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

• URL: http://arxiv.org/abs/2602.21645v1
• Date: Wed, 25 Feb 2026 07:19:18 GMT
• Title: Lie Flow: Video Dynamic Fields Modeling and Predicting with Lie Algebra as Geometric Physics Principle
• Authors: Weidong Qiao, Wangmeng Zuo, Hui Li,
• Abstract summary: LieFlow is a dynamic radiance representation framework that explicitly models motion.<n>The SE(3) transformation field enforces physically inspired constraints to maintain motion continuity and geometric consistency.<n>Results confirm that SE(3)-based motion modeling offers a robust and physically grounded framework for representing dynamic 4D scenes.
• Score: 48.28007238304401
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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