# Ladder Variational Autoencoders

arXiv: https://arxiv.org/abs/1602.02282 · HTML: https://mlsanity.com/paper/1602.02282/

## Key facts

- Cited by 318 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2016.

## Built on by (most cited first, 30 of 318)

- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
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- [Explainable artificial intelligence (XAI) in deep learning-based medical image analysis](https://mlsanity.com/paper/2107.10912/) (2021)
- [ImageBART: Bidirectional Context with Multinomial Diffusion for Autoregressive Image Synthesis](https://mlsanity.com/paper/2108.08827/) (2021)
- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latents](https://mlsanity.com/paper/2201.00308/) (2022)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Human Motion Generation: A Survey](https://mlsanity.com/paper/2307.10894/) (2023)
- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [An Introduction to Neural Data Compression](https://mlsanity.com/paper/2202.06533/) (2022)
- [SetVAE: Learning Hierarchical Composition for Generative Modeling of Set-Structured Data](https://mlsanity.com/paper/2103.15619/) (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)
- [AirFormer: Predicting Nationwide Air Quality in China with Transformers](https://mlsanity.com/paper/2211.15979/) (2022)
- [MUSE-VAE: Multi-Scale VAE for Environment-Aware Long Term Trajectory Prediction](https://mlsanity.com/paper/2201.07189/) (2022)
- [Hierarchical VAEs Know What They Don't Know](https://mlsanity.com/paper/2102.08248/) (2021)
- [High Fidelity Image Counterfactuals with Probabilistic Causal Models](https://mlsanity.com/paper/2306.15764/) (2023)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [Learning Disentangled Representations in the Imaging Domain](https://mlsanity.com/paper/2108.12043/) (2021)
- [Clockwork Variational Autoencoders](https://mlsanity.com/paper/2102.09532/) (2021)
- [Long Document Summarization with Top-down and Bottom-up Inference](https://mlsanity.com/paper/2203.07586/) (2022)
- [MuseMorphose: Full-Song and Fine-Grained Piano Music Style Transfer with One Transformer VAE](https://mlsanity.com/paper/2105.04090/) (2021)
- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [SwitchTab: Switched Autoencoders Are Effective Tabular Learners](https://mlsanity.com/paper/2401.02013/) (2024)
- [Efficient Iterative Amortized Inference for Learning Symmetric and Disentangled Multi-Object Representations](https://mlsanity.com/paper/2106.03630/) (2021)
- [Diagonal Attention and Style-based GAN for Content-Style Disentanglement in Image Generation and Translation](https://mlsanity.com/paper/2103.16146/) (2021)
- [Lossy Image Compression with Quantized Hierarchical VAEs](https://mlsanity.com/paper/2208.13056/) (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)

## Abstract (arXiv)

Variational Autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared to the purely bottom-up inference in layered Variational Autoencoders and other generative models. We provide a detailed analysis of the learned hierarchical latent representation and show that our new inference model is qualitatively different and utilizes a deeper more distributed hierarchy of latent variables. Finally, we observe that batch normalization and deterministic warm-up (gradually turning on the KL-term) are crucial for training variational models with many stochastic layers.