Title: Flow Equivariant World Modeling for Partially Observed Dynamic Environments
Primary area: generative models
Keywords: World Model, Memory, Partial Observability, Equivariance, Structured Representation Learning

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 motion 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 sharing model weights over locations and motions, eliminating redundant re-learning, and providing a stable latent world representation over hundreds of timesteps. On both 2D and 3D partially observed world modeling benchmarks, we demonstrate Flow Equivariant World Models significantly outperform comparable state-of-the-art diffusion-based and memory-augmented world-modeling architectures, training faster and reaching lower error -- 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 page: https://flowm-anonymous.github.io/Flow-Equivariant-World-Models/

TL;DR: We introduce generalized flow equivariance for partially observable dynamic world modeling, evaluated on 2D and 3D datasets, beating SOTA Diffusion models.