Batch Normalization (BN), a widely-used technique in neural networks, enhances generalization and expedites training by normalizing each mini-batch to the same mean and variance. However, its effectiveness diminishes when confronted with diverse data distributions. To address this challenge, we propose Supervised Batch Normalization (SBN), a pioneering approach. We expand normalization beyond traditional single mean and variance parameters, enabling the identification of data modes prior to training. This ensures effective normalization for samples sharing common features. We define contexts as modes, categorizing data with similar characteristics. These contexts are explicitly defined, such as domains in domain adaptation or modalities in multimodal systems, or implicitly defined through clustering algorithms based on data similarity. We illustrate the superiority of our approach over BN and other commonly employed normalization techniques through various experiments on both single and multi-task datasets. Integrating SBN with Vision Transformer results in a remarkable \textit{15.13}\% accuracy enhancement on CIFAR-100. Additionally, in domain adaptation scenarios, employing AdaMatch demonstrates an impressive \textit{22.25}\% accuracy improvement on MNIST and SVHN compared to BN.