# Discrete Bridges for Mutual Information Estimation

arXiv: https://arxiv.org/abs/2602.08894 · HTML: https://mlsanity.com/paper/2602.08894/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Formal Limitations on the Measurement of Mutual Information](https://mlsanity.com/paper/1811.04251/) (2018)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Chaining Mutual Information and Tightening Generalization Bounds](https://mlsanity.com/paper/1806.03803/) (2018)
- [The Schr"odinger Bridge between Gaussian Measures has a Closed Form](https://mlsanity.com/paper/2202.05722/) (2022)
- [Bayesian Learning via Neural Schr"odinger-F"ollmer Flows](https://mlsanity.com/paper/2111.10510/) (2021)
- [Light and Optimal Schr"odinger Bridge Matching](https://mlsanity.com/paper/2402.03207/) (2024)
- [RetroBridge: Modeling Retrosynthesis with Markov Bridges](https://mlsanity.com/paper/2308.16212/) (2023)
- [MINDE: Mutual Information Neural Diffusion Estimation](https://mlsanity.com/paper/2310.09031/) (2023)
- [Mutual Information Estimation via Normalizing Flows](https://mlsanity.com/paper/2403.02187/) (2024)
- [Discrete Diffusion Schr"odinger Bridge Matching for Graph Transformation](https://mlsanity.com/paper/2410.01500/) (2024)
- [Information Bottleneck Analysis of Deep Neural Networks via Lossy Compression](https://mlsanity.com/paper/2305.08013/) (2023)
- [Mutual Information Estimation via f-Divergence and Data Derangements](https://mlsanity.com/paper/2305.20025/) (2023)
- [Exponential Family Variational Flow Matching for Tabular Data Generation](https://mlsanity.com/paper/2506.05940/) (2025)
- [A Benchmark Suite for Evaluating Neural Mutual Information Estimators on Unstructured Datasets](https://mlsanity.com/paper/2410.10924/) (2024)
- [Conditional Independence Testing via Latent Representation Learning](https://mlsanity.com/paper/2209.01547/) (2022)
- [InfoBridge: Mutual Information estimation via Bridge Matching](https://mlsanity.com/paper/2502.01383/) (2025)
- [textttCOSMIC: Mutual Information for Task-Agnostic Summarization Evaluation](https://mlsanity.com/paper/2402.19457/) (2024)
- [Efficient Distribution Matching of Representations via Noise-Injected Deep InfoMax](https://mlsanity.com/paper/2410.06993/) (2024)
- [INFO-SEDD: Continuous Time Markov Chains as Scalable Information Metrics Estimators](https://mlsanity.com/paper/2502.19183/) (2025)

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

- [Tilted Schr"odinger Bridge Matching](https://mlsanity.com/paper/2609.34642/) (2026)

## Abstract (arXiv)

Diffusion bridge models in both continuous and discrete state spaces have recently become powerful tools in the field of generative modeling. In this work, we leverage the discrete state space formulation of bridge matching models to address another important problem in machine learning and information theory: the estimation of the mutual information (MI) between discrete random variables. By neatly framing MI estimation as a domain transfer problem, we construct a Discrete Bridge Mutual Information (DBMI) estimator suitable for discrete data, which poses difficulties for conventional MI estimators. We showcase the performance of our estimator on two MI estimation settings: low-dimensional and image-based.