# Precision-Recall Divergence Optimization for Generative Modeling with GANs and Normalizing Flows

arXiv: https://arxiv.org/abs/2305.18910 · HTML: https://mlsanity.com/paper/2305.18910/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 57 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 30 of 39)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [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)
- [StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasets](https://mlsanity.com/paper/2202.00273/) (2022)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [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)
- [Unrolled Generative Adversarial Networks](https://mlsanity.com/paper/1611.02163/) (2016)
- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [Mode Regularized Generative Adversarial Networks](https://mlsanity.com/paper/1612.02136/) (2016)
- [Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks](https://mlsanity.com/paper/1701.04722/) (2017)
- [Refining Generative Process with Discriminator Guidance in Score-based Diffusion Models](https://mlsanity.com/paper/2211.17091/) (2022)
- [Input Perturbation Reduces Exposure Bias in Diffusion Models](https://mlsanity.com/paper/2301.11706/) (2023)
- [Discriminator Rejection Sampling](https://mlsanity.com/paper/1810.06758/) (2018)
- [Densely connected normalizing flows](https://mlsanity.com/paper/2106.04627/) (2021)
- [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)

## Built on by (most cited first, 9 of 9)

- [Exploring Precision and Recall to assess the quality and diversity of LLMs](https://mlsanity.com/paper/2402.10693/) (2024)
- [Improving Diversity in Language Models: When Temperature Fails, Change the Loss](https://mlsanity.com/paper/2508.09654/) (2025)
- [Optimal Budgeted Rejection Sampling for Generative Models](https://mlsanity.com/paper/2311.00460/) (2023)
- [A Practical Diffusion Path for Sampling](https://mlsanity.com/paper/2406.14040/) (2024)
- [Improving Discriminator Guidance in Diffusion Models](https://mlsanity.com/paper/2503.16117/) (2025)
- [R'enyi Neural Processes](https://mlsanity.com/paper/2405.15991/) (2024)
- [Conditional Distribution Quantization in Machine Learning](https://mlsanity.com/paper/2502.07151/) (2025)
- [Approximating f-Divergences with Rank Statistics](https://mlsanity.com/paper/2601.22784/) (2026)
- [Investigating Permutation-Invariant Discrete Representation Learning for Spatially Aligned Images](https://mlsanity.com/paper/2604.01843/) (2026)

## Abstract (arXiv)

Achieving a balance between image quality (precision) and diversity (recall) is a significant challenge in the domain of generative models. Current state-of-the-art models primarily rely on optimizing heuristics, such as the Fr'echet Inception Distance. While recent developments have introduced principled methods for evaluating precision and recall, they have yet to be successfully integrated into the training of generative models. Our main contribution is a novel training method for generative models, such as Generative Adversarial Networks and Normalizing Flows, which explicitly optimizes a user-defined trade-off between precision and recall. More precisely, we show that achieving a specified precision-recall trade-off corresponds to minimizing a unique f-divergence from a family we call the textitPR-divergences. Conversely, any f-divergence can be written as a linear combination of PR-divergences and corresponds to a weighted precision-recall trade-off. Through comprehensive evaluations, we show that our approach improves the performance of existing state-of-the-art models like BigGAN in terms of either precision or recall when tested on datasets such as ImageNet.