  We consider the phenomenology of a 750 GeV resonance X which can be produced
at the LHC by only photon fusion and subsequently decay into di-photons. We
propose that the spin-zero state X is coupled to a heavy lepton that lives in
the bulk of a higher-dimensional theory and interacts only with the photons of
the Standard Model. We compute the di-photon rate in these models with two and
more compact extra dimensions and demonstrate that they allow for a compelling
explanation of the di-photon excess recently observed by the ATLAS and CMS
collaborations. The central role in our approach is played by the summation
over the Kaluza-Klein modes of the new leptons, thus providing a significant
enhancement of the $X\to \gamma\gamma$ loops for the production and decay
subprocesses. It is expected that the jet activity accompanying these purely
electromagnetic (at the partonic level) processes is numerically suppressed by
factors such as $\alpha_{em}^2 C_{q\bar{q}}/C_{\gamma\gamma}\sim 10^{-3}$.
