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.

翻译：过去几年中，生成高保真度逼真人脸的技术取得了巨大进展。尽管取得这些进展，一个关键问题仍未得到解答：“给定一个生成式人脸模型，它能生成多少个独特身份？”换言之，生成式人脸模型的生物特征容量是多少？回答这一问题的科学基础将有助于评估和比较不同的生成式人脸模型，并确定其可扩展性的上限。本文提出了一种统计方法，用于在超球面特征空间中估计生成人脸图像的生物特征容量。我们将该方法应用于多个生成模型，包括无条件的生成器（如StyleGAN、潜在扩散模型和“Generated Photos”）以及类条件生成器DCFace。我们还针对性别和年龄等人口统计属性估计了容量。我们的容量估计表明：（a）在ArcFace表示下，当错误接受率（FAR）为0.1%时，StyleGAN3和DCFace的容量上限分别为$1.43\times10^6$和$1.190\times10^4$；（b）当降低目标FAR时，容量急剧下降，对于StyleGAN3，在FAR为1%和10%时，估计容量分别为$1.796\times10^4$和$562$；（c）容量在性别方面没有显著差异；（d）对于某些生成模型，容量在年龄方面存在显著差异。代码可在https://github.com/human-analysis/capacity-generative-face-models获取。