We study privacy amplification by synthetic data release, a phenomenon in which differential privacy guarantees are improved by releasing only synthetic data rather than the private generative model itself. Recent work by Pierquin et al. (2025) established the first formal amplification guarantees for a linear generator, but they apply only in asymptotic regimes where the model dimension far exceeds the number of released synthetic records, limiting their practical relevance. In this work, we show a surprising result: under a bounded-parameter assumption, privacy amplification persists even when releasing an unbounded number of synthetic records, thereby improving upon the bounds of Pierquin et al. (2025). Our analysis provides structural insights that may guide the development of tighter privacy guarantees for more complex release mechanisms.

翻译：我们研究了通过合成数据发布实现的隐私增强现象，这种现象通过仅发布合成数据而非私有生成模型本身来改进差分隐私保证。Pierquin等人（2025）的最新研究首次为线性生成器建立了形式化的增强保证，但这些保证仅适用于模型维度远超已发布合成记录数量的渐近机制，限制了其实际应用价值。在本研究中，我们展示了一个令人惊讶的结果：在有界参数假设下，即使发布无限数量的合成记录，隐私增强效应仍然持续存在，从而改进了Pierquin等人（2025）的边界。我们的分析提供了结构性见解，可能为开发更复杂发布机制的更严格隐私保证提供指导。