Flow Equivariant World Models: Memory for Partially Observed Dynamic Environments

TL;DR

This paper introduces Flow Equivariant World Models that unify self-motion and external object motion as Lie group flows, leveraging symmetry to improve long-term predictions in partially observed dynamic environments.

Contribution

It proposes a novel framework that incorporates group equivariance for both self and external motion, enhancing stability and generalization in world modeling.

Findings

Outperforms state-of-the-art diffusion and memory models on 2D and 3D benchmarks.

Provides stable latent representations over hundreds of timesteps.

Excels in long-term predictions, especially with predictable external dynamics.

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, 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.