Paper 2512.00425
What about gravity in video generation? Post-Training Newton's Laws with Verifiable Rewards
- Published
- Nov 2025
- Research lab
- Independent
- Citations
- 18
- GitHub
- 16 stars
01 In brief
Summary
The paper introduces NewtonRewards, a physics-grounded post-training framework for video generation that enforces Newton's laws of motion using verifiable rewards.
It addresses the issue that video diffusion models often produce visually realistic but physically implausible motion.
The method uses optical flow as a proxy for velocity and visual features (from V-JEPA 2) as a proxy for mass.
Two rewards are defined: a kinematic constraint enforcing constant acceleration (via a discrete second-order derivative of optical flow) and a mass conservation reward that prevents degenerate solutions.
The framework is evaluated on NewtonBench-60K, a new large-scale simulated dataset with five Newtonian Motion Primitives (free fall, horizontal/parabolic throw, ramp sliding down/up).
Experiments show consistent improvements over prior post-training methods (e.g., PISA) in both visual and physics metrics, for in-distribution and out-of-distribution settings.
The mass reward is shown to mitigate reward hacking.
The approach also transfers to real-world free-fall videos from the PISA benchmark.
02 From the paper
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.