Diffusion models for video generation have achieved remarkable success, yet precise motion control under explicit user guidance remains challenging. Recent noise-warping methods introduce temporal correlations by warping the noise according to the user-provided motion signal. However, standard spatial warping generally disrupts the noise's i.i.d. Gaussian structure, requiring distribution correction, such as Jacobian-based correction, but at a substantial computational overhead. We propose Householder Motion Embedding (HME), which encodes the motion signal into the noise through a sequence of Householder reflections that together form an orthogonal transformation applied to each location's channel vector. HME exactly preserves the spatial Gaussian structure within each frame while introducing cross-frame correlations that promote temporally consistent video. HME is agnostic to the network architecture and integrates directly into standard video diffusion fine-tuning pipelines. Experiments on different scenarios show that HME matches or outperforms the state of the art, while achieving a 2.7x speedup over noise warping. These results demonstrate that channel-space Householder transformations offer a principled and efficient alternative to noise warping for motion-controllable video generation.

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