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

TL;DR

This paper introduces a novel flow-based method for efficiently estimating density ratios between intractable distributions, with applications in genomics for comparing cellular states across conditions.

Contribution

It proposes a condition-aware flow matching approach that simplifies density ratio estimation along generative trajectories, improving computational efficiency and versatility.

Findings

Competitive performance on simulated benchmarks

Supports cellular state comparisons in genomics

Enables treatment effect estimation and batch correction

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 and covariates. While exact-likelihood models such as normalizing flows offer a promising approach to density ratio estimation, naive flow-based evaluations are computationally expensive, as they require simulating costly likelihood integrals for each distribution separately. 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.