Privacy auditing provides an important safeguard by estimating the actual information leaked by a model, thus ensuring that theoretical privacy guarantees hold in practice. We study empirical privacy auditing for differentially private (DP) machine learning, focusing on efficient one-run methods for mechanisms such as DP-SGD. Prior one-run approaches threshold training examples or "canaries" into binary membership guesses, which discards useful information. We show that, in the white-box DP-SGD setting, canary-aligned signals naturally form a sequence of random variables whose normalized sum is asymptotically Gaussian. We show that this gaussian perspective can also be naturally extended to other composition mechanisms that satisfy a classical, triangular-array, or martingale central limit theorem. Leveraging this distributional perspective, we develop a DP-auditing framework that leads to tighter privacy lower bounds from a single training run.

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