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

arXiv: https://arxiv.org/abs/2512.00425 · HTML: https://mlsanity.com/paper/2512.00425/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Placed in Video generation, one of 14 directions in Diffusion models.
- Builds on 70 of its 78 references that are in the map.
- First posted on arXiv 29 Nov 2025.

## Placed in

- Diffusion models / [Video generation](https://mlsanity.com/diffusion/video-generation/)

## Builds on (most cited first, 30 of 70)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [SAM 2: Segment Anything in Images and Videos](https://mlsanity.com/paper/2408.00714/) (2024)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [HunyuanVideo: A Systematic Framework For Large Video Generative Models](https://mlsanity.com/paper/2412.03603/) (2024)
- [Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2304.08818/) (2023)
- [Depth Anything V2](https://mlsanity.com/paper/2406.09414/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [CogVideo: Large-scale Pretraining for Text-to-Video Generation via Transformers](https://mlsanity.com/paper/2205.15868/) (2022)
- [Cosmos World Foundation Model Platform for Physical AI](https://mlsanity.com/paper/2501.03575/) (2025)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [Open-Sora: Democratizing Efficient Video Production for All](https://mlsanity.com/paper/2412.20404/) (2024)
- [Language Model Beats Diffusion -- Tokenizer is Key to Visual Generation](https://mlsanity.com/paper/2310.05737/) (2023)
- [GAIA-1: A Generative World Model for Autonomous Driving](https://mlsanity.com/paper/2309.17080/) (2023)
- [Google Scanned Objects: A High-Quality Dataset of 3D Scanned Household Items](https://mlsanity.com/paper/2204.11918/) (2022)
- [LTX-Video: Realtime Video Latent Diffusion](https://mlsanity.com/paper/2501.00103/) (2024)
- [Learning Interactive Real-World Simulators](https://mlsanity.com/paper/2310.06114/) (2023)
- [Lumiere: A Space-Time Diffusion Model for Video Generation](https://mlsanity.com/paper/2401.12945/) (2024)
- [Kubric: A scalable dataset generator](https://mlsanity.com/paper/2203.03570/) (2022)
- [LAVIE: High-Quality Video Generation with Cascaded Latent Diffusion Models](https://mlsanity.com/paper/2309.15103/) (2023)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Navigation World Models](https://mlsanity.com/paper/2412.03572/) (2024)

## Built on by (most cited first, 25 of 25)

- [VGGRPO: Towards World-Consistent Video Generation with 4D Latent Reward](https://mlsanity.com/paper/2603.26599/) (2026)
- [Olaf-World: Orienting Latent Actions for Video World Modeling](https://mlsanity.com/paper/2602.10104/) (2026)
- [ACWM-Phys: Investigating Generalized Physical Interaction in Action-Conditioned Video World Models](https://mlsanity.com/paper/2605.08567/) (2026)
- [PhysInOne: Visual Physics Learning and Reasoning in One Suite](https://mlsanity.com/paper/2604.09415/) (2026)
- [PhyRPR: Training-Free Physics-Constrained Video Generation](https://mlsanity.com/paper/2601.09255/) (2026)
- [Evolution of Video Generative Foundations](https://mlsanity.com/paper/2604.06339/) (2026)
- [Toward Native Multimodal Modeling: A Roadmap](https://mlsanity.com/paper/2605.25343/) (2026)
- [Human Cognition in Machines: A Unified Perspective of World Models](https://mlsanity.com/paper/2604.16592/) (2026)
- [LaMo: Self-Supervised Latent Motion Priors for Physical Realism in Video Generation](https://mlsanity.com/paper/2605.23878/) (2026)
- [CausalMotion: Structured Physical Reasoning as Keyframe and Trajectory Guidance for Training-Free Video Generation](https://mlsanity.com/paper/2606.14317/) (2026)
- [When Physical Preferences Meet Semantic Constraints: Physical and Semantic Direct Preference Optimization for Text-to-Video Generation](https://mlsanity.com/paper/2607.16947/) (2026)
- [PISCES: Annotation-free Text-to-Video Post-Training via Optimal Transport-Aligned Rewards](https://mlsanity.com/paper/2602.01624/) (2026)
- [PhysEditWorld: A Large-Scale Dataset Toward Physics-Editable World Models](https://mlsanity.com/paper/2606.26694/) (2026)
- [PhysiFormer: Learning to Simulate Mechanics in World Space](https://mlsanity.com/paper/2606.27364/) (2026)
- [KineBench: Benchmarking Embodied World Models via IDM-Free Kinematic Grounding](https://mlsanity.com/paper/2607.19876/) (2026)
- [Off-Manifold Refinement: Guiding Video Generators with a Frozen World Model](https://mlsanity.com/paper/2608.29904/) (2026)
- [Principia: Relational Physics Tests for Video Models](https://mlsanity.com/paper/2609.04200/) (2026)
- [FrameDiT: Diffusion Transformer with Matrix Attention for Efficient Video Generation](https://mlsanity.com/paper/2603.09721/) (2026)
- [Physics-Informed Video Generation via Mixture-of-Experts Latent Alignment](https://mlsanity.com/paper/2606.04737/) (2026)
- [NEXUS: Neural Energy Fields for Physically Consistent Contact-Rich 3D Object Dynamics](https://mlsanity.com/paper/2606.15015/) (2026)
- [Apple-π: Benchmarking Thinking with Video Towards Law-Grounded Physical Intelligence](https://mlsanity.com/paper/2607.16401/) (2026)
- [Thinking in Video: Can Video Generators Really Reason About the Real World?](https://mlsanity.com/paper/2607.17523/) (2026)
- [Video Generation Models: A Survey of Post-Training and Alignment](https://mlsanity.com/paper/2610.00812/) (2026)
- [PhysicsLENS: Diagnosing Physical Property Blindness in Video Generation Models](https://mlsanity.com/paper/2610.01162/) (2026)
- [World Models' Last Exam in Physics](https://mlsanity.com/paper/2610.08791/) (2026)

## Abstract (arXiv)

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 textttNewtonRewards, the first physics-grounded post-training framework for video generation based on textitverifiable rewards. Instead of relying on human or VLM feedback, textttNewtonRewards extracts textitmeasurable 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 textttNewtonRewards on five Newtonian Motion Primitives (free fall, horizontal/parabolic throw, and ramp sliding down/up) using our newly constructed large-scale benchmark, textttNewtonBench-60K. Across all primitives in visual and physics metrics, textttNewtonRewards 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.