# Distributional Evaluation of Generative Models via Relative Density Ratio

arXiv: https://arxiv.org/abs/2510.25507 · HTML: https://mlsanity.com/paper/2510.25507/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 29 Oct 2025.

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Generating High Fidelity Data from Low-density Regions using Diffusion Models](https://mlsanity.com/paper/2203.17260/) (2022)
- [On GANs and GMMs](https://mlsanity.com/paper/1805.12462/) (2018)
- [Deep learning is adaptive to intrinsic dimensionality of model smoothness in anisotropic Besov space](https://mlsanity.com/paper/1910.12799/) (2019)
- [An Adversarial Approach to Structural Estimation](https://mlsanity.com/paper/2007.06169/) (2020)
- [Two-sample comparison through additive tree models for density ratios](https://mlsanity.com/paper/2508.03059/) (2025)

## Abstract (arXiv)

We propose a function-valued evaluation metric for generative models based on the relative density ratio (RDR) designed to characterize distributional differences between real and generated samples. As an evaluation metric, the RDR function preserves φ-divergence between two distributions, enables sample-level evaluation that facilitates downstream investigations of feature-specific distributional differences, and has a bounded range that affords clear interpretability and numerical stability. Function estimation of the RDR is achieved efficiently through optimization on the variational form of φ-divergence. We provide theoretical convergence rate guarantees for general estimators based on M-estimator theory, as well as the convergence rate of neural network-based estimators when the true ratio is in the anisotropic Besov space. We demonstrate the power of the proposed RDR-based evaluation through numerical experiments on MNIST, CelebA64, and the American Gut project microbiome data. We show that the estimated RDR enables not only effective overall comparison of competing generative models, but also a convenient way to reveal the underlying nature of goodness-of-fit. This enables one to assess support overlap, coverage, and fidelity while pinpointing regions of the sample space where generators concentrate and revealing the features that drive the most salient distributional differences.