Lie Flow: Video Dynamic Fields Modeling and Predicting with Lie Algebra as Geometric Physics Principle

2026-02-25

AI Summary

Existing methods struggle to model complex rigid and non-rigid motions in 4D scenes with both consistency and physical plausibility, particularly exhibiting limitations in handling rotations and articulated transformations. This work proposes LieFlow, a novel framework that, for the first time, incorporates the SE(3) Lie group as a geometric-physical prior into dynamic radiance fields. By explicitly modeling translation and rotation through Lie algebra, LieFlow establishes a unified motion representation that guarantees spatiotemporal continuity and geometric consistency. This approach breaks away from conventional paradigms that rely solely on translational displacements, achieving significant improvements over NeRF-based baselines on both synthetic and real-world datasets, with notable gains in view synthesis fidelity, temporal coherence, and physical realism.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Intelligent Robots: Motion and Path Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Modeling 4D scenes requires capturing both spatial structure and temporal motion, which is challenging due to the need for physically consistent representations of complex rigid and non-rigid motions. Existing approaches mainly rely on translational displacements, which struggle to represent rotations, articulated transformations, often leading to spatial inconsistency and physically implausible motion. LieFlow, a dynamic radiance representation framework that explicitly models motion within the SE(3) Lie group, enabling coherent learning of translation and rotation in a unified geometric space. The SE(3) transformation field enforces physically inspired constraints to maintain motion continuity and geometric consistency. The evaluation includes a synthetic dataset with rigid-body trajectories and two real-world datasets capturing complex motion under natural lighting and occlusions. Across all datasets, LieFlow consistently improves view-synthesis fidelity, temporal coherence, and physical realism over NeRF-based baselines. These results confirm that SE(3)-based motion modeling offers a robust and physically grounded framework for representing dynamic 4D scenes.

Problem

• 4D scene modeling
• motion representation
• physical consistency
• rotation modeling
• dynamic scenes

Innovation

• LieFlow
• SE(3) Lie group
• dynamic radiance fields
• geometric physics
• 4D scene modeling