I disagree. Diffusion models are trained to generate the probability distribution of their training dataset, like other generative models (GAN, VAE, etc). The fact that the architecture is a Transformer (or a CNN with attention like in Stable Diffusion) is orthogonal to the generative vs discriminative divide.
Unsupervised is a confusing term as there is always an underlying loss being optimized and working as a supervision signal, even for good old kmeans. But generative models are generally considered to be part of unsupervised methods.
While you're right about GANs, diffusion models as transformers as transformers are most commonly trained with supervised learning.