  The optical absorption of the Fr\"{o}hlich polaron model is obtained by an
approximation-free Diagrammatic Monte Carlo method and compared with two new
approximate approaches that treat lattice relaxation effects in different ways.
We show that: i) a strong coupling expansion, based on the the Franck-Condon
principle, well describes the optical conductivity for large coupling strengths
($\alpha >10$); ii) a Memory Function Formalism with phonon broadened levels
reproduces the optical response for weak coupling strengths ($\alpha <6$)
taking the dynamic lattice relaxation into account. In the coupling regime
$6<\alpha<10$ the optical conductivity is a rapidly changing superposition of
both Franck-Condon and dynamic contributions.
