Would it make sense to compare the output images to their nearest neighbors in the training set in order to establish some metric of "originality"? Sorry if that is a basic question, I haven't read much on image synthesis with neural nets.
Yes, and they don't usually look too much alike (see the BigGAN appendix nearest-neighbors for example of doing this) but some people argue this isn't a good enough check because the GAN could just be shuffling around patches of textures or something, which is a little goal-post-move-y for my taste.