  We point out that pure supergravity theories in $AdS$ with enough
supersymmetry lead, upon taking the large radius limit, to flat space quantum
gravities with a nonperturbatively exact global symmetry, and are therefore in
the Swampland. The argument applies to any $AdS$ supergravity with gauged
R-symmetry group, including truncations of most well known examples, such as
$AdS_5$ without the $S^5$ or $AdS_4$ without the $S^7$. This demonstrates that
extreme scale separation, at least with enough supersymmetry, is not
realizable. Moreover pure $AdS$ theories are also in conflict with some other
Swampland principles including the Weak Gravity Conjecture and the
(generalized) Distance Conjecture.
