# A visual introduction to Gaussian Belief Propagation

arXiv: https://arxiv.org/abs/2107.02308 · HTML: https://mlsanity.com/paper/2107.02308/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 58 references that are in the map.
- First posted on arXiv 5 Jul 2021.

## Builds on (most cited first, 19 of 19)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Efficient Processing of Deep Neural Networks: A Tutorial and Survey](https://mlsanity.com/paper/1703.09039/) (2017)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [DeepFactors: Real-Time Probabilistic Dense Monocular SLAM](https://mlsanity.com/paper/2001.05049/) (2020)
- [The Consciousness Prior](https://mlsanity.com/paper/1709.08568/) (2017)
- [Loopy Belief Propagation for Approximate Inference: An Empirical Study](https://mlsanity.com/paper/1301.6725/) (2013)
- [Neural Enhanced Belief Propagation on Factor Graphs](https://mlsanity.com/paper/2003.01998/) (2020)
- [Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference](https://mlsanity.com/paper/1707.07383/) (2017)
- [FutureMapping: The Computational Structure of Spatial AI Systems](https://mlsanity.com/paper/1803.11288/) (2018)
- [Belief Propagation Neural Networks](https://mlsanity.com/paper/2007.00295/) (2020)
- [FutureMapping 2: Gaussian Belief Propagation for Spatial AI](https://mlsanity.com/paper/1910.14139/) (2019)
- [Bundle Adjustment on a Graph Processor](https://mlsanity.com/paper/2003.03134/) (2020)
- [A Survey on Graph Processing Accelerators: Challenges and Opportunities](https://mlsanity.com/paper/1902.10130/) (2019)
- [Ego-Motion Alignment from Face Detections for Collaborative Augmented Reality](https://mlsanity.com/paper/2010.02153/) (2020)
- [Fundamental Linear Algebra Problem of Gaussian Inference](https://mlsanity.com/paper/2010.08022/) (2020)
- [Differentiable Nonparametric Belief Propagation](https://mlsanity.com/paper/2101.05948/) (2021)

## Built on by (most cited first, 13 of 13)

- [A Robot Web for Distributed Many-Device Localisation](https://mlsanity.com/paper/2202.03314/) (2022)
- [Distributing Collaborative Multi-Robot Planning with Gaussian Belief Propagation](https://mlsanity.com/paper/2203.11618/) (2022)
- [Incremental Abstraction in Distributed Probabilistic SLAM Graphs](https://mlsanity.com/paper/2109.06241/) (2021)
- [Gaussian Ensemble Belief Propagation for Efficient Inference in High-Dimensional Systems](https://mlsanity.com/paper/2402.08193/) (2024)
- [Compositional Visual Planning via Inference-Time Diffusion Scaling](https://mlsanity.com/paper/2603.02646/) (2026)
- [A Blueprint for Equilibrium-Based Differentiable Continuous-Variable Thermodynamic Computing](https://mlsanity.com/paper/2607.16183/) (2026)
- [Learning in Deep Factor Graphs with Gaussian Belief Propagation](https://mlsanity.com/paper/2311.14649/) (2023)
- [Hyperion -- A fast, versatile symbolic Gaussian Belief Propagation framework for Continuous-Time SLAM](https://mlsanity.com/paper/2407.07074/) (2024)
- [See What the Robot Can't See: Learning Cooperative Perception for Visual Navigation](https://mlsanity.com/paper/2208.00759/) (2022)
- [PixRO: Pixel-Distributed Rotational Odometry with Gaussian Belief Propagation](https://mlsanity.com/paper/2406.09726/) (2024)
- [Aggregating Direct and Indirect Neighbors through Graph Linear Transformations](https://mlsanity.com/paper/2511.16871/) (2025)
- [PixVOD: Pixel-Distributed Direct Visual Odometry and Depth Estimation](https://mlsanity.com/paper/2606.03989/) (2026)
- [Hierarchy-GBP: Accelerating Factor Graph Inference via Abstraction and Recovery](https://mlsanity.com/paper/2610.06978/) (2026)

## Abstract (arXiv)

In this article, we present a visual introduction to Gaussian Belief Propagation (GBP), an approximate probabilistic inference algorithm that operates by passing messages between the nodes of arbitrarily structured factor graphs. A special case of loopy belief propagation, GBP updates rely only on local information and will converge independently of the message schedule. Our key argument is that, given recent trends in computing hardware, GBP has the right computational properties to act as a scalable distributed probabilistic inference framework for future machine learning systems.