Differential privacy (DP) has achieved remarkable results in the field of privacy-preserving machine learning. However, existing DP frameworks do not satisfy all the conditions for becoming metrics, which prevents them from deriving better basic private properties and leads to exaggerated values on privacy budgets. We propose Wasserstein differential privacy (WDP), an alternative DP framework to measure the risk of privacy leakage, which satisfies the properties of symmetry and triangle inequality. We show and prove that WDP has 13 excellent properties, which can be theoretical supports for the better performance of WDP than other DP frameworks. In addition, we derive a general privacy accounting method called Wasserstein accountant, which enables WDP to be applied in stochastic gradient descent (SGD) scenarios containing sub-sampling. Experiments on basic mechanisms, compositions and deep learning show that the privacy budgets obtained by Wasserstein accountant are relatively stable and less influenced by order. Moreover, the overestimation on privacy budgets can be effectively alleviated. The code is available at https://github.com/Hifipsysta/WDP.

差分隐私（DP）在隐私保护机器学习领域取得了显著成果，但现有的DP框架无法满足成为度量标准的所有条件，这阻碍了它们从基本的隐私属性中得到更好的结果，使隐私预算的值夸大化。我们提出了Wasserstein差分隐私（WDP），一种用于衡量隐私泄露风险的替代DP框架，它满足对称性和三角不等式。我们展示并证明WDP具有13个优秀的属性，这些属性可以作为WDP相较于其他DP框架更好性能的理论支持。此外，我们推导了一种称为Wasserstein账户的通用隐私计算方法，使WDP可以应用于包含子采样的随机梯度下降（SGD）场景。基本机制、组合和深度学习的实验证明Wasserstein账户得到的隐私预算相对稳定且不受顺序的影响较小。此外，隐私预算的高估可以得到有效缓解。代码可在此 https URL 上获取。