  Traditional Variational Autoencoders (VAEs) are constrained by the
limitations of the Evidence Lower Bound (ELBO) formulation, particularly when
utilizing simplistic, non-analytic, or unknown prior distributions. These
limitations inhibit the VAE's ability to generate high-quality samples and
provide clear, interpretable latent representations. This work introduces the
Entropy Decomposed Variational Autoencoder (ED-VAE), a novel re-formulation of
the ELBO that explicitly includes entropy and cross-entropy components. This
reformulation significantly enhances model flexibility, allowing for the
integration of complex and non-standard priors. By providing more detailed
control over the encoding and regularization of latent spaces, ED-VAE not only
improves interpretability but also effectively captures the complex
interactions between latent variables and observed data, thus leading to better
generative performance.
