Flow Equivariant World Models: Memory for Partially Observed Dynamic Environments

📝 Original Info

• Title: Flow Equivariant World Models: Memory for Partially Observed Dynamic Environments
• ArXiv ID: 2601.01075
• Date: 2026-01-03
• Authors: Hansen Jin Lillemark, Benhao Huang, Fangneng Zhan, Yilun Du, Thomas Anderson Keller

📝 Abstract

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 streams obey smooth, timeparameterized symmetries, which combine through a precisely structured algebra; yet most neural network world models ignore this structure and instead repeatedly re-learn the same transformations from data. In this work, we introduce 'Flow Equivariant World Models', a framework in which both self-motion and external object motion are unified as one-parameter Lie group 'flows'. We leverage this unification to implement group equivariance with respect to these transformations, thereby providing a stable latent world representation over hundreds of timesteps. On both 2D and 3D partially observed video world modeling benchmarks, we demonstrate that Flow Equivariant World Models significantly outperform comparable state-of-the-art diffusion-based and memory-augmented world modeling architectures -particularly when there are predictable world dynamics outside the agent's current field of view. We show that flow equivariance is particularly beneficial for long rollouts, ge...

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