Advancements in deep generative modeling have changed the paradigm of drug discovery. Among such approaches, target-aware methods that exploit 3D structures of protein pockets were spotlighted for generating ligand molecules with their plausible binding modes. While docking scores superficially assess the quality of generated ligands, closer inspection of the binding structures reveals the inconsistency in local interactions between a pocket and generated ligands. Here, we address the issue by explicitly generating non-covalent interactions (NCIs), which are universal patterns throughout protein-ligand complexes. Our proposed model, NCIDiff, simultaneously denoises NCI types of protein-ligand edges along with a 3D graph of a ligand molecule during the sampling. With the NCI-generating strategy, our model generates ligands with more reliable NCIs, especially outperforming the baseline diffusion-based models. We further adopted inpainting techniques on NCIs to further improve the quality of the generated molecules. Finally, we showcase the applicability of NCIDiff on drug design tasks for real-world settings with specialized objectives by guiding the generation process with desired NCI patterns.