A search for signatures of extra spatial dimensions in the diphoton invariant-mass spectrum has been performed with the CMS detector at the LHC. No excess of events above the standard model expectation is observed using a data sample collected in proton-proton collisions at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$ corresponding to an integrated luminosity of $2.2\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$. In the context of the large-extra-dimensions model, lower limits are set on the effective Planck scale in the range of 2.3--3.8 TeV at the 95% confidence level. These limits are the most restrictive bounds on virtual-graviton exchange to date. The most restrictive lower limits to date are also set on the mass of the first graviton excitation in the Randall-Sundrum model in the range of 0.86--1.84 TeV, for values of the associated coupling parameter between 0.01 and 0.10.