Despite progress in speech-to-video synthesis, existing methods often struggle to capture cross-individual dependencies and provide fine-grained control over reactive behaviors in dyadic settings. To address these challenges, we propose InterDyad, a framework that enables naturalistic interactive dynamics synthesis via querying structural motion guidance. Specifically, we first design an Interactivity Injector that achieves video reenactment based on identity-agnostic motion priors extracted from reference videos. Building upon this, we introduce a MetaQuery-based modality alignment mechanism to bridge the gap between conversational audio and these motion priors. By leveraging a Multimodal Large Language Model (MLLM), our framework is able to distill linguistic intent from audio to dictate the precise timing and appropriateness of reactions. To further improve lip-sync quality under extreme head poses, we propose Role-aware Dyadic Gaussian Guidance (RoDG) for enhanced lip-synchronization and spatial consistency. Finally, we introduce a dedicated evaluation suite with novelly designed metrics to quantify dyadic interaction. Comprehensive experiments demonstrate that InterDyad significantly outperforms state-of-the-art methods in producing natural and contextually grounded two-person interactions. Please refer to our project page for demo videos: https://interdyad.github.io/.

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