From Local Recovery to Unified Generation: Discovering Triple Set in Knowledge Graphs via Observation-Anchored Latent Diffusion

Triple set prediction (TSP) aims to discover missing facts from an incomplete knowledge graph without predefined queries. Existing approaches typically construct the predicted set through triple-level scoring, sometimes preceded by entity pair filtering that can exclude valid missing facts. We propose DiffTSP, a conditional discrete diffusion model that formulates missing fact discovery as conditional subgraph generation. In each subgraph, DiffTSP directly predicts the missing relational structure without a separate entity pair selection stage. The model learns to generate masked target relation states at different corruption levels, with the observed support subgraph retained as conditioning context. Our structure-aware denoising network integrates a Relational Context Encoder, which captures local relational patterns through relation-guided message passing, and a Relational Graph Diffusion Transformer, which models broader structural interactions through relational attention. During generation, partially generated relations can also serve as provisional context for subsequent predictions. Experiments on three public datasets demonstrate improved TSP performance over strong baselines. Additional analyses show lower conflict rates in the predicted triple sets relative to the evaluated baselines. Code: https://anonymous.4open.science/r/DiffTSP-0F92/.

Knowledge graphs (KGs) organize real-world knowledge as triplets and underpin many downstream applications. Due to their inherent incompleteness, knowledge graph completion (KGC) is widely studied and is typically formulated as triplet prediction, with link prediction as the dominant paradigm. However, this formulation focuses on the incompleteness of triplet-wise information and overlooks the incompleteness of entity-relation compatibility information. To address this limitation, we introduce a relation set completion task (RSC), which complements the link prediction task and aims to reason about missing relations that are semantically compatible with a given entity. We further propose a Relation Set Embedding model (RelSetE), which models latent patterns among the observed relations of entities to infer missing ones. To evaluate RelSetE, we derive three benchmark datasets from standard KG benchmarks. Extensive experiments demonstrate that RelSetE effectively captures entity-relation compatibility patterns and performs favorably in inferring missing relations of entities. Code and data are publicly available.

Knowledge Graphs (KGs) are widely used to represent structured knowledge, yet their automatic construction, especially with Large Language Models (LLMs), often results in incomplete or noisy outputs. Knowledge Graph Completion (KGC) aims to infer and add missing triples, but most existing methods either rely on structural embeddings that overlook semantics or language models that ignore the graph's structure and depend on external sources. In this work, we present OMNIA, a two-stage approach that bridges structural and semantic reasoning for KGC. It first generates candidate triples by clustering semantically related entities and relations within the KG, then validates them through lightweight embedding filtering followed by LLM-based semantic validation. OMNIA performs on the internal KG, without external sources, and specifically targets implicit semantics that are most frequent in LLM-generated graphs. Extensive experiments on multiple datasets demonstrate that OMNIA significantly improves F1-score compared to traditional embedding-based models. These results highlight OMNIA's effectiveness and efficiency, as its clustering and filtering stages reduce both search space and validation cost while maintaining high-quality completion.