  We study large deviations of the one-point height distribution,
$\mathcal{P}(H,T)$, of a stochastic interface, governed by the
Golubovi\'{c}-Bruinsma equation $$
\partial_{t}h=-\nu\partial_{x}^{4}h+\frac{\lambda}{2}\left(\partial_{x}h\right)^{2}+\sqrt{D}\,\xi(x,t)\,,
$$ where $h(x,t)$ is the interface height at point $x$ and time $t$, and
$\xi(x,t)$ is the Gaussian white noise. The interface is initially flat, and
$H$ is defined by the relation $h(x=0,t=T)=H$. Using the optimal fluctuation
method (OFM), we focus on the short-time limit. Here the typical fluctuations
of $H$ are Gaussian, and we evaluate the strongly asymmetric and non-Gaussian
tails of $\mathcal{P}(H,T)$. We show that the upper tail scales as $-\ln
\mathcal{P}(H,T) \sim H^{11/6}/T^{5/6}$. The lower tail, which scales as $-\ln
\mathcal{P}(H,T) \sim H^{5/2}/T^{1/2}$, coincides with its counterpart for the
Kardar-Parisi-Zhang equation, and we uncover a simple physical mechanism behind
this universality. Finally, we verify our asymptotic results for the tails, and
compute the large deviation function of $H$, numerically.
