用几何曲率指导扰动，平衡数据隐私与可用性

Machine learning models require datasets for effective training, but directly sharing raw data poses significant privacy risk such as membership inference attacks (MIA). To mitigate the risk, privacy-preserving techniques such as data perturbation, generalization, and synthetic data generation are commonly utilized. However, these methods often degrade data accuracy, specificity, and diversity, limiting the performance of downstream tasks and thus reducing data utility. Therefore, striking an optimal balance between privacy preservation and data utility remains a critical challenge. To address this issue, we introduce a novel bilevel optimization framework for the publication of private datasets, where the upper-level task focuses on data utility and the lower-level task focuses on data privacy. In the upper-level task, a discriminator guides the generation process to ensure that perturbed latent variables are mapped to high-quality samples, maintaining fidelity for downstream tasks. In the lower-level task, our framework employs local extrinsic curvature on the data manifold as a quantitative measure of individual vulnerability to MIA, providing a geometric foundation for targeted privacy protection. By perturbing samples toward low-curvature regions, our method effectively suppresses distinctive feature combinations that are vulnerable to MIA. Through alternating optimization of both objectives, we achieve a synergistic balance between privacy and utility. Extensive experimental evaluations demonstrate that our method not only enhances resistance to MIA in downstream tasks but also surpasses existing methods in terms of sample quality and diversity.