# Realising Synthetic Active Inference Agents, Part II: Variational Message Updates

arXiv: https://arxiv.org/abs/2306.02733 · HTML: https://mlsanity.com/paper/2306.02733/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 38 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 8 of 8)

- [Active inference on discrete state-spaces: a synthesis](https://mlsanity.com/paper/2001.07203/) (2020)
- [Whence the Expected Free Energy?](https://mlsanity.com/paper/2004.08128/) (2020)
- [Reactive Message Passing for Scalable Bayesian Inference](https://mlsanity.com/paper/2112.13251/) (2021)
- [A Factor Graph Approach to Automated Design of Bayesian Signal Processing Algorithms](https://mlsanity.com/paper/1811.03407/) (2018)
- [Active Inference and Epistemic Value in Graphical Models](https://mlsanity.com/paper/2109.00541/) (2021)
- [Chance-Constrained Active Inference](https://mlsanity.com/paper/2102.08792/) (2021)
- [Realising Active Inference in Variational Message Passing: the Outcome-blind Certainty Seeker](https://mlsanity.com/paper/2104.11798/) (2021)
- [Deriving time-averaged active inference from control principles](https://mlsanity.com/paper/2208.10601/) (2022)

## Built on by (most cited first, 7 of 7)

- [Expected Free Energy-based Planning as Variational Inference](https://mlsanity.com/paper/2504.14898/) (2025)
- [Realising Synthetic Active Inference Agents, Part I: Epistemic Objectives and Graphical Specification Language](https://mlsanity.com/paper/2306.08014/) (2023)
- [What Type of Inference is Active Inference?](https://mlsanity.com/paper/2606.04935/) (2026)
- [Message passing-based inference in an autoregressive active inference agent](https://mlsanity.com/paper/2509.25482/) (2025)
- [Expected Free Energy-based Planning as Variational Inference](https://mlsanity.com/paper/2606.20658/) (2026)
- [Sophisticated Policies from Epistemic Priors](https://mlsanity.com/paper/2607.19518/) (2026)
- [Expected free energy as an information constraint on the Bethe Lagrangian](https://mlsanity.com/paper/2608.17167/) (2026)

## Abstract (arXiv)

The Free Energy Principle (FEP) describes (biological) agents as minimising a variational Free Energy (FE) with respect to a generative model of their environment. Active Inference (AIF) is a corollary of the FEP that describes how agents explore and exploit their environment by minimising an expected FE objective. In two related papers, we describe a scalable, epistemic approach to synthetic AIF, by message passing on free-form Forney-style Factor Graphs (FFGs). A companion paper (part I) introduces a Constrained FFG (CFFG) notation that visually represents (generalised) FE objectives for AIF. The current paper (part II) derives message passing algorithms that minimise (generalised) FE objectives on a CFFG by variational calculus. A comparison between simulated Bethe and generalised FE agents illustrates how the message passing approach to synthetic AIF induces epistemic behaviour on a T-maze navigation task. Extension of the T-maze simulation to 1) learning goal statistics, and 2) a multi-agent bargaining setting, illustrate how this approach encourages reuse of nodes and updates in alternative settings. With a full message passing account of synthetic AIF agents, it becomes possible to derive and reuse message updates across models and move closer to industrial applications of synthetic AIF.