# World Models as Group Actions

arXiv: https://arxiv.org/abs/2605.24578 · HTML: https://mlsanity.com/paper/2605.24578/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Video-generation world models and simulators, one of 11 directions in World models.
- Builds on 70 of its 81 references that are in the map.
- First posted on arXiv 23 May 2026.

## Placed in

- World models / [Video-generation world models and simulators](https://mlsanity.com/wm/video-generation-world-models-and-simulators/)

## Builds on (most cited first, 30 of 70)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2304.08818/) (2023)
- [AnimateDiff: Animate Your Personalized Text-to-Image Diffusion Models without Specific Tuning](https://mlsanity.com/paper/2307.04725/) (2023)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [DROID-SLAM: Deep Visual SLAM for Monocular, Stereo, and RGB-D Cameras](https://mlsanity.com/paper/2108.10869/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Open-Sora: Democratizing Efficient Video Production for All](https://mlsanity.com/paper/2412.20404/) (2024)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [World Action Models are Zero-shot Policies](https://mlsanity.com/paper/2602.15922/) (2026)
- [LLM-Planner: Few-Shot Grounded Planning for Embodied Agents with Large Language Models](https://mlsanity.com/paper/2212.04088/) (2022)
- [Learning Interactive Real-World Simulators](https://mlsanity.com/paper/2310.06114/) (2023)
- [DreamSim: Learning New Dimensions of Human Visual Similarity using Synthetic Data](https://mlsanity.com/paper/2306.09344/) (2023)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Diffusion for World Modeling: Visual Details Matter in Atari](https://mlsanity.com/paper/2405.12399/) (2024)
- [NavGPT: Explicit Reasoning in Vision-and-Language Navigation with Large Language Models](https://mlsanity.com/paper/2305.16986/) (2023)
- [Navigation World Models](https://mlsanity.com/paper/2412.03572/) (2024)
- [NoMaD: Goal Masked Diffusion Policies for Navigation and Exploration](https://mlsanity.com/paper/2310.07896/) (2023)
- [ViNT: A Foundation Model for Visual Navigation](https://mlsanity.com/paper/2306.14846/) (2023)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)

## Built on by (most cited first, 3 of 3)

- [ATM: Action-Consistency Transfer Matrix for Diagnosing and Improving Latent World Models](https://mlsanity.com/paper/2606.09028/) (2026)
- [Diagnosing JEPA World Models with Action-Conditioned Predictive Consistency](https://mlsanity.com/paper/2608.12939/) (2026)
- [ARDepth: Auto-regressive Monocular Depth Estimation with Progressive Visual Conditioning](https://mlsanity.com/paper/2607.12433/) (2026)

## Abstract (arXiv)

Video world models have achieved strong visual realism, but this does not ensure that their dynamics are truly governed by actions. In this work, we argue that action faithfulness should be understood through the compositional structure of actions, which in many embodied settings follows a group structure (e.g., SE(2) for navigation). Based on this insight, we formalize action-conditioned world modeling as realizing a group action on the state space, providing a principled criterion for evaluating dynamics beyond visual quality. To operationalize this framework, we propose a unified approach that enforces identity, inverse, and composition consistency via latent-space regularization with synthesized supervision, avoiding additional data collection. We further introduce two metrics: Group-Action Consistency (GAC) and Group-Action Robustness (GAR), to evaluate structural correctness and rollout stability. Extensive experimental results show that our method consistently improves both GAC and GAR in state-of-the-art video world models without degrading perceptual quality.