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 $t^3$VAE 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-$t^3$VAE, 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-$t^3$VAE consistently attains lower FID scores than $t^3$VAE 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 $ρ\geq 5$ our approach yields improved class-balanced generation and mode coverage.

翻译：变分自编码器（VAEs）在非平衡经验类分布下训练全局先验，可能导致潜在空间中尾部类别的代表性不足。虽然$t^3$VAE通过重尾学生$t$分布先验提升了鲁棒性，但其单一全局先验仍按类别频率成比例分配质量。我们通过引入C-$t^3$VAE解决了这一潜在几何偏差，该模型为每个类别分配一个学生$t$联合先验，用于潜在变量和输出变量。这种设计促进了跨类条件组件的均匀先验质量。为优化模型，我们从$γ$-幂散度推导出闭式目标函数，并引入等权重潜在混合以实现类平衡生成。在SVHN-LT、CIFAR100-LT和CelebA数据集上，C-$t^3$VAE在严重类不平衡下始终获得比$t^3$VAE和基于高斯分布的VAE基线更低的FID分数，同时在平衡或轻度不平衡设置中保持竞争力。在每类F1评估中，我们的模型在高度不平衡设置下优于条件高斯VAE。此外，我们识别出轻度不平衡阈值$ρ< 5$，在此范围内基于高斯分布的模型仍具竞争力。然而，对于$ρ\geq 5$，我们的方法可实现改进的类平衡生成和模式覆盖。