Transfer entropy measures directed information flow in time series, and it has become a fundamental quantity in applications spanning neuroscience, finance, and complex systems analysis. However, existing estimation methods suffer from the curse of dimensionality, require restrictive distributional assumptions, or need exponentially large datasets for reliable convergence. We address these limitations in the literature by proposing TENDE (Transfer Entropy Neural Diffusion Estimation), a novel approach that leverages score-based diffusion models to estimate transfer entropy through conditional mutual information. By learning score functions of the relevant conditional distributions, TENDE provides flexible, scalable estimation while making minimal assumptions about the underlying data-generating process. We demonstrate superior accuracy and robustness compared to existing neural estimators and other state-of-the-art approaches across synthetic benchmarks and real data.

翻译：传递熵用于度量时间序列中的定向信息流，已成为神经科学、金融和复杂系统分析等领域应用中的基本量。然而，现有估计方法面临维数灾难、需要严格的分布假设或依赖指数级增长的数据集以实现可靠收敛等问题。针对文献中这些局限性，我们提出TENDE（传递熵神经扩散估计），一种基于得分扩散模型通过条件互信息估计传递熵的新方法。通过学习相关条件分布的得分函数，TENDE在对底层数据生成过程做出最小假设的同时，实现了灵活可扩展的估计。实验结果表明，在合成基准测试和真实数据上，该方法相比现有神经估计器及其他最先进方法展现出更高的准确性和鲁棒性。