Flow-Based Density Ratio Estimation for Intractable Distributions With Applications in Genomics

MCML Authors

Egor Antipov

→ Group Niki Kilbertus
 Ethics in Systems Design and Machine Learning

Alessandro Palma

→ Group Fabian Theis
 Mathematical Modelling of Biological Systems

Stephan Günnemann

Prof. Dr.

Core PI

Data Analytics & Machine Learning

Andrea Dittadi

Dr.

* Former Member

→ Group Stefan Bauer
 Algorithmic Machine Learning & Explainable AI

Fabian Theis

Prof. Dr.

Core PI

Mathematical Modelling of Biological Systems

Abstract

Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions. While exact-likelihood models such as normalizing flows offer a promising approach to density ratio estimation, naive evaluations are computationally expensive and prone to discretization errors because they require simulating each distribution's likelihood independently. In this work, we leverage condition-aware flow matching to derive a single dynamical formulation for tracking density ratios along generative trajectories. We demonstrate competitive performance on simulated benchmarks for closed-form ratio estimation, and show that our method supports versatile tasks in single-cell genomics data analysis, where likelihood-based comparisons of cellular states across experimental conditions enable treatment effect estimation and batch correction evaluation.

inproceedings APC+26

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ICML 2026

43rd International Conference on Machine Learning. Seoul, South Korea, Jul 06-11, 2026. To be published. Preprint available.

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Authors

E. Antipov • A. Palma • L. Consoli • S. Günnemann • A. Dittadi • F. J. Theis

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Links

URL GitHub

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Research Areas

 A1 | Statistical Foundations & Explainability

 A3 | Computational Models

 C2 | Biology