  Generative AI has received much attention in the image and language domains,
with the transformer neural network continuing to dominate the state of the
art. Application of these models to time series generation is less explored,
however, and is of great utility to machine learning, privacy preservation, and
explainability research. The present survey identifies this gap at the
intersection of the transformer, generative AI, and time series data, and
reviews works in this sparsely populated subdomain. The reviewed works show
great variety in approach, and have not yet converged on a conclusive answer to
the problems the domain poses. GANs, diffusion models, state space models, and
autoencoders were all encountered alongside or surrounding the transformers
which originally motivated the survey. While too open a domain to offer
conclusive insights, the works surveyed are quite suggestive, and several
recommendations for best practice, and suggestions of valuable future work, are
provided.
