# TopP&R: Robust Support Estimation Approach for Evaluating Fidelity and Diversity in Generative Models

arXiv: https://arxiv.org/abs/2306.08013 · HTML: https://mlsanity.com/paper/2306.08013/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 51 references that are in the map.
- First posted on arXiv 13 Jun 2023.

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [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)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasets](https://mlsanity.com/paper/2202.00273/) (2022)
- [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)
- [Identifying Mislabeled Data using the Area Under the Margin Ranking](https://mlsanity.com/paper/2001.10528/) (2020)
- [The Role of ImageNet Classes in Fr'echet Inception Distance](https://mlsanity.com/paper/2203.06026/) (2022)
- [Projected GANs Converge Faster](https://mlsanity.com/paper/2111.01007/) (2021)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Stochastic Convergence of Persistence Landscapes and Silhouettes](https://mlsanity.com/paper/1312.0308/) (2013)
- [Optimality of the Johnson-Lindenstrauss Lemma](https://mlsanity.com/paper/1609.02094/) (2016)
- [StudioGAN: A Taxonomy and Benchmark of GANs for Image Synthesis](https://mlsanity.com/paper/2206.09479/) (2022)
- [Rarity Score : A New Metric to Evaluate the Uncommonness of Synthesized Images](https://mlsanity.com/paper/2206.08549/) (2022)
- [Manifold Topology Divergence: a Framework for Comparing Data Manifolds](https://mlsanity.com/paper/2106.04024/) (2021)
- [Robust Topological Inference: Distance To a Measure and Kernel Distance](https://mlsanity.com/paper/1412.7197/) (2014)
- [Confidence sets for persistence diagrams](https://mlsanity.com/paper/1303.7117/) (2013)
- [The Johnson-Lindenstrauss lemma is optimal for linear dimensionality reduction](https://mlsanity.com/paper/1411.2404/) (2014)
- [GeomCA: Geometric Evaluation of Data Representations](https://mlsanity.com/paper/2105.12486/) (2021)
- [On the Bootstrap for Persistence Diagrams and Landscapes](https://mlsanity.com/paper/1311.0376/) (2013)

## Built on by (most cited first, 14 of 14)

- [Exploring Precision and Recall to assess the quality and diversity of LLMs](https://mlsanity.com/paper/2402.10693/) (2024)
- [Position: All Current Generative Fidelity and Diversity Metrics are Flawed](https://mlsanity.com/paper/2505.22450/) (2025)
- [Slight Corruption in Pre-training Data Makes Better Diffusion Models](https://mlsanity.com/paper/2405.20494/) (2024)
- [STREAM: Spatio-TempoRal Evaluation and Analysis Metric for Video Generative Models](https://mlsanity.com/paper/2403.09669/) (2024)
- [Optimal Budgeted Rejection Sampling for Generative Models](https://mlsanity.com/paper/2311.00460/) (2023)
- [Nickel and Diming Your GAN: A Dual-Method Approach to Enhancing GAN Efficiency via Knowledge Distillation](https://mlsanity.com/paper/2405.11614/) (2024)
- [VQalAttent: a Transparent Speech Generation Pipeline based on Transformer-learned VQ-VAE Latent Space](https://mlsanity.com/paper/2411.14642/) (2024)
- [Temporal Representation Learning for Stock Similarities and Its Applications in Investment Management](https://mlsanity.com/paper/2407.13751/) (2024)
- [Enhanced Generative Model Evaluation with Clipped Density and Coverage](https://mlsanity.com/paper/2507.01761/) (2025)
- [Equalized Generative Treatment: Matching f-divergences for Fairness in Generative Models](https://mlsanity.com/paper/2602.08660/) (2026)
- [A New Perspective on Precision and Recall for Generative Models](https://mlsanity.com/paper/2511.02414/) (2025)
- [Learning To Sample From Diffusion Models Via Inverse Reinforcement Learning](https://mlsanity.com/paper/2602.08689/) (2026)
- [GICDM: Mitigating Hubness for Reliable Distance-Based Generative Model Evaluation](https://mlsanity.com/paper/2602.16449/) (2026)
- [PLDiv: Measuring Dataset Diversity and Semantic Collapse via Persistence Landscapes](https://mlsanity.com/paper/2610.14031/) (2026)

## Abstract (arXiv)

We propose a robust and reliable evaluation metric for generative models by introducing topological and statistical treatments for rigorous support estimation. Existing metrics, such as Inception Score (IS), Frechet Inception Distance (FID), and the variants of Precision and Recall (P&R), heavily rely on supports that are estimated from sample features. However, the reliability of their estimation has not been seriously discussed (and overlooked) even though the quality of the evaluation entirely depends on it. In this paper, we propose Topological Precision and Recall (TopP&R, pronounced 'topper'), which provides a systematic approach to estimating supports, retaining only topologically and statistically important features with a certain level of confidence. This not only makes TopP&R strong for noisy features, but also provides statistical consistency. Our theoretical and experimental results show that TopP&R is robust to outliers and non-independent and identically distributed (Non-IID) perturbations, while accurately capturing the true trend of change in samples. To the best of our knowledge, this is the first evaluation metric focused on the robust estimation of the support and provides its statistical consistency under noise.