# On the Theoretical Equivalence of Several Trade-Off Curves Assessing Statistical Proximity

arXiv: https://arxiv.org/abs/2006.11809 · HTML: https://mlsanity.com/paper/2006.11809/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2020.

## Built on by (most cited first, 6 of 6)

- [Position: All Current Generative Fidelity and Diversity Metrics are Flawed](https://mlsanity.com/paper/2505.22450/) (2025)
- [Precision-Recall Divergence Optimization for Generative Modeling with GANs and Normalizing Flows](https://mlsanity.com/paper/2305.18910/) (2023)
- [On f-Divergence Principled Domain Adaptation: An Improved Framework](https://mlsanity.com/paper/2402.01887/) (2024)
- [Unifying and extending Precision Recall metrics for assessing generative models](https://mlsanity.com/paper/2405.01611/) (2024)
- [A New Perspective on Precision and Recall for Generative Models](https://mlsanity.com/paper/2511.02414/) (2025)
- [Approximating f-Divergences with Rank Statistics](https://mlsanity.com/paper/2601.22784/) (2026)

## Abstract (arXiv)

The recent advent of powerful generative models has triggered the renewed development of quantitative measures to assess the proximity of two probability distributions. As the scalar Frechet inception distance remains popular, several methods have explored computing entire curves, which reveal the trade-off between the fidelity and variability of the first distribution with respect to the second one. Several of such variants have been proposed independently and while intuitively similar, their relationship has not yet been made explicit. In an effort to make the emerging picture of generative evaluation more clear, we propose a unification of four curves known respectively as: the precision-recall (PR) curve, the Lorenz curve, the receiver operating characteristic (ROC) curve and a special case of R'enyi divergence frontiers. In addition, we discuss possible links between PR / Lorenz curves with the derivation of domain adaptation bounds.