Large Language Models (LLMs) have been recently proposed for supporting domain modeling tasks mostly related to the completion of partial models by recommending additional model elements. However, there are many more modeling tasks, one of them being the instantiation of domain models to represent concrete domain objects. While there is considerable work supporting the generation of structurally valid instantiations, there are still open challenges to incorporating real-world semantics by having realistic values contained in instances and ensuring the generation of semantically diverse models. Only then will such generated models become human-understandable and helpful in educational or data-driven research contexts. To tackle these challenges, this paper presents an approach that employs LLMs and two prompting strategies in combination with existing model validation tools for instantiating semantically realistic and diverse domain models expressed as UML class diagrams. We have applied our approach to models used in education and available in the literature from different domains and evaluated the generated instances in terms of syntactic correctness, model conformance, semantic correctness, and diversity of the generated values. The results show that the generated instances are mostly syntactically correct, that they conform to the domain model, and that there are only a few semantic errors. Moreover, the generated instance values are semantically diverse, i.e., concrete realistic examples in line with the domain and the combination of the values within one model are semantically coherent.