{"ID":2896582,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.06830","arxiv_id":"2507.06830","title":"Physics-Grounded Motion Forecasting via Equation Discovery for Trajectory-Guided Image-to-Video Generation","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2507.06830","url_pdf":"https://arxiv.org/pdf/2507.06830v1","authors":"[\"Tao Feng\",\"Xianbing Zhao\",\"Zhenhua Chen\",\"Tien Tsin Wong\",\"Hamid Rezatofighi\",\"Gholamreza Haffari\",\"Lizhen Qu\"]","published":"2025-07-09T13:28:42Z","proceeding":"cs.CV","tasks":"[\"cs.CV\",\"cs.AI\"]","methods":"[\"Diffusion Model\"]","has_code":false}