From mock Hubble Space Telescope images, we quantify non-parametric statistics of galaxy morphology, thereby predicting the emergence of relationships among stellar mass, star formation, and observed rest-frame optical structure at 1 < z < 3. We measure automated diagnostics of galaxy morphology in cosmological simulations of the formation of 22 central galaxies with 9.3 < log 10 M * /M < 10.7. These highspatial-resolution zoom-in calculations enable accurate modeling of the rest-frame UV and optical morphology. Even with small numbers of galaxies, we find that structural evolution is neither universal nor monotonic: galaxy interactions can trigger either bulge or disc formation, and optically bulge-dominated galaxies at this mass may not remain so forever. Simulated galaxies with M * > 10 10 M contain relatively more disc-dominated light profiles than those with lower mass, reflecting significant disc brightening in some haloes at 1 < z < 2. By this epoch, simulated galaxies with specific star formation rates below 10 −9.7 yr −1 are more likely than normal starformers to have a broader mix of structural types, especially at M * > 10 10 M . We analyze a cosmological major merger at z ∼ 1.5 and find that the newly proposed MID morphology diagnostics trace later merger stages while Gini-M 20 trace earlier ones. MID is sensitive also to clumpy star-forming discs. The observability time of typical MID-enhanced events in our simulation sample is < 100 Myr. A larger sample of cosmological assembly histories may be required to calibrate such diagnostics in the face of their sensitivity to viewing angle, segmentation algorithm, and various phenomena such as clumpy star formation and minor mergers.