It is known that the thin-film equation has a gradient flow structure with respect to a (generalized) Wasserstein metric and the usual Dirichlet energy. Based on that, the fluctuation-dissipation theorem gives rise to a stochastic thin-film equation. This equation is a singular stochastic partial differential equation which is out of scope of the framework of regularity structures for now. In order to circumvent this issue, we discretize the gradient flow structure and rediscover a well-known discretization of the (deterministic) thin-film equation that preserves the so-called entropy estimate. In the stochastic setting this entropy estimate then yields positivity for the solution in the case that the mobility arises from the no-slip boundary condition. Moreover, we show that previous discretizations of the stochastic thin-film equation considered in the literature do not preserve positivity. This is joint work with Benjamin Gess, Rishabh Gvalani and Felix Otto.