  We consider strictly positive solutions to a class of fourth-order
conservative quasilinear SPDEs on the $d$-dimensional torus modeled after the
stochastic thin-film equation. We prove local Lipschitz estimates in Bessel
potential spaces under minimal assumptions on the parameters and corresponding
stochastic maximal $L^p$-regularity estimates for thin-film type operators with
measurable in-time coefficients. As a result, we deduce local well-posedness of
the stochastic thin-film equation as well as blow-up criteria and instantaneous
regularization for the solution. In dimension one, we additionally close
$\alpha$-entropy estimates and subsequently an energy estimate for the
stochastic thin-film equation with an interface potential so that global
well-posedness follows. We allow for a wide range of mobility functions
including the power laws $u^n$ for $n\in [0,6)$ as long as the interface
potential is sufficiently repulsive.
