# DyMD: Preserving Interaction Dynamics through Distribution Matching Distillation in Few-Step Video World Models

arXiv: https://arxiv.org/abs/2609.31349 · HTML: https://mlsanity.com/paper/2609.31349/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Embodied and robot world models, one of 11 directions in World models.
- Builds on 35 of its 38 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Placed in

- World models / [Embodied and robot world models](https://mlsanity.com/wm/embodied-and-robot-world-models/)
- Diffusion models / [Video generation](https://mlsanity.com/diffusion/video-generation/)

## Builds on (most cited first, 30 of 35)

- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [HunyuanVideo: A Systematic Framework For Large Video Generative Models](https://mlsanity.com/paper/2412.03603/) (2024)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [Cosmos World Foundation Model Platform for Physical AI](https://mlsanity.com/paper/2501.03575/) (2025)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [Learning Universal Policies via Text-Guided Video Generation](https://mlsanity.com/paper/2302.00111/) (2023)
- [RoboTwin 2.0: A Scalable Data Generator and Benchmark with Strong Domain Randomization for Robust Bimanual Robotic Manipulation](https://mlsanity.com/paper/2506.18088/) (2025)
- [Learning Loss for Active Learning](https://mlsanity.com/paper/1905.03677/) (2019)
- [Video Prediction Policy: A Generalist Robot Policy with Predictive Visual Representations](https://mlsanity.com/paper/2412.14803/) (2024)
- [Efficient Diffusion Training via Min-SNR Weighting Strategy](https://mlsanity.com/paper/2303.09556/) (2023)
- [DreamGen: Unlocking Generalization in Robot Learning through Video World Models](https://mlsanity.com/paper/2505.12705/) (2025)
- [V-JEPA 2.1: Unlocking Dense Features in Video Self-Supervised Learning](https://mlsanity.com/paper/2603.14482/) (2026)
- [VideoJAM: Joint Appearance-Motion Representations for Enhanced Motion Generation in Video Models](https://mlsanity.com/paper/2502.02492/) (2025)
- [Reward Forcing: Efficient Streaming Video Generation with Rewarded Distribution Matching Distillation](https://mlsanity.com/paper/2512.04678/) (2025)
- [An elementary introduction to information geometry](https://mlsanity.com/paper/1808.08271/) (2018)
- [WorldArena: A Unified Benchmark for Evaluating Perception and Functional Utility of Embodied World Models](https://mlsanity.com/paper/2602.08971/) (2026)
- [Distribution Matching Distillation Meets Reinforcement Learning](https://mlsanity.com/paper/2511.13649/) (2025)
- [PAI-Bench: A Comprehensive Benchmark For Physical AI](https://mlsanity.com/paper/2512.01989/) (2025)
- [Rethinking Video Generation Model for the Embodied World](https://mlsanity.com/paper/2601.15282/) (2026)
- [ABot-PhysWorld: Interactive World Foundation Model for Robotic Manipulation with Physics Alignment](https://mlsanity.com/paper/2603.23376/) (2026)
- [Phased DMD: Few-step Distribution Matching Distillation via Score Matching within Subintervals](https://mlsanity.com/paper/2510.27684/) (2025)
- [Optimizing Few-Step Generation with Adaptive Matching Distillation](https://mlsanity.com/paper/2602.07345/) (2026)

## Abstract (arXiv)

Large video diffusion models offer expressive priors for embodied prediction and learning, yet their many-step sampling remains costly for interactive downstream use. Distribution Matching Distillation (DMD) enables few-step video generation, but can suppress robot--object motion while preserving visual quality. Examining DMD's teacher and fake-score signals, we find that weak re-noising keeps the teacher posterior concentrated near motion-deficient rollouts, limiting motion-restoring guidance. Meanwhile, stronger-motion rollouts tend to incur larger fake-score fitting errors, which can hinder the generator's learning of interaction dynamics. We propose DyMD, a DMD framework that adapts both teacher supervision and critic fitting to the evolving student. Temporal affinity--conditioned re-noise sampling adapts the timestep distribution to each rollout's current interaction fidelity by mixing the base schedule with a teacher prior motivated by local posterior variation, thereby balancing motion recovery and appearance refinement. To better track stronger-motion rollouts, dynamics-guided fake-score tracking uses a noise-conditioned predictor to estimate noise-relative fitting difficulty from latent temporal dynamics, then upweights predicted-hard rollouts in the critic loss. Using DyMD, we distill a 14B teacher into a four-step 1.3B student with no auxiliary modules at inference. On embodied-video benchmarks, the student improves R-Bench task adherence by 9.6 percentage points and PAI-Bench-G Domain score by 5.1 points over Base DMD while maintaining comparable visual quality. As a backbone for downstream action planning, our student achieves 34% mean success across two WorldArena tasks, compared with 16% for Base DMD.