Is there proof of the inverse function theorem via Moser's trick?
By the inverse function theorem I mean the $C^\infty$ version usually stated for open regions of $\mathbb R^n$. Moser's trick is the one folks typically use to prove Morse's lemma and Darboux's theorem.
The vague idea I have in mind is deforming the smooth map stated in the inverse function theorem by its linearization at a point.