  Dilaton gravities in two dimensions can be formulated as particular Poisson
sigma models. Target space diffeomorphisms map different models to each other
and establish a one-to-one correspondence between their classical solutions. We
obtain a general form of such diffeomorphisms in Lorentzian and Euclidean
signatures and use them to extend known holographic results, including the
Schwarzian action on the asymptotic boundary, from JT to a large class of
dilaton gravity models.
