  There has been tremendous progress in generating realistic faces with high
fidelity over the past few years. Despite this progress, a crucial question
remains unanswered: "Given a generative face model, how many unique identities
can it generate?" In other words, what is the biometric capacity of the
generative face model? A scientific basis for answering this question will
benefit evaluating and comparing different generative face models and establish
an upper bound on their scalability. This paper proposes a statistical approach
to estimate the biometric capacity of generated face images in a hyperspherical
feature space. We employ our approach on multiple generative models, including
unconditional generators like StyleGAN, Latent Diffusion Model, and "Generated
Photos," as well as DCFace, a class-conditional generator. We also estimate
capacity w.r.t. demographic attributes such as gender and age. Our capacity
estimates indicate that (a) under ArcFace representation at a false acceptance
rate (FAR) of 0.1%, StyleGAN3 and DCFace have a capacity upper bound of
$1.43\times10^6$ and $1.190\times10^4$, respectively; (b) the capacity reduces
drastically as we lower the desired FAR with an estimate of $1.796\times10^4$
and $562$ at FAR of 1% and 10%, respectively, for StyleGAN3; (c) there is no
discernible disparity in the capacity w.r.t gender; and (d) for some generative
models, there is an appreciable disparity in the capacity w.r.t age. Code is
available at https://github.com/human-analysis/capacity-generative-face-models.
