  Coleman-de Luccia transitions are spontaneous processes of nucleation of
bubbles within metastable gravitational vacua including in their interior a
true stable vacuum. From the perspective of lower-dimensional gauged
supergravities obtained by truncating Type II and M-theory, these instantonic
processes are represented by smooth domain walls featured by de Sitter
foliations. These geometries must connect two different AdS vacua in such a way
that the wall is defined by an interior and an exterior. We propose a
first-order formulation for such radial flows and present two fully backreacted
examples of gravitational instantons obtained through this technique, beyond
the thin-wall approximation. In the first we consider minimal 7d supergravity
describing the truncation of M-theory over a squashed 4-sphere and admitting
two AdS$_7$ vacua, one supersymmetric and the other not. Secondly we apply the
same strategy to 6d Romans supergravity obtained with consistent truncation of
massive IIA supergravity. Also in this case we derive a dS domain wall
interpolating between the Brandhuber-Oz vacuum and the non-supersymmetric
AdS$_6$ vacuum of the theory.
