  Recommender Systems are built to retrieve relevant items to satisfy users'
information needs. The candidate corpus usually consists of a finite set of
items that are ready to be served, such as videos, products, or articles. With
recent advances in Generative AI such as GPT and Diffusion models, a new form
of recommendation task is yet to be explored where items are to be created by
generative models with personalized prompts. Taking image generation as an
example, with a single prompt from the user and access to a generative model,
it is possible to generate hundreds of new images in a few minutes. How shall
we attain personalization in the presence of "infinite" items? In this
preliminary study, we propose a two-stage framework, namely Prompt-Model
Retrieval and Generated Item Ranking, to approach this new task formulation. We
release GEMRec-18K, a prompt-model interaction dataset with 18K images
generated by 200 publicly-available generative models paired with a diverse set
of 90 textual prompts. Our findings demonstrate the promise of generative model
recommendation as a novel personalization problem and the limitations of
existing evaluation metrics. We highlight future directions for the RecSys
community to advance towards generative recommender systems. Our code and
dataset are available at https://github.com/MAPS-research/GEMRec.
