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arXiv 2507.06830cs.CVcs.AI
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基于方程发现的物理接地运动预测用于轨迹引导的图像到视频生成

Physics-Grounded Motion Forecasting via Equation Discovery for Trajectory-Guided Image-to-Video Generation

Monash University(墨尔本大学);Harbin Institute of Technology(哈尔滨工业大学);Institute for Clarity in Documentation(文档清晰研究所);Inria Paris-Rocquencourt(巴黎-罗quentcourt研究所);Rajiv Gandhi University(拉朱·甘地大学);Tsinghua University(清华大学);Palmer Research Laboratories(帕勒尔研究实验室)

Tao Feng, Xianbing Zhao, Zhenhua Chen, Tien Tsin Wong, Hamid Rezatofighi, Gholamreza Haffari, Lizhen Qu

AI总结:

提出融合符号回归与轨迹引导图像到视频生成的框架,通过发现运动方程预测物理准确轨迹,无需微调即可提升生成视频的物理对齐性。

摘要:

近年来,基于扩散和自回归的视频生成模型在视觉真实感方面取得了显著进展。然而,这些模型通常缺乏精确的物理对齐能力,无法在物体运动中复现真实世界的动力学特性。这一局限主要源于它们依赖学习到的统计相关性,而非捕捉符合物理规律的机制。为解决这一问题,我们提出了一种新颖框架,将符号回归(SR)与轨迹引导的图像到视频(I2V)模型相结合,用于物理接地的视频预测。我们的方法从输入视频中提取运动轨迹,利用基于检索的预训练机制增强符号回归,并发现运动方程以预测物理上准确的未来轨迹。这些轨迹随后引导视频生成,无需对现有模型进行微调。在经典力学场景(包括弹簧-质量系统、摆和抛体运动)上的评估中,我们的方法成功恢复了真实解析方程,并在生成视频的物理对齐方面优于基线方法。

英文摘要:

Recent advances in diffusion-based and autoregressive video generation models have achieved remarkable visual realism. However, these models typically lack accurate physical alignment, failing to replicate real-world dynamics in object motion. This limitation arises primarily from their reliance on learned statistical correlations rather than capturing mechanisms adhering to physical laws. To address this issue, we introduce a novel framework that integrates symbolic regression (SR) and trajectory-guided image-to-video (I2V) models for physics-grounded video forecasting. Our approach extracts motion trajectories from input videos, uses a retrieval-based pre-training mechanism to enhance symbolic regression, and discovers equations of motion to forecast physically accurate future trajectories. These trajectories then guide video generation without requiring fine-tuning of existing models. Evaluated on scenarios in Classical Mechanics, including spring-mass, pendulums, and projectile motions, our method successfully recovers ground-truth analytical equations and improves the physical alignment of generated videos over baseline methods.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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