When constructing random forests, it is of prime importance to ensure high accuracy and low correlation of individual tree classifiers for good performance. Nevertheless, it is typically difficult for existing random forest methods to strike a good balance between these conflicting factors. In this work, we propose a generalized convolutional forest networks to learn a feature space to maximize the strength of individual tree classifiers while minimizing the respective correlation. The feature space is iteratively constructed by a probabilistic triplet sampling method based on the distribution obtained from the splits of the random forest. The sampling process is designed to pull the data of the same label together for higher strength and push away the data frequently falling to the same leaf nodes. We perform extensive experiments on five image classification and two domain generalization datasets with ResNet-50 and DenseNet-161 backbone networks. Experimental results show that the proposed algorithm performs favorably against state-of-the-art methods.