Abstract: Role-based network embedding methods aim to preserve node-centric connectivity patterns, which are expressions of node roles, into low-dimensional vectors. However, almost all the existing methods are designed for capturing a relaxation of automorphic equivalence or regular equivalence. They may be good at structure identification but could show poorer performance on role identification. Because automorphic equivalence and regular equivalence strictly tie the role of a node to the identities of all its neighbors. To mitigate this problem, we construct a framework called Curvature-based Network Embedding with Stochastic Equivalence (CNESE) to embed stochastic equivalence. More specifically, we estimate the role distribution of nodes based on discrete Ricci curvature for its excellent ability to concisely representing local topology. We use a Variational Auto-Encoder to generate embeddings while a degree-guided regularizer and a contrastive learning regularizer are leveraged to improving both its robustness and discrimination ability. The effectiveness of our proposed CNESE is demonstrated by extensive experiments on real-world networks.