Introduction: "Democratizing" artificial intelligence (AI) in medicine and healthcare is a vague term that encompasses various meanings, issues, and visions. This article maps the ways this term is used in discourses on AI in medicine and healthcare and uses this map for a normative reflection on how to direct AI in medicine and healthcare towards desirable futures. Methods: We searched peer-reviewed articles from Scopus, Google Scholar, and PubMed along with grey literature using search terms "democrat*", "artificial intelligence" and "machine learning". We approached both as documents and analyzed them qualitatively, asking: What is the object of democratization? What should be democratized, and why? Who is the demos who is said to benefit from democratization? And what kind of theories of democracy are (tacitly) tied to specific uses of the term? Results: We identified four clusters of visions of democratizing AI in healthcare and medicine: 1) democratizing medicine and healthcare through AI, 2) multiplying the producers and users of AI, 3) enabling access to and oversight of data, and 4) making AI an object of democratic governance. Discussion: The envisioned democratization in most visions mainly focuses on patients as consumers and relies on or limits itself to free market-solutions. Democratization in this context requires defining and envisioning a set of social goods, and deliberative processes and modes of participation to ensure that those affected by AI in healthcare have a say on its development and use.