EquiVDM: Equivariant Video Diffusion Models with Temporally Consistent Noise

Temporally consistent video-to-video generation is essential for applications of video diffusion models in areas such as sim-to-real, style-transfer, video upsampling, etc. In this paper, we propose a video diffusion framework that leverages temporally consistent noise to generate coherent video frames without specialized modules or additional constraints. We show that the standard training objective of diffusion models, when applied with temporally consistent noise, encourages the model to be equivariant to spatial transformations in input video and noise. This enables our model to better follow motion patterns from the input video, producing aligned motion and high-fidelity frames. Furthermore, we extend our approach to 3D-consistent video generation by attaching noise as textures on 3D meshes, ensuring 3D consistency in sim-to-real applications. Experimental results demonstrate that our method surpasses state-of-the-art baselines in motion alignment, 3D consistency, and video quality while requiring only a few sampling steps in practice.