Data augmentation is widely used in vision to introduce variation and mitigate overfitting, by enabling models to learn invariant properties. However, augmentation only indirectly captures these properties and does not explicitly constrain the learned function to satisfy them beyond the empirical training set. We propose generative hints, a training methodology that directly enforces known functional invariances over the input distribution. Our approach leverages a generative model trained on the training data to approximate the input distribution and to produce unlabeled synthetic images, which we refer to as virtual examples. On these virtual examples, we impose hint objectives that explicitly constrain the model's predictions to satisfy known invariance properties, such as spatial invariance. Although the original training dataset is fully labeled, generative hints train the model in a semi-supervised manner by combining the standard classification objective on real data with an auxiliary hint objectives applied to unlabeled virtual examples. Across multiple datasets, architectures, invariance types, and loss functions, generative hints consistently outperform standard data augmentation, achieving accuracy improvements of up to 2.10% on fine-grained visual classification benchmarks and an average gain of 1.29% on the CheXpert medical imaging dataset.