Flow-Modulated Scoring for Semantic-Aware Knowledge Graph Completion

Knowledge graph completion demands effective modeling of multifaceted semantic relationships between entities. Yet, prevailing methods, which rely on static scoring functions over learned embeddings, struggling to simultaneously capture rich semantic context and the dynamic nature of relations. To overcome this limitation, we propose the Flow-Modulated Scoring (FMS) framework, conceptualizing a relation as a dynamic evolutionary process governed by its static semantic environment. FMS operates in two stages: it first learns context-aware entity embeddings via a Semantic Context Learning module, and then models a dynamic flow between them using a Conditional Flow-Matching module. This learned flow dynamically modulates a base static score for the entity pair. By unifying context-rich static representations with a conditioned dynamic flow, FMS achieves a more comprehensive understanding of relational semantics. Extensive experiments demonstrate that FMS establishes a new state of the art across both canonical knowledge graph completion tasks: relation prediction and entity prediction. On the standard relation prediction benchmark FB15k-237, FMS achieves a near-perfect MRR of 99.8\% and Hits@1 of 99.7\% using a mere 0.35M parameters, while also attaining a 99.9\% MRR on WN18RR. Its dominance extends to entity prediction, where it secures a 25.2\% relative MRR gain in the transductive setting and substantially outperforms all baselines in challenging inductive settings. By unifying a dynamic flow mechanism with rich static contexts, FMS offers a highly effective and parameter-efficient new paradigm for knowledge graph completion. Code published at: https://github.com/yuanwuyuan9/FMS.