# On Equivariance and Fast Sampling in Video Diffusion Models Trained with Warped Noise

arXiv: https://arxiv.org/abs/2504.09789 · HTML: https://mlsanity.com/paper/2504.09789/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Video generation, one of 14 directions in Diffusion models.
- Builds on 53 of its 69 references that are in the map.
- First posted on arXiv 14 Apr 2025.

## Placed in

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

## Builds on (most cited first, 30 of 53)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [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)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (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)
- [Towards Accurate Generative Models of Video: A New Metric & Challenges](https://mlsanity.com/paper/1812.01717/) (2018)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [MUSIQ: Multi-scale Image Quality Transformer](https://mlsanity.com/paper/2108.05997/) (2021)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://mlsanity.com/paper/2407.01392/) (2024)
- [Text2Video-Zero: Text-to-Image Diffusion Models are Zero-Shot Video Generators](https://mlsanity.com/paper/2303.13439/) (2023)
- [Open-Sora: Democratizing Efficient Video Production for All](https://mlsanity.com/paper/2412.20404/) (2024)
- [Holistically-Nested Edge Detection](https://mlsanity.com/paper/1504.06375/) (2015)
- [VideoCrafter2: Overcoming Data Limitations for High-Quality Video Diffusion Models](https://mlsanity.com/paper/2401.09047/) (2024)
- [VACE: All-in-One Video Creation and Editing](https://mlsanity.com/paper/2503.07598/) (2025)
- [VideoComposer: Compositional Video Synthesis with Motion Controllability](https://mlsanity.com/paper/2306.02018/) (2023)
- [Video Instance Segmentation](https://mlsanity.com/paper/1905.04804/) (2019)
- [Panda-70M: Captioning 70M Videos with Multiple Cross-Modality Teachers](https://mlsanity.com/paper/2402.19479/) (2024)
- [Pyramidal Flow Matching for Efficient Video Generative Modeling](https://mlsanity.com/paper/2410.05954/) (2024)
- [OpenVid-1M: A Large-Scale High-Quality Dataset for Text-to-video Generation](https://mlsanity.com/paper/2407.02371/) (2024)
- [EvalCrafter: Benchmarking and Evaluating Large Video Generation Models](https://mlsanity.com/paper/2310.11440/) (2023)

## Built on by (most cited first, 5 of 5)

- [Efficient Video Diffusion Models: Advancements and Challenges](https://mlsanity.com/paper/2604.15911/) (2026)
- [Time-Correlated Video Bridge Matching](https://mlsanity.com/paper/2510.12453/) (2025)
- [Score Augmentation for Diffusion Models](https://mlsanity.com/paper/2508.07926/) (2025)
- [HumANDiff: Articulated Noise Diffusion for Motion-Consistent Human Video Generation](https://mlsanity.com/paper/2604.05961/) (2026)
- [SymRegFlow: Symmetry-Regularized Flow Matching for Video World Models](https://mlsanity.com/paper/2610.02726/) (2026)

## Abstract (arXiv)

Temporally consistent video-to-video generation is critical for applications such as style transfer and upsampling. In this paper, we provide a theoretical analysis of warped noise - a recently proposed technique for training video diffusion models - and show that pairing it with the standard denoising objective implicitly trains models to be equivariant to spatial transformations of the input noise, which we term EquiVDM. This equivariance enables motion in the input noise to align naturally with motion in the generated video, yielding coherent, high-fidelity outputs without the need for specialized modules or auxiliary losses. A further advantage is sampling efficiency: EquiVDM achieves comparable or superior quality in far fewer sampling steps. When distilled into one-step student models, EquiVDM preserves equivariance and delivers stronger motion controllability and fidelity than distilled nonequivariant baselines. Across benchmarks, EquiVDM consistently outperforms prior methods in motion alignment, temporal consistency, and perceptual quality, while substantially lowering sampling cost.