用物理方程发现提升视频生成的运动真实性
Physics-Grounded Motion Forecasting via Equation Discovery for Trajectory-Guided Image-to-Video Generation
- 通过符号回归从轨迹中提取物理方程
- 在弹簧、摆和抛体场景中复现真实物理方程
- 无需微调现有模型即可提升运动合理性
基于扩散和自回归的视频生成模型虽在视觉真实感上取得进展，但通常缺乏物理一致性，无法准确模拟物体运动。这主要源于其依赖学习到的统计相关性，而非遵循物理定律的机制。为此，我们提出一种新框架，结合符号回归（SR）与轨迹引导的图像到视频（I2V）模型，实现物理基础的运动预测。方法从输入视频中提取运动轨迹，采用基于检索的预训练增强符号回归，并发现运动方程以预测物理上准确的未来轨迹。这些轨迹用于指导视频生成，无需微调现有模型。在经典力学场景（如弹簧-质量系统、摆动、抛体运动）中的评估显示，该方法成功恢复了真实解析方程，且生成视频的物理一致性优于基线方法。
原文摘要 · Abstract (English)
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.
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