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.