  We introduce new diffuse approximations of the Willmore functional and the
Willmore flow. They are based on a corresponding approximation of the perimeter
that has been studied by Amstutz-van Goethem [{\em Interfaces Free Bound. 14
(2012)}]. We identify the candidate for the $\Gamma$--convergence, prove the
$\Gamma$--limsup statement and justify the convergence to the Willmore flow by
an asymptotic expansion. Furthermore, we present numerical simulations that are
based on the new approximation.
