According to OpenAI’s policy, you own the images you generate with AI and thus, own the copyright. Google does not claim copyright over the images generated by AI.
However, you also need to be aware of the local and University law. While each country has different laws governing the copyright of AI generated images, in Hong Kong, under section 11(3) of the Copyright Ordinance (Cap. 528), the law states that “in the case of literary, dramatic, musical or artistic work which is computer-generated, the author is taken to be the person by whom the arrangements necessary for the creation of work are undertaken”. In the case of AI image generation, the author would be the user, who enters the prompt.
Please bear in mind that you are only permitted to use HKU GenAI services limited to teaching, learning, work and research-related purposes only. The University gives you the right to the image as long as you use it for the aforementioned reasons.