The generalized parton distributions (GPDs) are important to our understanding of hadron structures, especially for their tomography images. We propose a new type of exclusive single-diffractive processes with two high-transverse-momentum particles in the final state and show that they can be factorized into the GPDs as long as the transverse momentum q_T of the two final-state particles is much greater than the \Lambda_{\rm QCD}. We illustrate that this type of processes are generic enough to cover nearly all the GPD-associated processes existing in the literature, and we point out that this new type of processes can provide a roadmap to organize the GPD-related processes. By using a specific example of exclusive production of a pair of high-transverse-momentum photons in diffractive pion-nucleon scattering, we show that this new type of processes are not only complementary to the existing processes in probing GPDs, but also capable of providing an enhanced sensitivity to the x-dependence of GPDs.