We report a search for diphoton events with large missing transverse energy produced in $p\overline{p}$ collisions at $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$. The data were collected with the D0 detector at the Fermilab Tevatron Collider and correspond to $6.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity. The observed missing transverse energy distribution is well described by the standard model prediction, and 95% C.L. limits are derived on two realizations of theories beyond the standard model. In a gauge-mediated supersymmetry breaking scenario, the breaking scale $\ensuremath{\Lambda}$ is excluded for $\ensuremath{\Lambda}<124\text{ }\text{ }\mathrm{TeV}$. In a universal extra dimension model including gravitational decays, the compactification radius ${R}_{c}$ is excluded for ${R}_{c}^{\ensuremath{-}1}<477\text{ }\text{ }\mathrm{GeV}$.