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.