Privacy Amplification Persists under Unlimited Synthetic Data Release

We study privacy amplification by synthetic data release, a phenomenon in which differential privacy guarantees improve when 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 linear generators, but they apply only in asymptotic regimes where the model dimension far exceeds the number of released synthetic records, limiting practical relevance. In this work, we show that this restriction is not fundamental and establish that, surprisingly, for linear generators, privacy amplification can persist even when releasing an unbounded number of synthetic records. To prove this result, we develop new analytical tools for characterizing the privacy loss induced by synthetic data release. In particular, we leverage a sufficient-statistics reduction to characterize privacy leakage, and introduce a novel criterion that upper bounds Rényi divergences in terms of Fisher information. Our analysis provides structural insights that may guide the development of tighter privacy guarantees for more complex release mechanisms. Finally, experiments with variational autoencoders trained using DP-SGD further support the relevance of our theory beyond the linear setting.