We present a physical model for the origin of z \sim 2 Dust-Obscured Galaxies ( DOGs ) , a class of high-redshift ULIRGs selected at 24 µm which are particularly optically faint ( F _ { 24 \mu m } / F _ { R } > 1000 ) . By combining N -body/SPH simulations of high redshift galaxy evolution with 3D polychromatic dust radiative transfer models , we find that luminous DOGs ( with F _ { 24 } \ga 0.3 mJy at z \sim 2 ) are well-modeled as extreme gas-rich mergers in massive ( \sim 5 \times 10 ^ { 12 } -10 ^ { 13 } M _ { \sun } ) halos , with elevated star formation rates ( \sim 500 - 1000 M _ { \sun } yr ^ { -1 } ) and/or significant AGN growth ( \dot { M } _ { BH } \ga 0.5 M _ { \sun } yr ^ { -1 } ) , 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 shaped mid-IR ( IRAC ) spectral energy distribution ( SED ) . After the DOG phase , the galaxy settles back to exhibiting a “ bump ” SED with bluer colors and lower star formation rates . While canonically power-law galaxies are associated with being AGN-dominated , we find that the power-law mid-IR SED can owe both to direct AGN contribution , as well as to a heavily dust obscured stellar bump at times that the galaxy is starburst dominated . Thus power-law galaxies can be either starburst or AGN dominated . Less luminous DOGs can be well-represented either by mergers , or by massive ( M _ { baryon } \approx 5 \times 10 ^ { 11 } M _ { \sun } ) secularly evolving gas-rich disc galaxies ( with SFR \ga 50 M _ { \sun } yr ^ { -1 } ) . By utilising similar models as those employed in the SMG formation study of Narayanan et al . ( 2010 ) , 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 ( SMGs ) , 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 line widths and location on the M _ { BH } - M _ { bulge } relation of DOGs . Finally , we provide public SED templates derived from these simulations .