In this study, we apply the information-theoretic Privacy Funnel (PF) model to face recognition and develop a method for privacy-preserving representation learning within an end-to-end trainable framework. Our approach addresses the trade-off between utility and obfuscation of sensitive information under logarithmic loss. We study the integration of information-theoretic privacy principles with representation learning, with a particular focus on face recognition systems. We also highlight the compatibility of the proposed framework with modern face recognition networks such as AdaFace and ArcFace. In addition, we introduce the Generative Privacy Funnel ($\mathsf{GenPF}$) model, which extends the traditional discriminative PF formulation, referred to here as the Discriminative Privacy Funnel ($\mathsf{DisPF}$). The proposed $\mathsf{GenPF}$ model extends the privacy-funnel framework to generative formulations under information-theoretic and estimation-theoretic criteria. Complementing these developments, we present the deep variational PF (DVPF) model, which yields a tractable variational bound for measuring information leakage and enables optimization in deep representation-learning settings. The DVPF framework, associated with both the $\mathsf{DisPF}$ and $\mathsf{GenPF}$ models, also clarifies connections with generative models such as variational autoencoders (VAEs), generative adversarial networks (GANs), and diffusion models. Finally, we validate the framework on modern face recognition systems and show that it provides a controllable privacy--utility trade-off while substantially reducing leakage about sensitive attributes. To support reproducibility, we also release a PyTorch implementation of the proposed framework.

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