Generative AI systems are rapidly being integrated into global systems of cultural communication, consumption, and production. As these technologies shape our cultures, we urgently need conceptual foundations for investigating the cultural inclusivity of generative AI pipelines (from data collection, to model development and deployment, to evaluation), as well as methods to study the varying societal and cultural impacts of generative AI. This Dagstuhl Seminar wants to bring together scholars and practitioners from computer science, social sciences, the tech industry, and creative industries to discuss the cultural implications of generative AI and find paths toward building generative AI that can be responsive to the diverse needs of individuals, groups, and societies around the world. Together, seminar participants will build shared language and frameworks for reshaping the technical and social architectures of generative AI.