# BIVA: A Very Deep Hierarchy of Latent Variables for Generative Modeling

arXiv: https://arxiv.org/abs/1902.02102 · HTML: https://mlsanity.com/paper/1902.02102/

## Key facts

- Cited by 109 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2019.

## Built on by (most cited first, 30 of 109)

- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [A Comprehensive Survey of AI-Generated Content (AIGC): A History of Generative AI from GAN to ChatGPT](https://mlsanity.com/paper/2303.04226/) (2023)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [The Values Encoded in Machine Learning Research](https://mlsanity.com/paper/2106.15590/) (2021)
- [ImageBART: Bidirectional Context with Multinomial Diffusion for Autoregressive Image Synthesis](https://mlsanity.com/paper/2108.08827/) (2021)
- [Diffusion Models for Image Restoration and Enhancement: A Comprehensive Survey](https://mlsanity.com/paper/2308.09388/) (2023)
- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [Understanding Failures in Out-of-Distribution Detection with Deep Generative Models](https://mlsanity.com/paper/2107.06908/) (2021)
- [Greedy Hierarchical Variational Autoencoders for Large-Scale Video Prediction](https://mlsanity.com/paper/2103.04174/) (2021)
- [Multimodal Conditional Image Synthesis with Product-of-Experts GANs](https://mlsanity.com/paper/2112.05130/) (2021)
- [Generate What You Prefer: Reshaping Sequential Recommendation via Guided Diffusion](https://mlsanity.com/paper/2310.20453/) (2023)
- [BDDM: Bilateral Denoising Diffusion Models for Fast and High-Quality Speech Synthesis](https://mlsanity.com/paper/2203.13508/) (2022)
- [Unsupervised Out-of-Distribution Detection with Diffusion Inpainting](https://mlsanity.com/paper/2302.10326/) (2023)
- [Hierarchical VAEs Know What They Don't Know](https://mlsanity.com/paper/2102.08248/) (2021)
- [Posterior Collapse and Latent Variable Non-identifiability](https://mlsanity.com/paper/2301.00537/) (2023)
- [High Fidelity Image Counterfactuals with Probabilistic Causal Models](https://mlsanity.com/paper/2306.15764/) (2023)
- [Densely connected normalizing flows](https://mlsanity.com/paper/2106.04627/) (2021)
- [Long Document Summarization with Top-down and Bottom-up Inference](https://mlsanity.com/paper/2203.07586/) (2022)
- [VQ-GNN: A Universal Framework to Scale up Graph Neural Networks using Vector Quantization](https://mlsanity.com/paper/2110.14363/) (2021)
- [Understanding Masked Autoencoders via Hierarchical Latent Variable Models](https://mlsanity.com/paper/2306.04898/) (2023)
- [Few-Shot Diffusion Models](https://mlsanity.com/paper/2205.15463/) (2022)
- [Bilateral Denoising Diffusion Models](https://mlsanity.com/paper/2108.11514/) (2021)
- [Scaling Up Probabilistic Circuits by Latent Variable Distillation](https://mlsanity.com/paper/2210.04398/) (2022)
- [Identifying Weight-Variant Latent Causal Models](https://mlsanity.com/paper/2208.14153/) (2022)
- [Measuring axiomatic soundness of counterfactual image models](https://mlsanity.com/paper/2303.01274/) (2023)
- [VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming](https://mlsanity.com/paper/2202.04178/) (2022)
- [Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions](https://mlsanity.com/paper/2302.07261/) (2023)
- [Conditional Image Synthesis with Diffusion Models: A Survey](https://mlsanity.com/paper/2409.19365/) (2024)
- [Multi-Facet Clustering Variational Autoencoders](https://mlsanity.com/paper/2106.05241/) (2021)

## Abstract (arXiv)

With the introduction of the variational autoencoder (VAE), probabilistic latent variable models have received renewed attention as powerful generative models. However, their performance in terms of test likelihood and quality of generated samples has been surpassed by autoregressive models without stochastic units. Furthermore, flow-based models have recently been shown to be an attractive alternative that scales well to high-dimensional data. In this paper we close the performance gap by constructing VAE models that can effectively utilize a deep hierarchy of stochastic variables and model complex covariance structures. We introduce the Bidirectional-Inference Variational Autoencoder (BIVA), characterized by a skip-connected generative model and an inference network formed by a bidirectional stochastic inference path. We show that BIVA reaches state-of-the-art test likelihoods, generates sharp and coherent natural images, and uses the hierarchy of latent variables to capture different aspects of the data distribution. We observe that BIVA, in contrast to recent results, can be used for anomaly detection. We attribute this to the hierarchy of latent variables which is able to extract high-level semantic features. Finally, we extend BIVA to semi-supervised classification tasks and show that it performs comparably to state-of-the-art results by generative adversarial networks.