arXiv:2405.13012v2 Announce Type: replace-cross Abstract: The recent surge of Large Language Models (LLMs) has led to claims that they are approaching a level of creativity akin to human capabilities. This idea has sparked a blend of excitement and apprehension. However, a critical piece that has been missing in this discourse is a systematic evaluation of LLMs' semantic diversity, particularly in comparison to human divergent thinking. To bridge this gap, we leverage recent advances in computational creativity to analyze semantic divergence in both state-of-the-art LLMs and a substantial dataset of 100,000 humans. We found evidence that LLMs can surpass average human performance on the Divergent Association Task, and approach human creative writing abilities, though they fall short of the typical performance of highly creative humans. Notably, even the top performing LLMs are still largely surpassed by highly creative individuals, underscoring a ceiling that current LLMs still fail to surpass. Our human-machine benchmarking framework addresses the polemic surrounding the imminent replacement of human creative labour by AI, disentangling the quality of the respective creative linguistic outputs using established objective measures. While prompting deeper exploration of the distinctive elements of human inventive thought compared to those of AI systems, we lay out a series of techniques to improve their outputs with respect to semantic diversity, such as prompt design and hyper-parameter tuning.