What about gravity in video generation? Post-Training Newton's Laws with Verifiable Rewards

Abstract

Recent video diffusion models can synthesize visually compelling clips, yet often violate basic physical laws-objects float, accelerations drift, and collisions behave inconsistently-revealing a persistent gap between visual realism and physical realism. We propose $\texttt{NewtonRewards}$, the first physics-grounded post-training framework for video generation based on $\textit{verifiable rewards}$. Instead of relying on human or VLM feedback, $\texttt{NewtonRewards}$ extracts $\textit{measurable proxies}$ from generated videos using frozen utility models: optical flow serves as a proxy for velocity, while high-level appearance features serve as a proxy for mass. These proxies enable explicit enforcement of Newtonian structure through two complementary rewards: a Newtonian kinematic constraint enforcing constant-acceleration dynamics, and a mass conservation reward preventing trivial, degenerate solutions. We evaluate $\texttt{NewtonRewards}$ on five Newtonian Motion Primitives (free fall, horizontal/parabolic throw, and ramp sliding down/up) using our newly constructed large-scale benchmark, $\texttt{NewtonBench-60K}$. Across all primitives in visual and physics metrics, $\texttt{NewtonRewards}$ consistently improves physical plausibility, motion smoothness, and temporal coherence over prior post-training methods. It further maintains strong performance under out-of-distribution shifts in height, speed, and friction. Our results show that physics-grounded verifiable rewards offer a scalable path toward physics-aware video generation.