(Gen)AI diversity is not merely an ethical issue. From the perspective of geographic information science (GIScience), it could be interpreted as a function of uncertainty and as a form of cognitive bias, embedded in AI outputs. Recent work has sought to develop information-theoretic diversity measures and apply them to evaluate AI-chatbot outputs in a geographic context. As the AI ecosystem to which we are exposed on a daily basis becomes rapidly multimodal, we believe it is important to examine <em>geographic diversity</em> across various modalities. Focusing on images, this paper aims to fill this research gap. First, we select the GPT and DALL·E models as state-of-the-art examples and point out how assessing their geographic diversity involves various stages, including prompt revision and image generation. Then, taking inspiration from species diversity measures in ecological research, we incorporate similarity weighting into the measurement of geographic diversity. Next, we demonstrate how to evaluate geographic diversity in image generation through a case study. Our analysis reveals several counterintuitive findings. For instance, older models can exhibit greater geographic diversity despite producing lower-quality images, and prompt revision yields greater geographic diversity than image generation. At the same time, we observe explicit model homogeneity underlying the lack of geographic diversity, as the selected models consistently depict the same prototypical geo-specific feature or similar features. This is concerning, as it risks producing stereotypical representations of places.</p> <p><a href="https://doi.org/10.17605/OSF.IO/vcgy2" target="_blank" rel="noopener"><img src="https://contentmanager.copernicus.org/779365/10/locale/ssl" width="150px" /></a> Reproducibility review available at: <a href="https://doi.org/10.17605/OSF.IO/vcgy2" target="_blank" rel="noopener">https://doi.org/10.17605/OSF.IO/vcgy2</a>