Artificial intelligence (AI) systems capable of generating creative outputs are reshaping our understanding of creativity. This shift presents an opportunity for creativity researchers to reevaluate the key components of the creative process. In particular, the advanced capabilities of AI underscore the importance of studying the internal processes of creativity. This paper explores the neurobiological machinery that underlies these internal processes and describes the experiential component of creativity. It is concluded that although the products of artificial and human creativity can be similar, the internal processes are different. The paper also discusses how AI may negatively affect the internal processes of human creativity, such as the development of skills, the authenticity of creativity, and the diversity of ideas.