Abstract
Variational Autoencoders (VAEs) with global priors trained under an imbalanced empirical class distribution can lead to underrepresentation of tail classes in the latent space. While t^3VAE improves robustness via heavy-tailed Student's t-distribution priors, its single global prior still allocates mass proportionally to class frequency. We address this latent geometric bias by introducing C-t^3VAE, which assigns a per-class Student's t joint prior over latent and output variables. This design promotes uniform prior mass across class-conditioned components. To optimize our model we derive a closed-form objective from the \gamma-power divergence, and we introduce an equal-weight latent mixture for class-balanced generation. On SVHN-LT, CIFAR100-LT, and CelebA datasets, C-t^3VAE consistently attains lower FID scores than t^3VAE and Gaussian-based VAE baselines under severe class imbalance while remaining competitive in balanced or mildly imbalanced settings. In per-class F1 evaluations, our model outperforms the conditional Gaussian VAE across highly imbalanced settings. Moreover, we identify the mild imbalance threshold \rho < 5, for which Gaussian-based models remain competitive. However, for \rho \geq 5 our approach yields improved class-balanced generation and mode coverage.
