Generative Artificial Intelligence (GenAI) has recently been associated with numerous concerns about its impact for democracy. This article aims to assess this debate from the perspective of different normative conceptions of democracy. This article argues that a more theoretically grounded discussion is needed to guide current efforts to understand and regulate GenAI. By systematically reviewing the emerging literature on GenAI and democracy, the authors discuss what exactly it is that GenAI is seen to threaten. Finally, this article connects the concerns with three different normative perspectives on democracy, with an aim to illustrate how perceptions of the impact of GenAI on democracy depend on the normative lenses adopted.