Models of inflation with arbitrary interactions are now florishing for their non-gaussianity signatures. Among them the DBI model describing a probe-brane moving along an extra dimension is special as pathological quantum corrections are protected by the fundamental 5d Poincare symmetry. I will show how to extend the DBI model to the most general Lovelock invariant arising in 5 dimensions giving rise to a new set of inflationary models and establish a link with the Galileon in the non-relativistic limit.