Proper Hölder-Kullback Dirichlet Diffusion: A Framework for High Dimensional Generative Modeling

Diffusion-based generative models have long depended on Gaussian priors, with little exploration of alternative distributions. We introduce a Proper Hölder-Kullback Dirichlet framework that uses time-varying multiplicative transformations to define both forward and reverse diffusion processes. Moving beyond conventional reweighted evidence lower bounds (ELBO) or Kullback-Leibler upper bounds (KLUB), we propose two novel divergence measures: the Proper Hölder Divergence (PHD) and the Proper Hölder-Kullback (PHK) divergence, the latter designed to restore symmetry missing in existing formulations. When optimizing our Dirichlet diffusion model with PHK, we achieve a Fréchet Inception Distance (FID) of 2.78 on unconditional CIFAR-10. Comprehensive experiments on natural-image datasets validate the generative strengths of model and confirm PHK's effectiveness in model training. These contributions expand the diffusion-model family with principled non-Gaussian processes and effective optimization tools, offering new avenues for versatile, high-fidelity generative modeling.