Generative artificial intelligence (AI) algorithms for both text-to-text and text-to-image applications have seen rapid and widespread adoption in the general and medical communities. While limitations of generative AI have been widely reported, there remain valuable applications in patient and professional communities. Here, the limitations and biases of both text-to-text and text-to-image generative AI are explored using purported applications in medical imaging as case examples. A direct comparison of the capabilities of four common text-to-image generative AI algorithms is reported and recommendations for the most appropriate use, DALL-E 3, justified. The risks use and biases are outlined, and appropriate use guidelines framed for use of generative AI in nuclear medicine. Generative AI text-to-text and text-to-image generation includes inherent biases, particularly gender and ethnicity, that could misrepresent nuclear medicine. The assimilation of generative AI tools into medical education, image interpretation, patient education, health promotion and marketing in nuclear medicine risks propagating errors and amplification of biases. Mitigation strategies should reside inside appropriate use criteria and minimum standards for quality and professionalism for the application of generative AI in nuclear medicine.