DP-aware AdaLN-Zero: Taming Conditioning-Induced Heavy-Tailed Gradients in Differentially Private Diffusion

TL;DR

This paper introduces DP-aware AdaLN-Zero, a sensitivity-aware conditioning mechanism for differentially private diffusion models that reduces heavy-tailed gradients and improves utility in time-series tasks.

Contribution

It proposes a novel conditioning method that limits gradient tail events without altering DP-SGD, enhancing private diffusion model performance.

Findings

Improves interpolation, imputation, and forecasting under privacy constraints.

Reduces gradient tail events and clipping bias in private training.

Achieves better utility on real-world and benchmark datasets.

Abstract

Condition injection enables diffusion models to generate context-aware outputs, which is essential for many time-series tasks. However, heterogeneous conditional contexts (e.g., observed history, missingness patterns or outlier covariates) can induce heavy-tailed per-example gradients. Under Differentially Private Stochastic Gradient Descent (DP-SGD), these rare conditioning-driven heavy-tailed gradients disproportionately trigger global clipping, resulting in outlier-dominated updates, larger clipping bias, and degraded utility under a fixed privacy budget. In this paper, we propose DP-aware AdaLN-Zero, a drop-in sensitivity-aware conditioning mechanism for conditional diffusion transformers that limits conditioning-induced gain without modifying the DP-SGD mechanism. DP-aware AdaLN-Zero jointly constrains conditioning representation magnitude and AdaLN modulation parameters via bounded re-parameterization, suppressing extreme gradient tail events before gradient clipping and noise injection. Empirically, DP-SGD equipped with DP-aware AdaLN-Zero improves interpolation/imputation and forecasting under matched privacy settings. We observe consistent gains on a real-world power dataset and two public ETT benchmarks over vanilla DP-SGD. Moreover, gradient diagnostics attribute these improvements to conditioning-specific tail reshaping and reduced clipping distortion, while preserving expressiveness in non-private training. Overall, these results show that sensitivity-aware conditioning can substantially improve private conditional diffusion training without sacrificing standard performance.