Modern clustering approaches often trade interpretability for performance, particularly in deep learning-based methods. We present Generative Kernel Spectral Clustering (GenKSC), a novel model combining kernel spectral clustering with generative modeling to produce both well-defined clusters and interpretable representations. By augmenting weighted variance maximization with reconstruction and clustering losses, our model creates an explorable latent space where cluster characteristics can be visualized through traversals along cluster directions. Results on MNIST and FashionMNIST datasets demonstrate the model's ability to learn meaningful cluster representations.