# Learning Hierarchical Priors in VAEs

arXiv: https://arxiv.org/abs/1905.04982 · HTML: https://mlsanity.com/paper/1905.04982/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2019.

## Built on by (most cited first, 30 of 53)

- [VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming](https://mlsanity.com/paper/2202.04178/) (2022)
- [Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder](https://mlsanity.com/paper/2105.00026/) (2021)
- [Efficient-VDVAE: Less is more](https://mlsanity.com/paper/2203.13751/) (2022)
- [Particle algorithms for maximum likelihood training of latent variable models](https://mlsanity.com/paper/2204.12965/) (2022)
- [Pythae: Unifying Generative Autoencoders in Python -- A Benchmarking Use Case](https://mlsanity.com/paper/2206.08309/) (2022)
- [You Only Sample Once: Taming One-Step Text-to-Image Synthesis by Self-Cooperative Diffusion GANs](https://mlsanity.com/paper/2403.12931/) (2024)
- [Conditional Image Generation by Conditioning Variational Auto-Encoders](https://mlsanity.com/paper/2102.12037/) (2021)
- [A Geometric Perspective on Variational Autoencoders](https://mlsanity.com/paper/2209.07370/) (2022)
- [Multiresolution Equivariant Graph Variational Autoencoder](https://mlsanity.com/paper/2106.00967/) (2021)
- [Fuse It More Deeply! A Variational Transformer with Layer-Wise Latent Variable Inference for Text Generation](https://mlsanity.com/paper/2207.06130/) (2022)
- [NVDiff: Graph Generation through the Diffusion of Node Vectors](https://mlsanity.com/paper/2211.10794/) (2022)
- [Mind the Gap when Conditioning Amortised Inference in Sequential Latent-Variable Models](https://mlsanity.com/paper/2101.07046/) (2021)
- [A prior-based approximate latent Riemannian metric](https://mlsanity.com/paper/2103.05290/) (2021)
- [On Incorporating Inductive Biases into VAEs](https://mlsanity.com/paper/2106.13746/) (2021)
- [Revisiting Structured Variational Autoencoders](https://mlsanity.com/paper/2305.16543/) (2023)
- [Lewis's Signaling Game as beta-VAE For Natural Word Lengths and Segments](https://mlsanity.com/paper/2311.04453/) (2023)
- [Uncertainty Estimation Using Riemannian Model Dynamics for Offline Reinforcement Learning](https://mlsanity.com/paper/2102.11327/) (2021)
- [VTAE: Variational Transformer Autoencoder with Manifolds Learning](https://mlsanity.com/paper/2304.00948/) (2023)
- [Tree Variational Autoencoders](https://mlsanity.com/paper/2306.08984/) (2023)
- [Diffusion Variational Autoencoder for Tackling Stochasticity in Multi-Step Regression Stock Price Prediction](https://mlsanity.com/paper/2309.00073/) (2023)
- [Personalized Federated Collaborative Filtering: A Variational AutoEncoder Approach](https://mlsanity.com/paper/2408.08931/) (2024)
- [Combining Hierachical VAEs with LLMs for clinically meaningful timeline summarisation in social media](https://mlsanity.com/paper/2401.16240/) (2024)
- [Hierarchical VAE with a Diffusion-based VampPrior](https://mlsanity.com/paper/2412.01373/) (2024)
- [Multi-Task Neural Processes](https://mlsanity.com/paper/2111.05820/) (2021)
- [Counterfactual Concept Bottleneck Models](https://mlsanity.com/paper/2402.01408/) (2024)
- [eVAE: Evolutionary Variational Autoencoder](https://mlsanity.com/paper/2301.00011/) (2023)
- [A Review of Bayesian Uncertainty Quantification in Deep Probabilistic Image Segmentation](https://mlsanity.com/paper/2411.16370/) (2024)
- [Disentangling Generative Factors of Physical Fields Using Variational Autoencoders](https://mlsanity.com/paper/2109.07399/) (2021)
- [Towards Flexibility and Interpretability of Gaussian Process State-Space Model](https://mlsanity.com/paper/2301.08843/) (2023)
- [Variational Mixture of HyperGenerators for Learning Distributions Over Functions](https://mlsanity.com/paper/2302.06223/) (2023)

## Abstract (arXiv)

We propose to learn a hierarchical prior in the context of variational autoencoders to avoid the over-regularisation resulting from a standard normal prior distribution. To incentivise an informative latent representation of the data, we formulate the learning problem as a constrained optimisation problem by extending the Taming VAEs framework to two-level hierarchical models. We introduce a graph-based interpolation method, which shows that the topology of the learned latent representation corresponds to the topology of the data manifold---and present several examples, where desired properties of latent representation such as smoothness and simple explanatory factors are learned by the prior.