# Variational Causal Dynamics: Discovering Modular World Models from Interventions

arXiv: https://arxiv.org/abs/2206.11131 · HTML: https://mlsanity.com/paper/2206.11131/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in World models for language agents, one of 11 directions in World models.
- Builds on 40 of its 55 references that are in the map.
- First posted on arXiv 22 Jun 2022.

## Placed in

- World models / [World models for language agents](https://mlsanity.com/wm/world-models-for-language-agents/)

## Builds on (most cited first, 30 of 40)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Planning to Explore via Self-Supervised World Models](https://mlsanity.com/paper/2005.05960/) (2020)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [Stochastic Video Generation with a Learned Prior](https://mlsanity.com/paper/1802.07687/) (2018)
- [Recurrent Independent Mechanisms](https://mlsanity.com/paper/1909.10893/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Contrastive Learning of Structured World Models](https://mlsanity.com/paper/1911.12247/) (2019)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [CausalWorld: A Robotic Manipulation Benchmark for Causal Structure and Transfer Learning](https://mlsanity.com/paper/2010.04296/) (2020)
- [GENESIS-V2: Inferring Unordered Object Representations without Iterative Refinement](https://mlsanity.com/paper/2104.09958/) (2021)
- [Invariant Causal Prediction for Block MDPs](https://mlsanity.com/paper/2003.06016/) (2020)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [Counterfactual Data Augmentation using Locally Factored Dynamics](https://mlsanity.com/paper/2007.02863/) (2020)
- [High Fidelity Video Prediction with Large Stochastic Recurrent Neural Networks](https://mlsanity.com/paper/1911.01655/) (2019)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [CoPhy: Counterfactual Learning of Physical Dynamics](https://mlsanity.com/paper/1909.12000/) (2019)
- [Causal Discovery in Physical Systems from Videos](https://mlsanity.com/paper/2007.00631/) (2020)
- [Neural Production Systems: Learning Rule-Governed Visual Dynamics](https://mlsanity.com/paper/2103.01937/) (2021)

## Built on by (most cited first, 16 of 16)

- [Causal Triplet: An Open Challenge for Intervention-centric Causal Representation Learning](https://mlsanity.com/paper/2301.05169/) (2023)
- [Neuro-Symbolic Causal Reasoning Meets Signaling Game for Emergent Semantic Communications](https://mlsanity.com/paper/2210.12040/) (2022)
- [SPARTAN: A Sparse Transformer World Model Attending to What Matters](https://mlsanity.com/paper/2411.06890/) (2024)
- [Graph World Models: Concepts, Taxonomy, and Future Directions](https://mlsanity.com/paper/2604.27895/) (2026)
- [Causal Representation Learning in Temporal Data via Single-Parent Decoding](https://mlsanity.com/paper/2410.07013/) (2024)
- [Out-of-Variable Generalization for Discriminative Models](https://mlsanity.com/paper/2304.07896/) (2023)
- [Compete and Compose: Learning Independent Mechanisms for Modular World Models](https://mlsanity.com/paper/2404.15109/) (2024)
- [From Observation to Insight: Mechanistic World Models and the Quest for Autonomous Discovery](https://mlsanity.com/paper/2607.12474/) (2026)
- [From Pixels to Factors: Learning Independently Controllable State Variables for Reinforcement Learning](https://mlsanity.com/paper/2510.02484/) (2025)
- [Disentangling Dynamical Systems: Causal Representation Learning Meets Local Sparse Attention](https://mlsanity.com/paper/2603.14483/) (2026)
- [Toward Consistent World Models with Multi-Token Prediction and Latent Semantic Enhancement](https://mlsanity.com/paper/2604.06155/) (2026)
- [Reliable Beamforming at Terahertz Bands: Are Causal Representations the Way Forward?](https://mlsanity.com/paper/2303.08017/) (2023)
- [On the Emergence and Test-Time Use of Structural Information in Large Language Models](https://mlsanity.com/paper/2601.17869/) (2026)
- [Disentangled Representations for Causal Cognition](https://mlsanity.com/paper/2407.00744/) (2024)
- [Event-Conditioned Diagnostics of Kinematic, Contact, and Object-Permanence Structure in Passive Object-State World Models](https://mlsanity.com/paper/2606.28455/) (2026)
- [Do-JEPA: From Masking to Intervention in Latent World Models](https://mlsanity.com/paper/2609.37378/) (2026)

## Abstract (arXiv)

Latent world models allow agents to reason about complex environments with high-dimensional observations. However, adapting to new environments and effectively leveraging previous knowledge remain significant challenges. We present variational causal dynamics (VCD), a structured world model that exploits the invariance of causal mechanisms across environments to achieve fast and modular adaptation. By causally factorising a transition model, VCD is able to identify reusable components across different environments. This is achieved by combining causal discovery and variational inference to learn a latent representation and transition model jointly in an unsupervised manner. Specifically, we optimise the evidence lower bound jointly over a representation model and a transition model structured as a causal graphical model. In evaluations on simulated environments with state and image observations, we show that VCD is able to successfully identify causal variables, and to discover consistent causal structures across different environments. Moreover, given a small number of observations in a previously unseen, intervened environment, VCD is able to identify the sparse changes in the dynamics and to adapt efficiently. In doing so, VCD significantly extends the capabilities of the current state-of-the-art in latent world models while also comparing favourably in terms of prediction accuracy.