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

Reliable 3D dynamic perception requires models that can anticipate motion beyond predefined categories, yet progress is hindered by the scarcity of dense, high-quality motion annotations. While self-supervision on unlabeled real data offers a path forward, empirical evidence suggests that scaling unlabeled data fails to close the performance gap due to noisy proxy signals. In this paper, we propose learning robust real-world motion priors entirely from scalable simulation. We introduce SynFlow, a data generation pipeline for large-scale synthetic LiDAR scene flow. Unlike prior works that prioritize sensor-specific realism, SynFlow employs a motion-oriented strategy to synthesize diverse kinematic patterns across 4,000 sequences ($\sim$940k frames), termed SynFlow-4k. This represents a $34\times$ scale-up in annotated volume over existing real-world benchmarks. Our experiments demonstrate that SynFlow-4k provides a highly domain-invariant motion prior. In a zero-shot regime, models trained only on our synthetic data generalize across multiple real-world benchmarks, comparable to in-domain supervised baselines on nuScenes and outperforming state-of-the-art methods on TruckScenes by 31.8%. Furthermore, SynFlow-4k serves as a label-efficient foundation: fine-tuning with only 5% of real-world labels surpasses models trained from scratch on the full available budget. We open-source the pipeline and dataset to facilitate research in generalizable 3D motion estimation. More detail can be found at https://kin-zhang.github.io/SynFlow.

4D scene reconstruction aims to recover the evolving geometry, appearance, and motion of dynamic environments from visual observations. Despite substantial progress in neural scene representations, reconstructing dynamic scenes remains challenging due to non-rigid motion, occlusions, temporal inconsistencies, and the trade-offs between reconstruction fidelity and computational efficiency. Recent advances in Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) have introduced diverse approaches to representing and reconstructing dynamic scenes, yet their relationships, underlying design choices, and evaluation protocols remain fragmented. In this paper, we present a unified perspective on 4D scene reconstruction, organizing existing methods around their scene representations, temporal modeling strategies, reconstruction pipelines, and optimization objectives. Through this framework, we examine how different design choices affect geometric fidelity, appearance consistency, motion representation, and computational efficiency. We further consolidate commonly used datasets and evaluation metrics, identify limitations in current experimental practices, and discuss open challenges in reconstructing complex, dynamic real-world environments. By connecting methodological developments with their underlying assumptions and evaluation evidence, this work provides a structured foundation for understanding existing approaches and identifying future research directions. An evolving collection of relevant papers and resources is available at https://github.com/ZiyangYan/Awesome-4D-Scene-Reconstruction.

Reconstructing dynamic 4D scenes is an important yet challenging task. While 3D foundation models like VGGT excel in static settings, they often struggle with dynamic sequences where motion causes significant geometric ambiguity. To address this, we present a framework designed to disentangle dynamic and static components by modeling uncertainty across different stages of the reconstruction process. Our approach introduces three synergistic mechanisms: (1) Entropy-Guided Subspace Projection, which leverages information-theoretic weighting to adaptively aggregate multi-head attention distributions, effectively isolating dynamic motion cues from semantic noise; (2) Local-Consistency Driven Geometry Purification, which enforces spatial continuity via radius-based neighborhood constraints to eliminate structural outliers; and (3) Uncertainty-Aware Cross-View Consistency, which formulates multi-view projection refinement as a heteroscedastic maximum likelihood estimation problem, utilizing depth confidence as a probabilistic weight. Experiments on dynamic benchmarks show that our approach outperforms current state-of-the-art methods, reducing Mean Accuracy error by 13.43% and improving segmentation F-measure by 10.49%. Our framework maintains the efficiency of feed-forward inference and requires no task-specific fine-tuning or per-scene optimization.