Generating 3D ligand molecules that bind to specific protein targets via diffusion models has shown great promise for structure-based drug design. The key idea is to disrupt molecules into noise through a fixed forward process and learn its reverse process to generate molecules from noise in a denoising way. However, existing diffusion models primarily focus on incorporating protein-ligand interaction information solely in the reverse process, and neglect the interactions in the forward process. The inconsistency between forward and reverse processes may impair the binding affinity of generated molecules towards target protein. In this paper, we propose a novel Interaction Prior-guided Diffusion model (IPDiff) for the protein-specific 3D molecular generation by introducing geometric protein-ligand interactions into both diffusion and sampling process. Specifically, we begin by pretraining a protein-ligand interaction prior network (IPNet) by utilizing the binding affinity signals as supervision. Subsequently, we leverage the pretrained prior network to (1) integrate interactions between the target protein and the molecular ligand into the forward process for adapting the molecule diffusion trajectories (prior-shifting), and (2) enhance the binding-aware molecule sampling process (prior-conditioning). Empirical studies on CrossDocked2020 dataset show IPDiff can generate molecules with more realistic 3D structures and state-of-the-art binding affinities towards the protein targets, with up to -6.42 Avg. Vina Score, while maintaining proper molecular properties. https://github.com/YangLing0818/IPDiff