# On the Relationship Between Active Inference and Control as Inference

arXiv: https://arxiv.org/abs/2006.12964 · HTML: https://mlsanity.com/paper/2006.12964/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2020.

## Built on by (most cited first, 30 of 42)

- [Active Inference in Robotics and Artificial Agents: Survey and Challenges](https://mlsanity.com/paper/2112.01871/) (2021)
- [Predictive Coding: Towards a Future of Deep Learning beyond Backpropagation?](https://mlsanity.com/paper/2202.09467/) (2022)
- [pymdp: A Python library for active inference in discrete state spaces](https://mlsanity.com/paper/2201.03904/) (2022)
- [World Models and Predictive Coding for Cognitive and Developmental Robotics: Frontiers and Challenges](https://mlsanity.com/paper/2301.05832/) (2023)
- [Maximum Likelihood Reinforcement Learning](https://mlsanity.com/paper/2602.02710/) (2026)
- [Hybrid Predictive Coding: Inferring, Fast and Slow](https://mlsanity.com/paper/2204.02169/) (2022)
- [The Free Energy Principle for Perception and Action: A Deep Learning Perspective](https://mlsanity.com/paper/2207.06415/) (2022)
- [Multimodal VAE Active Inference Controller](https://mlsanity.com/paper/2103.04412/) (2021)
- [Contrastive Active Inference](https://mlsanity.com/paper/2110.10083/) (2021)
- [On efficient computation in active inference](https://mlsanity.com/paper/2307.00504/) (2023)
- [Active Inference as a Model of Agency](https://mlsanity.com/paper/2401.12917/) (2024)
- [Understanding the Origin of Information-Seeking Exploration in Probabilistic Objectives for Control](https://mlsanity.com/paper/2103.06859/) (2021)
- [A Unified View on Solving Objective Mismatch in Model-Based Reinforcement Learning](https://mlsanity.com/paper/2310.06253/) (2023)
- [Active Inference for Stochastic Control](https://mlsanity.com/paper/2108.12245/) (2021)
- [Adaptation through prediction: multisensory active inference torque control](https://mlsanity.com/paper/2112.06752/) (2021)
- [Chance-Constrained Active Inference](https://mlsanity.com/paper/2102.08792/) (2021)
- [A Whole Brain Probabilistic Generative Model: Toward Realizing Cognitive Architectures for Developmental Robots](https://mlsanity.com/paper/2103.08183/) (2021)
- [Habits and goals in synergy: a variational Bayesian framework for behavior](https://mlsanity.com/paper/2304.05008/) (2023)
- [Value of Information and Reward Specification in Active Inference and POMDPs](https://mlsanity.com/paper/2408.06542/) (2024)
- [Online reinforcement learning with sparse rewards through an active inference capsule](https://mlsanity.com/paper/2106.02390/) (2021)
- [Towards Stochastic Fault-tolerant Control using Precision Learning and Active Inference](https://mlsanity.com/paper/2109.05870/) (2021)
- [Successor Representation Active Inference](https://mlsanity.com/paper/2207.09897/) (2022)
- [A Unified View of Algorithms for Path Planning Using Probabilistic Inference on Factor Graphs](https://mlsanity.com/paper/2106.10442/) (2021)
- [Life-inspired Interoceptive Artificial Intelligence for Autonomous and Adaptive Agents](https://mlsanity.com/paper/2309.05999/) (2023)
- [Limitations of Agents Simulated by Predictive Models](https://mlsanity.com/paper/2402.05829/) (2024)
- [Emergence of Goal-Directed Behaviors via Active Inference with Self-Prior](https://mlsanity.com/paper/2504.11075/) (2025)
- [Active Inference as a Convex Markov Decision Process](https://mlsanity.com/paper/2607.20152/) (2026)
- [On Solving a Stochastic Shortest-Path Markov Decision Process as Probabilistic Inference](https://mlsanity.com/paper/2109.05866/) (2021)
- [Efficient search of active inference policy spaces using k-means](https://mlsanity.com/paper/2209.02550/) (2022)
- [Deep hybrid models: infer and plan in a dynamic world](https://mlsanity.com/paper/2402.10088/) (2024)

## Abstract (arXiv)

Active Inference (AIF) is an emerging framework in the brain sciences which suggests that biological agents act to minimise a variational bound on model evidence. Control-as-Inference (CAI) is a framework within reinforcement learning which casts decision making as a variational inference problem. While these frameworks both consider action selection through the lens of variational inference, their relationship remains unclear. Here, we provide a formal comparison between them and demonstrate that the primary difference arises from how value is incorporated into their respective generative models. In the context of this comparison, we highlight several ways in which these frameworks can inform one another.