We use a novel method to predict the contribution of normal star-forming galaxies, merger-induced bursts, and obscured AGN, to IR luminosity functions (LFs) and global SFR densities. We use empirical halo occupation constraints to populate halos with galaxies and determine the distribution of normal and merging galaxies. Each system can then be associated with high-resolution hydrodynamic simulations. We predict the distribution of observed luminosities and SFRs, from different galaxy classes, as a function of redshift from z=0-6. We provide fitting functions for the predicted LFs, quantify the uncertainties, and compare with observations. At all redshifts, normal galaxies dominate the LF at moderate luminosities ~L* (the knee). Merger-induced bursts increasingly dominate at L>>L*; at the most extreme luminosities, AGN are important. However, all populations increase in luminosity at higher redshifts, owing to increasing gas fractions. Thus the transition between normal and merger-dominated sources increases from the LIRG-ULIRG threshold at z~0 to bright Hyper-LIRG thresholds at z~2. The transition to dominance by obscured AGN evolves similarly, at factor of several higher L_IR. At all redshifts, non-merging systems dominate the total luminosity/SFR density, with merger-induced bursts constituting ~5-10% and AGN ~1-5%. Bursts contribute little to scatter in the SFR-stellar mass relation. In fact, many systems identified as ongoing mergers will be forming stars in their normal (non-burst) mode. Counting this as merger-induced star formation leads to a stronger apparent redshift evolution in the contribution of mergers to the SFR density.
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