Heavy-Tailed Class-Conditional Priors for Long-Tailed Generative Modeling

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 t3VAE 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-t3VAE, 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 γ-power divergence, and we introduce an equal-weight latent mixture for class-balanced generation. On SVHN-LT, CIFAR100-LT, and CelebA datasets, C-t3VAE consistently attains lower FID scores than t3VAE 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 ρ < 5, for which Gaussian-based models remain competitive. However, for ρ ≥ 5 our approach yields improved class-balanced generation and mode coverage.