# Training Normalizing Flows with the Precision-Recall Divergence

arXiv: https://arxiv.org/abs/2302.00628 · HTML: https://mlsanity.com/paper/2302.00628/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 1 Feb 2023.

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

- [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)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [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)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [Resampling Base Distributions of Normalizing Flows](https://mlsanity.com/paper/2110.15828/) (2021)
- [Learning disconnected manifolds: a no GANs land](https://mlsanity.com/paper/2006.04596/) (2020)
- [Latent reweighting, an almost free improvement for GANs](https://mlsanity.com/paper/2110.09803/) (2021)
- [Bootstrap Your Flow](https://mlsanity.com/paper/2111.11510/) (2021)

## Abstract (arXiv)

Generative models can have distinct mode of failures like mode dropping and low quality samples, which cannot be captured by a single scalar metric. To address this, recent works propose evaluating generative models using precision and recall, where precision measures quality of samples and recall measures the coverage of the target distribution. Although a variety of discrepancy measures between the target and estimated distribution are used to train generative models, it is unclear what precision-recall trade-offs are achieved by various choices of the discrepancy measures. In this paper, we show that achieving a specified precision-recall trade-off corresponds to minimising -divergences from a family we call the em PR-divergences . Conversely, any -divergence can be written as a linear combination of PR-divergences and therefore correspond to minimising a weighted precision-recall trade-off. Further, we propose a novel generative model that is able to train a normalizing flow to minimise any -divergence, and in particular, achieve a given precision-recall trade-off.