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Latent factors such as general intelligence, externalizing psychopathology, self-control, and risk tolerance play prominent roles in a wide variety of social science theories. When widespread correlations are observed within a constellation of observable measures, a latent common factor is typically invoked. However, a longstanding critique of latent variable theories is that the empirical patterns of correlations observed can often be plausibly produced by data generating mechanisms that that do not involve a common factor. In this simulation study we demonstrate how, by incorporating information on individual genetic variants, Genomic Structural Equation Modeling can be used to differentiate between different data generating mechanisms that give rise to otherwise indistinguishable patterns of empirical correlation. We generate genetically correlated phenotypes from 1) a common factor model in which all phenotypes rely on one or more general intermediate phenotypes, and 2) a process-overlap model in which pairs of phenotypes share subsets of overlapping intermediate phenotypes, but no intermediate phenotype is relevant for all phenotypes. Common factor models and process-overlap models give rise to covariance structures that are indistinguishable. However, by including individual genetic variants in our Genomic SEM models, we are able to differentiate between the two data generating mechanisms. When estimated on a genome-wide basis, Genomic SEM's heterogeneity statistic (QSNP) can be used to distinguish between common factor and process overlap models. Moreover, in cases in which the common factor model is accepted, QSNP can discern between individual SNPs that operate on the factor and those that operate through more specific pathways. These methods provide new opportunities for more rigorously testing the plausibility and utility of latent factor models, thereby helping to further our understanding of canonical social science constructs.