Although Hyper-relational Knowledge Graphs (HKGs) can model complex facts better than traditional KGs, the Hyper-relational Knowledge Graph Completion (HKGC) is more sensitive to inherent noise, particularly struggling with two prevalent HKG-specific noise types: Intra-fact Inconsistency and Cross-fact Association Noise.To address these challenges, we propose **HDiff**, a novel conditional denoising diffusion framework for robust HKGC that learns to reverse structured noise corruption. HDiff integrates a **Consistency-Enhanced Global Encoder (CGE)** using contrastive learning to enforce intra-fact consistency and a **Context-Guided Denoiser (CGD)** performing iterative refinement. The CGD features dual conditioning leveraging CGE’s global context and local confidence estimates, effectively combatting both noise types. Extensive experiments demonstrate that HDiff substantially outperforms state-of-the-art HKGC methods, highlighting its effectiveness and significant robustness, particularly under noisy conditions.