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.

Knowledge graph completion (KGC) aims to infer missing facts based on existing facts within a KG. Recently, research on generative models (GMs) has addressed the limitations of embedding methods in terms of generality and scalability. However, GM-based methods are sensitive to contextual facts on KG, so the contextual facts of poor quality can cause GMs to generate erroneous results. To improve the performance of GM-based methods for various KGC tasks, we propose a COntextual FactS GuIded GeneratioN (COSIGN) model. First, to enhance the inference ability of the generative model, we designed a contextual facts collector to achieve human-like retrieval behavior. Second, a contextual facts organizer is proposed to learn the organized capabilities of LLMs through knowledge distillation. Finally, the organized contextual facts as the input of the inference generator to generate missing facts. Experimental results demonstrate that COSIGN outperforms state-of-the-art baseline techniques in terms of performance.