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We present a physical model for the origin of dust-obscured galaxies (DOGs), a class of high-redshift ultraluminous infrared galaxies (ULIRGs) selected at 24 μm which are particularly optically faint . By combining N-body/smoothed particle hydrodynamic simulations of high-redshift galaxy evolution with 3D polychromatic dust radiative transfer models, we find that luminous DOGs (with mJy at ) are well modelled as extreme gas-rich mergers in massive haloes, with elevated star formation rates (SFR; ) and/or significant active galactic nuclei (AGN) growth , whereas less luminous DOGs are more diverse in nature. At final coalescence, merger-driven DOGs transition from being starburst dominated to AGN dominated, evolving from a ‘bump’ to a power-law (PL) shaped mid-IR (Infrared Array Camera, IRAC) spectral energy distribution (SED). After the DOG phase, the galaxy settles back to exhibiting a ‘bump’ SED with bluer colours and lower SFRs. While canonically PL galaxies are associated with being AGN dominated, we find that the PL mid-IR SED can owe both to direct AGN contribution and to a heavily dust obscured stellar bump at times that the galaxy is starburst dominated. Thus, PL galaxies can be either starburst or AGN dominated. Less luminous DOGs can be well-represented either by mergers or by massive secularly evolving gas-rich disc galaxies (with ). By utilizing similar models as those employed in the submillimetre galaxy (SMG) formation study of Narayanan et al., we investigate the connection between DOGs and SMGs. We find that the most heavily star-forming merger-driven DOGs can be selected as submillimetre galaxies, while both merger-driven and secularly evolving DOGs typically satisfy the BzK selection criteria. The model SEDs from the simulated galaxies match observed data reasonably well, though Mrk 231 and Arp 220 templates provide worse matches. Our models provide testable predictions of the physical masses, dust temperatures, CO linewidths and location on the relation of DOGs. Finally, we provide public SED templates derived from these simulations. [ABSTRACT FROM AUTHOR]