Publishing private face recognition~(FR) training datasets is privacy-sensitive because faces expose identity information. Private FR training dataset publication mitigates this risk by releasing protected proxies as substitutes for private training faces. However, training FR models with such data introduces an identity paradox: \emph{the identity cues that make released faces useful for recognition supervision are also the cues that make them linkable to real individuals.} A protected face should be decoupled from the original identity, yet still behave as a reliable identity sample for training. Removing these cues too aggressively may destroy the class structure needed for recognition learning, whereas preserving them too faithfully may increase source-identity linkability. We argue that this paradox stems from conflating source-aligned identity semantics with recognition-useful proxy identity geometry. The former should be suppressed to reduce linkage to private individuals, while the latter should be preserved for FR learning. Based on this insight, we propose \textbf{Private Face Distillation}, an identity-decoupling and geometry-preserving framework. It uses Orthogonal Geometry Preservation to construct decoupled proxy identities from private identity representations while maintaining hyperspherical geometry, and Relational Topology Alignment to preserve identity relations for recognition learning. Experiments across multiple domain-shifted FR scenarios show that Private Face Distillation achieves stronger utility than the evaluated publication baselines. On IJB-C surveillance, it improves $\mathrm{TAR}@\mathrm{FAR}{=}1\text{e-}{3}$ by 3.94\% over the baseline while reducing source-identity linkability. These results suggest that private FR training dataset publication should decouple source-identity correspondence while preserving proxy identity geometry.

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