We report a search for diphoton events with large missing transverse energy produced in pp collisions at √s=1.96 TeV. The data were collected with the D0 detector at the Fermilab Tevatron Collider and correspond to 6.3 fb(-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 Λ is excluded for Λ<124 TeV. In a universal extra dimension model including gravitational decays, the compactification radius R(c) is excluded for R(c)(-1)<477 GeV.