  We derive formulae for the soft limit of tree-level gluon and graviton
correlators in Anti-de Sitter space, which arise from Feynman diagrams encoding
the Weinberg soft theorems in flat space. Other types of diagrams can also
contribute to the soft limit at leading order in the soft momentum, but have a
different pole structure. We derive these results at four points using explicit
formulae recently obtained from the cosmological bootstrap and double copy, and
extend them to any multiplicity using bootstrap techniques in Mellin-momentum
space.
