  We study the soft behavior of two seemingly different particles that are both
referred to as dilatons in the literature, namely the one that appears in
theories of gravity and in string theory and the Nambu-Goldstone boson of
spontaneously broken conformal invariance. Our primary result is the discovery
of a soft theorem at subsubleading order for each dilaton, which in both cases
contains the operator of special conformal transformations. Interesting
similarities as well as differences between the dilaton soft theorems are
discussed.
