# FMMI: Flow Matching Mutual Information Estimation

arXiv: https://arxiv.org/abs/2511.08552 · HTML: https://mlsanity.com/paper/2511.08552/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 31 of its 62 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 31)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [Formal Limitations on the Measurement of Mutual Information](https://mlsanity.com/paper/1811.04251/) (2018)
- [Understanding the Limitations of Variational Mutual Information Estimators](https://mlsanity.com/paper/1910.06222/) (2019)
- [Information-Theoretic Generalization Bounds for SGLD via Data-Dependent Estimates](https://mlsanity.com/paper/1911.02151/) (2019)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Generalized Energy Based Models](https://mlsanity.com/paper/2003.05033/) (2020)
- [Wasserstein Dependency Measure for Representation Learning](https://mlsanity.com/paper/1903.11780/) (2019)
- [A Review of Feature Selection Methods Based on Mutual Information](https://mlsanity.com/paper/1509.07577/) (2015)
- [Chaining Mutual Information and Tightening Generalization Bounds](https://mlsanity.com/paper/1806.03803/) (2018)
- [Density Ratio Estimation via Infinitesimal Classification](https://mlsanity.com/paper/2111.11010/) (2021)
- [Beyond Normal: On the Evaluation of Mutual Information Estimators](https://mlsanity.com/paper/2306.11078/) (2023)
- [Quantifying High-order Interdependencies via Multivariate Extensions of the Mutual Information](https://mlsanity.com/paper/1902.11239/) (2019)
- [Mutual Information Estimation via Normalizing Flows](https://mlsanity.com/paper/2403.02187/) (2024)
- [Information Bottleneck Analysis of Deep Neural Networks via Lossy Compression](https://mlsanity.com/paper/2305.08013/) (2023)
- [Diffeomorphic Information Neural Estimation](https://mlsanity.com/paper/2211.10856/) (2022)
- [Conditional Independence Testing via Latent Representation Learning](https://mlsanity.com/paper/2209.01547/) (2022)
- [On the Effectiveness of Hybrid Mutual Information Estimation](https://mlsanity.com/paper/2306.00608/) (2023)
- [InfoBridge: Mutual Information estimation via Bridge Matching](https://mlsanity.com/paper/2502.01383/) (2025)
- [Efficient Distribution Matching of Representations via Noise-Injected Deep InfoMax](https://mlsanity.com/paper/2410.06993/) (2024)
- [Neural Mutual Information Estimation with Vector Copulas](https://mlsanity.com/paper/2510.20968/) (2025)
- [SOmegaI: Score-based O-INFORMATION Estimation](https://mlsanity.com/paper/2402.05667/) (2024)
- [Leveraging Superfluous Information in Contrastive Representation Learning](https://mlsanity.com/paper/2408.10292/) (2024)
- [RFMI: Estimating Mutual Information on Rectified Flow for Text-to-Image Alignment](https://mlsanity.com/paper/2503.14358/) (2025)
- [Curse of Slicing: Why Sliced Mutual Information is a Deceptive Measure of Statistical Dependence](https://mlsanity.com/paper/2506.04053/) (2025)

## Built on by (most cited first, 4 of 4)

- [Zero-Flow Two-Sample Tests](https://mlsanity.com/paper/2607.21542/) (2026)
- [MIST: Mutual Information Estimation Via Supervised Training](https://mlsanity.com/paper/2511.18945/) (2025)
- [Relative Entropy Estimation in Function Space: Theory and Applications to Trajectory Inference](https://mlsanity.com/paper/2604.20775/) (2026)
- [ALICE: In-context, Zero-shot, Mutual Information Estimation](https://mlsanity.com/paper/2609.34962/) (2026)

## Abstract (arXiv)

We introduce a novel Mutual Information (MI) estimator that fundamentally reframes the discriminative approach. Instead of training a classifier to discriminate between joint and marginal distributions, we learn a normalizing flow that transforms one into the other. This technique produces a computationally efficient and precise MI estimate that scales well to high dimensions and across a wide range of ground-truth MI values.