Flow Equivariant World Models: Memory for Partially Observed Dynamic Environments
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, time-parameterized 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, generalizing far beyond the training horizon. By structuring world model representations with respect to internal and external motion, flow equivariance charts a scalable route to data efficient, symmetry-guided, embodied intelligence. Project link: https://flowequivariantworldmodels.github.io.
69693de932f0333869ff9357
Hansen Jin Lillemark
claimed_verified
2026-01-16T10:30:54.847Z
63c7a750bce33b25442a400d
/avatars/2f95b30f0dc6a70725741d4b8d35f1f8.svg
Hansen Lillemark
hlillemark
user
hlillemark
69693de932f0333869ff9358
Benhao Huang
claimed_verified
2026-01-16T10:30:56.765Z
64b22e6b0a54158d66f18688
https://cdn-avatars.huggingface.co/v1/production/uploads/64b22e6b0a54158d66f18688/Cbl3oMMMANbnCMoSUYenI.png
Benhao Huang
HuskyDoge
user
HuskyDoge
69693de932f0333869ff9359
Fangneng Zhan
69693de932f0333869ff935a
Yilun Du
69693de932f0333869ff935b
Thomas Anderson Keller
Flow Equivariant World Models: Memory for Partially Observed Dynamic Environments
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, time-parameterized 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, generalizing far beyond the training horizon. By structuring world model representations with respect to internal and external motion, flow equivariance charts a scalable route to data efficient, symmetry-guided, embodied intelligence. Project link: https://flowequivariantworldmodels.github.io.
Flow Equivariant World Models unify self-motion and external object motion as one-parameter Lie group flows to create stable, symmetry-guided representations for embodied intelligence.
world models Lie group flows group equivariance embodied systems sensory input time-parameterized symmetries latent world representation diffusion-based models memory-augmented architectures long rollouts data efficiency