Audio-driven talking head synthesis strives to generate lifelike video portraits from provided audio. The diffusion model, recognized for its superior quality and robust generalization, has been explored for this task. However, establishing a robust correspondence between temporal audio cues and corresponding spatial facial expressions with diffusion models remains a significant challenge in talking head generation. To bridge this gap, we present DreamHead, a hierarchical diffusion framework that learns spatial-temporal correspondences in talking head synthesis without compromising the model's intrinsic quality and adaptability.~DreamHead learns to predict dense facial landmarks from audios as intermediate signals to model the spatial and temporal correspondences.~Specifically, a first hierarchy of audio-to-landmark diffusion is first designed to predict temporally smooth and accurate landmark sequences given audio sequence signals. Then, a second hierarchy of landmark-to-image diffusion is further proposed to produce spatially consistent facial portrait videos, by modeling spatial correspondences between the dense facial landmark and appearance. Extensive experiments show that proposed DreamHead can effectively learn spatial-temporal consistency with the designed hierarchical diffusion and produce high-fidelity audio-driven talking head videos for multiple identities.