FlowPath: From Discrete Paths to Continuous Semantic Flows for Knowledge Graph Completion

Knowledge graph completion (KGC) aims to infer missing facts based on existing triplets. Traditional path-based methods formulate reasoning as a discrete multi-hop traversal, which suffers from exponential search space and error accumulation.In this paper, we propose FlowPath, which rethinks the reasoning process by transforming discrete symbolic paths into a continuous semantic flow in the latent space. Specifically, we formalize the inference from a head entity to the target tail entity as an Ordinary Differential Equation (ODE) governed by a relation-conditioned neural velocity field, which learns to steer a smooth and expressive semantic transformation along the reasoning trajectory. To prevent the continuous flow from drifting into invalid semantic regions, we further introduce a structure-anchored guidance mechanism that leverages factual multi-hop paths from the knowledge graph as topological constraints, grounding the learned flow in the discrete relational structure. Moreover, a uncertainty weighting strategy is employed to adaptively balance the joint optimization of link prediction, flow generation, and structural guidance. By bridging discrete symbolic paths and continuous neural dynamics, FlowPath inherits the interpretability of path-based reasoning while possessing the flexibility and expressiveness of generative modeling. Extensive experiments on benchmark datasets demonstrate that FlowPath achieves competitive performance, and additional analysis confirms the effectiveness of modeling the reasoning paths of KGC as a continuous semantic flow.