This paper presents a theoretical analysis of warped noise, a novel technique for training video diffusion models. Combining warped noise with a standard denoising objective demonstrates that the model learns to be equivariant to the spatial transformations of the input noise. This equivariance (EquiVDM) naturally aligns the motion of the generated video with the motion of the input noise, without the need for special modules or auxiliary losses, resulting in consistent, high-fidelity output. Furthermore, EquiVDM achieves excellent quality with a small number of sampling steps, demonstrating superior sampling efficiency. EquiVDM maintains equivariance even when distilled into a single-step student model, and offers stronger motion control and fidelity than anisotropic baselines.
