A wide variety of creative practitioners are currently exploring the use of Ai in their work processes, for instance in poetry, music, performance, and visual arts. In this paper, we discuss the relationship between Ai and sustainability in general but focus on the relationship between the emerging area of Ai art and sustainability in particular. We highlight the importance of pursuing research concerning the sustainability of Ai art and take initial steps towards understanding how Ai art practices may influence how we save or waste resources. Developed through our online fieldwork by analyzing the environmental impact of three specific cases of Ai artworks, we provide a conceptual approach that can be used to map the environmental sustainability of Ai art. With this paper as a basis, we hope to elicit awareness among scientific and artistic communities about the environmental sustainability of Ai art.