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Despite significant progress in text-driven 4D human-object interaction (HOI) generation with supervised methods, the scalability remains limited by the scarcity of large-scale 4D HOI datasets. To overcome this, recent approaches attempt zero-shot 4D HOI generation with pre-trained image diffusion models. However, interaction cues are minimally distilled during the generation process, restricting their applicability across diverse scenarios. In this paper, we propose AnchorHOI, a novel framework that thoroughly exploits hybrid priors by incorporating video diffusion models beyond image diffusion models, advancing 4D HOI generation. Nevertheless, directly optimizing high-dimensional 4D HOI with such priors remains challenging, particularly for human pose and compositional motion. To address this challenge, AnchorHOI introduces an anchor-based prior distillation strategy, which constructs interaction-aware anchors and then leverages them to guide generation in a tractable two-step process. Specifically, two tailored anchors are designed for 4D HOI generation: anchor Neural Radiance Fields (NeRFs) for expressive interaction composition, and anchor keypoints for realistic motion synthesis. Extensive experiments demonstrate that AnchorHOI outperforms previous methods with superior diversity and generalization. Code will be released to facilitate further research in 4D HOI generation.