A reliable determination of the Higgs production mechanism in hadron collider experiments is essential to the program of Higgs coupling measurements. We employ weak supervision, CWoLa in particular, to train deep neural networks to distinguish vector boson fusion from gluon-gluon fusion events using simulated datasets as pseudo-experimental data, demonstrating the potential of reducing biases resulting from Monte Carlo simulations. Models based on the convolutional neural network and the transformer are tested and compared. In particular, the classification performance gets slightly better when the photon information is removed from training on the low-luminosity region of $H\to \gamma \gamma$. We explicitly show that the performance can be improved when the training dataset is enlarged by data augmentation using physics-motivated methods. We further demonstrate that the trained model can be successfully applied to the $H\to ZZ$ and $H\to Z\gamma$ events, showing that such classifiers are agnostic to Higgs decay modes, provided these decay modes do not involve strong QCD corrections.