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

arXiv: https://arxiv.org/abs/2509.02154 · HTML: https://mlsanity.com/paper/2509.02154/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 39 references that are in the map.
- First posted on arXiv 2 Sep 2025.

## Builds on (most cited first, 25 of 25)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Brain Imaging Generation with Latent Diffusion Models](https://mlsanity.com/paper/2209.07162/) (2022)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Social Biases through the Text-to-Image Generation Lens](https://mlsanity.com/paper/2304.06034/) (2023)
- [PacGAN: The power of two samples in generative adversarial networks](https://mlsanity.com/paper/1712.04086/) (2017)
- [Class-Balancing Diffusion Models](https://mlsanity.com/paper/2305.00562/) (2023)
- [Heavy-Tailed Diffusion Models](https://mlsanity.com/paper/2410.14171/) (2024)
- [Variational Autoencoder with Implicit Optimal Priors](https://mlsanity.com/paper/1809.05284/) (2018)
- [Multi-Facet Clustering Variational Autoencoders](https://mlsanity.com/paper/2106.05241/) (2021)
- [Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder](https://mlsanity.com/paper/2105.00026/) (2021)
- [t3-Variational Autoencoder: Learning Heavy-tailed Data with Student's t and Power Divergence](https://mlsanity.com/paper/2312.01133/) (2023)
- [Teaching a GAN What Not to Learn](https://mlsanity.com/paper/2010.15639/) (2020)
- [Variational auto-encoders with Student's t-prior](https://mlsanity.com/paper/2004.02581/) (2020)
- [RareGAN: Generating Samples for Rare Classes](https://mlsanity.com/paper/2203.10674/) (2022)
- [On the Statistical Capacity of Deep Generative Models](https://mlsanity.com/paper/2501.07763/) (2025)
- [LDFaceNet: Latent Diffusion-based Network for High-Fidelity Deepfake Generation](https://mlsanity.com/paper/2408.02078/) (2024)

## Built on by (most cited first, 1 of 1)

- [Phase-Type Variational Autoencoders for Heavy-Tailed Data](https://mlsanity.com/paper/2603.01800/) (2026)

## Abstract (arXiv)

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.