# Hierarchical Variational Models

arXiv: https://arxiv.org/abs/1511.02386 · HTML: https://mlsanity.com/paper/1511.02386/

## Key facts

- Cited by 89 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2015.

## Built on by (most cited first, 30 of 89)

- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [DIME:Diffusion-Based Maximum Entropy Reinforcement Learning](https://mlsanity.com/paper/2502.02316/) (2025)
- [Local Search GFlowNets](https://mlsanity.com/paper/2310.02710/) (2023)
- [Monte Carlo Variational Auto-Encoders](https://mlsanity.com/paper/2106.15921/) (2021)
- [Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions](https://mlsanity.com/paper/2302.07261/) (2023)
- [Beyond Verifiable Rewards: Scaling Reinforcement Learning for Language Models to Unverifiable Data](https://mlsanity.com/paper/2503.19618/) (2025)
- [Efficient-VDVAE: Less is more](https://mlsanity.com/paper/2203.13751/) (2022)
- [Unifying Generative Models with GFlowNets and Beyond](https://mlsanity.com/paper/2209.02606/) (2022)
- [Contrasting with Symile: Simple Model-Agnostic Representation Learning for Unlimited Modalities](https://mlsanity.com/paper/2411.01053/) (2024)
- [Multiresolution Equivariant Graph Variational Autoencoder](https://mlsanity.com/paper/2106.00967/) (2021)
- [Learning to Jump: Thinning and Thickening Latent Counts for Generative Modeling](https://mlsanity.com/paper/2305.18375/) (2023)
- [Non-Adversarial Imitation Learning and its Connections to Adversarial Methods](https://mlsanity.com/paper/2008.03525/) (2020)
- [Sparse Uncertainty Representation in Deep Learning with Inducing Weights](https://mlsanity.com/paper/2105.14594/) (2021)
- [Amortized Variational Inference: A Systematic Review](https://mlsanity.com/paper/2209.10888/) (2022)
- [Hierarchical Semi-Implicit Variational Inference with Application to Diffusion Model Acceleration](https://mlsanity.com/paper/2310.17153/) (2023)
- [Unified Brain MR-Ultrasound Synthesis using Multi-Modal Hierarchical Representations](https://mlsanity.com/paper/2309.08747/) (2023)
- [Order-Preserving GFlowNets](https://mlsanity.com/paper/2310.00386/) (2023)
- [Learning Energy-Based Prior Model with Diffusion-Amortized MCMC](https://mlsanity.com/paper/2310.03218/) (2023)
- [VAE Approximation Error: ELBO and Exponential Families](https://mlsanity.com/paper/2102.09310/) (2021)
- [A unified view of likelihood ratio and reparameterization gradients](https://mlsanity.com/paper/2105.14900/) (2021)
- [On Incorporating Inductive Biases into VAEs](https://mlsanity.com/paper/2106.13746/) (2021)
- [MixFlows: principled variational inference via mixed flows](https://mlsanity.com/paper/2205.07475/) (2022)
- [Alleviating Adversarial Attacks on Variational Autoencoders with MCMC](https://mlsanity.com/paper/2203.09940/) (2022)
- [Tree Variational Autoencoders](https://mlsanity.com/paper/2306.08984/) (2023)
- [Efficient Semi-Implicit Variational Inference](https://mlsanity.com/paper/2101.06070/) (2021)
- [Automatic variational inference with cascading flows](https://mlsanity.com/paper/2102.04801/) (2021)
- [Variational Predictive Routing with Nested Subjective Timescales](https://mlsanity.com/paper/2110.11236/) (2021)
- [Unified Cross-Modal Medical Image Synthesis with Hierarchical Mixture of Product-of-Experts](https://mlsanity.com/paper/2410.19378/) (2024)
- [Recursive Monte Carlo and Variational Inference with Auxiliary Variables](https://mlsanity.com/paper/2203.02836/) (2022)
- [Combining Hierachical VAEs with LLMs for clinically meaningful timeline summarisation in social media](https://mlsanity.com/paper/2401.16240/) (2024)

## Abstract (arXiv)

Black box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive variational distribution that maintains efficient computation? To address this, we develop hierarchical variational models (HVMs). HVMs augment a variational approximation with a prior on its parameters, which allows it to capture complex structure for both discrete and continuous latent variables. The algorithm we develop is black box, can be used for any HVM, and has the same computational efficiency as the original approximation. We study HVMs on a variety of deep discrete latent variable models. HVMs generalize other expressive variational distributions and maintains higher fidelity to the posterior.