Data uncertainty refers to the degree of uncertainty in model predictions caused by data variability, challenging the model robustness in multimedia applications. The increased variability of uncontrolled face images, such as mask occlusion and image blur, increases the intra-class differences and inter-class similarities. As a result, the ambiguity in the learned features exacerbates the uncertainty of sample-to-class membership. Traditional face recognition models are deterministic point embedding models that fail to measure data uncertainty. Probabilistic embedding models, such as advanced Data Uncertainty Learning (DUL), represent each face image as a Gaussian distribution to measure data uncertainty. However, these models perform random sampling from the distribution once per training, and the sampled points may fall into different class regions, leading to training oscillation. Therefore, we propose a robust Region Uncertainty Learning (RUL) method, which adopts the entire Gaussian distribution of each sample during each training epoch, and estimates the region relations between the sample distribution region and the class region to measure the sample-to-class membership. In fact, DUL is a special case of the proposed RUL. Specifically, DUL estimates point-with-region relations and only represents absolute membership and non-membership. In contrast, RUL estimates region-with-region relations, enabling it to additionally represent incomplete membership. This more comprehensive membership measurement fully represents the uncertainty of membership, enhancing the model performance and robustness in uncontrolled scenes. Furthermore, for robust face recognition, we propose two RUL-based angular margin losses, AngleFace and RegionFace, to adaptively adjust the learning weights according to the uncertainty of membership. Finally, we comprehensively evaluate the effectiveness of RUL on various face datasets, and profoundly analyze the role of region relations. In future, we will explore the applicability of RUL in other tasks.