# VAE with a VampPrior

arXiv: https://arxiv.org/abs/1705.07120 · HTML: https://mlsanity.com/paper/1705.07120/

## Key facts

- Cited by 248 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2017.

## Built on by (most cited first, 30 of 248)

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- [Diffusion-SDF: Conditional Generative Modeling of Signed Distance Functions](https://mlsanity.com/paper/2211.13757/) (2022)
- [Image-to-Image Translation: Methods and Applications](https://mlsanity.com/paper/2101.08629/) (2021)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [D2C: Diffusion-Denoising Models for Few-shot Conditional Generation](https://mlsanity.com/paper/2106.06819/) (2021)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [EQ-VAE: Equivariance Regularized Latent Space for Improved Generative Image Modeling](https://mlsanity.com/paper/2502.09509/) (2025)
- [PriorGrad: Improving Conditional Denoising Diffusion Models with Data-Dependent Adaptive Prior](https://mlsanity.com/paper/2106.06406/) (2021)
- [GIVT: Generative Infinite-Vocabulary Transformers](https://mlsanity.com/paper/2312.02116/) (2023)
- [Identifiability of deep generative models without auxiliary information](https://mlsanity.com/paper/2206.10044/) (2022)
- [Posterior Collapse and Latent Variable Non-identifiability](https://mlsanity.com/paper/2301.00537/) (2023)
- [Sample-dependent Adaptive Temperature Scaling for Improved Calibration](https://mlsanity.com/paper/2207.06211/) (2022)
- [A Langevin-like Sampler for Discrete Distributions](https://mlsanity.com/paper/2206.09914/) (2022)
- [Truncated Diffusion Probabilistic Models and Diffusion-based Adversarial Auto-Encoders](https://mlsanity.com/paper/2202.09671/) (2022)
- [Contrastively Disentangled Sequential Variational Autoencoder](https://mlsanity.com/paper/2110.12091/) (2021)
- [VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming](https://mlsanity.com/paper/2202.04178/) (2022)
- [Graph Out-of-Distribution Generalization via Causal Intervention](https://mlsanity.com/paper/2402.11494/) (2024)
- [Synthetic Data in Human Analysis: A Survey](https://mlsanity.com/paper/2208.09191/) (2022)
- [Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder](https://mlsanity.com/paper/2105.00026/) (2021)
- [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)
- [Future-conditioned Unsupervised Pretraining for Decision Transformer](https://mlsanity.com/paper/2305.16683/) (2023)
- [Diffusion Priors In Variational Autoencoders](https://mlsanity.com/paper/2106.15671/) (2021)
- [A Geometric Perspective on Variational Autoencoders](https://mlsanity.com/paper/2209.07370/) (2022)

## Abstract (arXiv)

Many different methods to train deep generative models have been introduced in the past. In this paper, we propose to extend the variational auto-encoder (VAE) framework with a new type of prior which we call "Variational Mixture of Posteriors" prior, or VampPrior for short. The VampPrior consists of a mixture distribution (e.g., a mixture of Gaussians) with components given by variational posteriors conditioned on learnable pseudo-inputs. We further extend this prior to a two layer hierarchical model and show that this architecture with a coupled prior and posterior, learns significantly better models. The model also avoids the usual local optima issues related to useless latent dimensions that plague VAEs. We provide empirical studies on six datasets, namely, static and binary MNIST, OMNIGLOT, Caltech 101 Silhouettes, Frey Faces and Histopathology patches, and show that applying the hierarchical VampPrior delivers state-of-the-art results on all datasets in the unsupervised permutation invariant setting and the best results or comparable to SOTA methods for the approach with convolutional networks.