Scientists have identified a diversity gap in genetic samples and health data, which have been drawn predominantly from individuals of European ancestry, as posing an existential threat to the promise of precision medicine. Inadequate inclusion as articulated by scientists, policymakers, and ethicists has prompted large-scale initiatives aimed at recruiting populations historically underrepresented in biomedical research. Despite explicit calls to increase diversity, the meaning of diversity - which dimensions matter for what outcomes and why - remain strikingly imprecise. Drawing on our document review and qualitative data from observations and interviews of funders and research teams involved in five precision medicine research (PMR) projects, we note that calls for increasing diversity often focus on representation as the goal of recruitment. The language of representation is used flexibly to refer to two objectives: achieving sufficient genetic variation across populations and including historically disenfranchised groups in research. We argue that these dual understandings of representation are more than rhetorical slippage, but rather allow for the contemporary collection of samples and data from marginalized populations to stand in as correcting historical exclusion of social groups towards addressing health inequity. We trace the unresolved historical debates over how and to what extent researchers should procure diversity in PMR and how they contributed to ongoing uncertainty about what axes of diversity matter and why. We argue that ambiguity in the meaning of representation at the outset of a study contributes to a lack of clear conceptualization of diversity downstream throughout subsequent phases of the study.