually studied in the context of
holographic RG flows. The wormholes compute the averaged product of partition
functions of CFTs on either boundary deformed by different marginal couplings
to the scalar operator dual to the dilaton. We observe that the renormalised
volumes of these wormholes increase monotonically with the difference in the
marginal couplings on the boundary thereby showing that the pair of CFTs on the
boundaries get increasingly decorrelated as the difference in the marginal
couplings increases. We use the partition functions of the three-dimensional
wormhole solutions to determine the variance of the OPE data of local operators
between the marginally deformed 2d CFTs and quantify how the variance decays
with the difference in marginal couplings. In addition, a family of wormholes
sourced by a thin shell of dust determine how the variance of the matrix
elements of the dual line defect decays with the difference in marginal
couplings. Applying the GKPW dictionary to wormholes, we compute averages of
integrated dilaton correlators treating the wormhole amplitude as a functional
of the dilaton sources. We observe that the crossed two-point correlators with
a dilaton insertion on either boundary decay montonically with the difference
in marginal couplings consistent with the observation that the CFTs
increasingly decorrelate as the difference in marginal couplings grows.
