Physics-Grounded Motion Forecasting via Equation Discovery for Trajectory-Guided Image-to-Video Generation
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912473065455616 |
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| author | Feng, Tao Zhao, Xianbing Chen, Zhenhua Wong, Tien Tsin Rezatofighi, Hamid Haffari, Gholamreza Qu, Lizhen |
| author_facet | Feng, Tao Zhao, Xianbing Chen, Zhenhua Wong, Tien Tsin Rezatofighi, Hamid Haffari, Gholamreza Qu, Lizhen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Physics-Grounded Motion Forecasting via Equation Discovery for Trajectory-Guided Image-to-Video Generation Feng, Tao Zhao, Xianbing Chen, Zhenhua Wong, Tien Tsin Rezatofighi, Hamid Haffari, Gholamreza Qu, Lizhen Computer Vision and Pattern Recognition Artificial Intelligence 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. |
| title | Physics-Grounded Motion Forecasting via Equation Discovery for Trajectory-Guided Image-to-Video Generation |
| topic | Computer Vision and Pattern Recognition Artificial Intelligence |
| url | https://arxiv.org/abs/2507.06830 |