Contrary to a still common belief that diversity lowers standards, current research in Higher Education indicates that an institution that wishes to maintain a competitive advantage needs to put well-managed diversity very high on its agenda, for reasons of academic and pedagogical excellence as well as to be responsive to changing local and global dynamics. In order to rearticulate diversity as an imperative driven by the search for excellence, the established institutional culture needs to be interrogated to understand why diversity is constructed as a "problem" and attitudes and values are maintained that are hostile to an inclusionary culture. A key element in this institutional culture is whiteness, and different forms of multiculturalism can be identified in terms of their relationship to the power of white privilege. This article names and discusses several assumptions that may underpin received practices and approaches within Historically White Universities (HWUs), which need to be rigorously challenged, and argues for an approach to diversity which can be described as "Critical Diversity".