  We study inflationary models where the kinetic sector of the theory has a
non-linearly realised symmetry which is broken by the inflationary potential.
We distinguish between kinetic symmetries which non-linearly realise an
internal or space-time group, and which yield a flat or curved scalar manifold.
This classification leads to well-known inflationary models such as monomial
inflation and $\alpha$-attractors, as well as a new model based on fixed
couplings between a dilaton and many axions which non-linearly realises
higher-dimensional conformal symmetries. In this model, inflation can be
realised along the dilatonic direction, leading to a tensor-to-scalar ratio $r
\sim 0.01$ and a spectral index $n_{s} \sim 0.975$. We refer to the new model
as ambient inflation since inflation proceeds along an isometry of an anti-de
Sitter ambient space-time, which fully determines the kinetic sector.
