  The dilaton gravity models in two dimensions, including the
Jackiw--Teitelboim model and its deformations, are particular cases of Poisson
sigma models. Target space diffeomorphisms map one Poisson sigma model to
another. We propose to use these diffsomorphisms to identify asymptotic
conditions, boundary actions, and asymptotic symmetries in distinct dilaton
gravity models. As an example, we use the asymptotic conditions in
Jackiw--Teitelboim gravity to construct an asymptotic problem with Virasoro
symmetry in a class of asymptotically Rindler models. We show, that the method
can be applied to a wide class of pairs of dilaton gravities and discuss
possible generalizations.
