# Conditional Sampling of Variational Autoencoders via Iterated Approximate Ancestral Sampling

arXiv: https://arxiv.org/abs/2308.09078 · HTML: https://mlsanity.com/paper/2308.09078/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 58 references that are in the map.
- First posted on arXiv 17 Aug 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference](https://mlsanity.com/paper/1703.09194/) (2017)
- [Unsupervised Learning of 3D Structure from Images](https://mlsanity.com/paper/1607.00662/) (2016)
- [Approximate Inference with Amortised MCMC](https://mlsanity.com/paper/1702.08343/) (2017)
- [Leveraging the Exact Likelihood of Deep Latent Variable Models](https://mlsanity.com/paper/1802.04826/) (2018)
- [Generalization Gap in Amortized Inference](https://mlsanity.com/paper/2205.11640/) (2022)
- [Learning to Generate with Memory](https://mlsanity.com/paper/1602.07416/) (2016)
- [Adaptive Independent Sticky MCMC algorithms](https://mlsanity.com/paper/1308.3779/) (2013)
- [Variational Gibbs Inference for Statistical Model Estimation from Incomplete Data](https://mlsanity.com/paper/2111.13180/) (2021)

## Built on by (most cited first, 2 of 2)

- [Tractable Representation Learning with Probabilistic Circuits](https://mlsanity.com/paper/2507.04385/) (2025)
- [Improving Variational Autoencoder Estimation from Incomplete Data with Mixture Variational Families](https://mlsanity.com/paper/2403.03069/) (2024)

## Abstract (arXiv)

Conditional sampling of variational autoencoders (VAEs) is needed in various applications, such as missing data imputation, but is computationally intractable. A principled choice for asymptotically exact conditional sampling is Metropolis-within-Gibbs (MWG). However, we observe that the tendency of VAEs to learn a structured latent space, a commonly desired property, can cause the MWG sampler to get "stuck" far from the target distribution. This paper mitigates the limitations of MWG: we systematically outline the pitfalls in the context of VAEs, propose two original methods that address these pitfalls, and demonstrate an improved performance of the proposed methods on a set of sampling tasks.