# Relational VAE: A Continuous Latent Variable Model for Graph Structured Data

arXiv: https://arxiv.org/abs/2106.16049 · HTML: https://mlsanity.com/paper/2106.16049/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 44 references that are in the map.
- First posted on arXiv 30 Jun 2021.

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Graphite: Iterative Generative Modeling of Graphs](https://mlsanity.com/paper/1803.10459/) (2018)
- [Graph Normalizing Flows](https://mlsanity.com/paper/1905.13177/) (2019)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [The Functional Neural Process](https://mlsanity.com/paper/1906.08324/) (2019)
- [Doubly Stochastic Variational Inference for Neural Processes with Hierarchical Latent Variables](https://mlsanity.com/paper/2008.09469/) (2020)
- [Bayesian Semi-supervised Learning with Graph Gaussian Processes](https://mlsanity.com/paper/1809.04379/) (2018)
- [Message Passing Neural Processes](https://mlsanity.com/paper/2009.13895/) (2020)
- [Continuous Representation of Molecules Using Graph Variational Autoencoder](https://mlsanity.com/paper/2004.08152/) (2020)

## Built on by (most cited first, 1 of 1)

- [Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Later](https://mlsanity.com/paper/2509.19929/) (2025)

## Abstract (arXiv)

Graph Networks (GNs) enable the fusion of prior knowledge and relational reasoning with flexible function approximations. In this work, a general GN-based model is proposed which takes full advantage of the relational modeling capabilities of GNs and extends these to probabilistic modeling with Variational Bayes (VB). To that end, we combine complementary pre-existing approaches on VB for graph data and propose an approach that relies on graph-structured latent and conditioning variables. It is demonstrated that Neural Processes can also be viewed through the lens of the proposed model. We show applications on the problem of structured probability density modeling for simulated and real wind farm monitoring data, as well as on the meta-learning of simulated Gaussian Process data. We release the source code, along with the simulated datasets.