# Flow Equivariant World Models: Memory for Partially Observed Dynamic Environments

arXiv: https://arxiv.org/abs/2601.01075 · HTML: https://mlsanity.com/paper/2601.01075/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 59 of its 77 references that are in the map.
- First posted on arXiv 3 Jan 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 30 of 59)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Towards Accurate Generative Models of Video: A New Metric & Challenges](https://mlsanity.com/paper/1812.01717/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [Cosmos World Foundation Model Platform for Physical AI](https://mlsanity.com/paper/2501.03575/) (2025)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://mlsanity.com/paper/2407.01392/) (2024)
- [Self Forcing: Bridging the Train-Test Gap in Autoregressive Video Diffusion](https://mlsanity.com/paper/2506.08009/) (2025)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [NICE-SLAM: Neural Implicit Scalable Encoding for SLAM](https://mlsanity.com/paper/2112.12130/) (2021)
- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [Learning Interactive Real-World Simulators](https://mlsanity.com/paper/2310.06114/) (2023)
- [From Slow Bidirectional to Fast Autoregressive Video Diffusion Models](https://mlsanity.com/paper/2412.07772/) (2024)
- [Minigrid & Miniworld: Modular & Customizable Reinforcement Learning Environments for Goal-Oriented Tasks](https://mlsanity.com/paper/2306.13831/) (2023)
- [Photorealistic Video Generation with Diffusion Models](https://mlsanity.com/paper/2312.06662/) (2023)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Matrix-game 2.0: An open-source real-time and streaming interactive world model](https://mlsanity.com/paper/2508.13009/) (2025)

## Built on by (most cited first, 8 of 8)

- [LiveWorld: Simulating Out-of-Sight Dynamics in Generative Video World Models](https://mlsanity.com/paper/2603.07145/) (2026)
- [Out of Sight, Out of Mind? Evaluating State Evolution in Video World Models](https://mlsanity.com/paper/2603.13215/) (2026)
- [MemoBench: Benchmarking World Modeling in Dynamically Changing Environments](https://mlsanity.com/paper/2606.27537/) (2026)
- [Echo-Memory: A Controlled Study of Memory in Action World Models](https://mlsanity.com/paper/2606.09803/) (2026)
- [Toward World Models for Epidemiology](https://mlsanity.com/paper/2604.09519/) (2026)
- [Can Video World Models Track Unobserved World States?](https://mlsanity.com/paper/2608.30692/) (2026)
- [In-Context Learning for Robots: Methods and Applications](https://mlsanity.com/paper/2609.36012/) (2026)
- [Grid or Nodes? Probing Object Memory in World Models Under Partial Observability](https://mlsanity.com/paper/2610.18637/) (2026)

## Abstract (arXiv)

Embodied systems experience the world as 'a symphony of flows': a combination of many continuous streams of sensory input coupled to self-motion, interwoven with the dynamics of external objects. These sensory streams and the underlying dynamics of the world obey smooth, time-parameterized symmetries which existing world models ignore. Without a memory that respects this structure, partial observability presents a major obstacle to existing methods: each observation reveals only a fraction of the world, while unobserved regions continue to evolve. In this work, we introduce Flow Equivariant World Modeling, a framework that leverages time-parameterized symmetries within a latent memory for stable and accurate dynamics prediction over long horizons. The latent memory shifts and transforms equivariantly with self-motion and inferred external object motion, keeping information about out-of-view regions aligned as time progresses. We demonstrate the advantage of this framework over state-of-the-art diffusion, memory-augmented, and recurrent world model architectures on 2D and 3D partially observed video world modeling benchmarks. More broadly, our results suggest that predictive representations become more powerful when they are organized in line with the temporal and dynamical structure of the world they model. Project page: https://flowequivariantworldmodels.github.io/