# Flow-Modulated Scoring for Semantic-Aware Knowledge Graph Completion

arXiv: https://arxiv.org/abs/2506.23137 · HTML: https://mlsanity.com/paper/2506.23137/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 95 references that are in the map.
- First posted on arXiv 29 Jun 2025.

## Builds on (most cited first, 30 of 61)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Unifying Large Language Models and Knowledge Graphs: A Roadmap](https://mlsanity.com/paper/2306.08302/) (2023)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [KG-BERT: BERT for Knowledge Graph Completion](https://mlsanity.com/paper/1909.03193/) (2019)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)

## Built on by (most cited first, 1 of 1)

- [Beyond Prefixes: Graph-as-Memory Cross-Attention for Knowledge Graph Completion with Large Language Models](https://mlsanity.com/paper/2510.08966/) (2025)

## Abstract (arXiv)

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.