# TENDE: Transfer Entropy Neural Diffusion Estimation

arXiv: https://arxiv.org/abs/2510.14096 · HTML: https://mlsanity.com/paper/2510.14096/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 55 references that are in the map.
- First posted on arXiv 15 Oct 2025.

## Builds on (most cited first, 17 of 17)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Formal Limitations on the Measurement of Mutual Information](https://mlsanity.com/paper/1811.04251/) (2018)
- [Information-Theoretic Diffusion](https://mlsanity.com/paper/2302.03792/) (2023)
- [MINDE: Mutual Information Neural Diffusion Estimation](https://mlsanity.com/paper/2310.09031/) (2023)
- [Demystifying Fixed k-Nearest Neighbor Information Estimators](https://mlsanity.com/paper/1604.03006/) (2016)
- [Max-Sliced Mutual Information](https://mlsanity.com/paper/2309.16200/) (2023)
- [Multi-modal Latent Diffusion](https://mlsanity.com/paper/2306.04445/) (2023)
- [Neural Joint Entropy Estimation](https://mlsanity.com/paper/2012.11197/) (2020)
- [Simplified vine copula models: state of science and affairs](https://mlsanity.com/paper/2410.16806/) (2024)
- [Asymmetric tail dependence modeling, with application to cryptocurrency market data](https://mlsanity.com/paper/1905.05056/) (2019)
- [ITENE: Intrinsic Transfer Entropy Neural Estimator](https://mlsanity.com/paper/1912.07277/) (2019)
- [Causality indices for bivariate time series data: a comparative review of performance](https://mlsanity.com/paper/2104.00718/) (2021)
- [Measuring Information Transfer Between Nodes in a Brain Network through Spectral Transfer Entropy](https://mlsanity.com/paper/2303.06384/) (2023)
- [Analysis of KNN Information Estimators for Smooth Distributions](https://mlsanity.com/paper/1810.11571/) (2018)
- [TREET: TRansfer Entropy Estimation via Transformers](https://mlsanity.com/paper/2402.06919/) (2024)
- [About Kendall's regression](https://mlsanity.com/paper/1802.07613/) (2018)

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

- [DIPHINE: Diffusion-based Phi-ID Neural Estimator](https://mlsanity.com/paper/2606.18997/) (2026)

## Abstract (arXiv)

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.