Privacy-Aware Dirichlet Process Mixture Models: Diffusion-Based Trajectory Protection and Differentially Private Weights

Mixture models are widely used to capture cluster structure in modern machine learning systems, particularly in time-varying applications such as smart grids and interacting large language models. However, releasing data from such systems can leak sensitive group information because the temporal trajectories of cluster centroids enable reconstruction of underlying group behavior. Static perturbation methods are insufficient, as repeated noise patterns can be filtered over time. We introduce a dynamic privacy framework based on a Dirichlet process mixture model (DDirPMM), in which centroids evolve through a diffusion process that injects temporally varying randomness to prevent trajectory reconstruction while preserving utility. In addition, our DDirPMM inherently induces static differential privacy for mixture weights, automatically protecting them without additional mechanisms. These two mechanisms address structurally distinct threat models, trajectory reconstruction and membership inference, respectively. Theoretical and empirical results demonstrate greater performance against filtering-based reconstruction and improved privacy-utility trade-offs compared with static trajectory protection methods.