Normalizing flows (NFs) are invertible and bijective generative models, capable of performing exact density estimation of complex data by mapping them from highly nonlinear ambient spaces to simpler latent ones. These mappings hold many promises for images since capturing their true distribution could greatly enhance the performance of downstream tasks such as image classification. In this paper, we devise a novel conditional normalizing flow model that achieves both conditional image generation and classification. The main contribution of our method consists in learning untangled continuums of gaussian distributions in the latent space that maximize the discrimination power of the learned NFs together with the quality, diversity and label reliability of the underlying generated images. This results into highly effective NF classifiers as well as convolutional and transformer networks built on top of the generated images. Extensive experiments conducted on different challenging datasets, including CIFAR100 and ImageNet show the highly balanced discrimination and generative properties of our proposed NF models and their outperformance w.r.t. the closely related work.