# Discriminative Estimation of Total Variation Distance: A Fidelity Auditor for Generative Data

arXiv: https://arxiv.org/abs/2405.15337 · HTML: https://mlsanity.com/paper/2405.15337/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [The Role of ImageNet Classes in Fr'echet Inception Distance](https://mlsanity.com/paper/2203.06026/) (2022)
- [Benchmarking Differentially Private Synthetic Data Generation Algorithms](https://mlsanity.com/paper/2112.09238/) (2021)
- [Improved Probabilistic Image-Text Representations](https://mlsanity.com/paper/2305.18171/) (2023)
- [Neural Estimation of Statistical Divergences](https://mlsanity.com/paper/2110.03652/) (2021)
- [Practical and Consistent Estimation of f-Divergences](https://mlsanity.com/paper/1905.11112/) (2019)
- [Direct Estimation of Information Divergence Using Nearest Neighbor Ratios](https://mlsanity.com/paper/1702.05222/) (2017)
- [Minimax optimal testing by classification](https://mlsanity.com/paper/2306.11085/) (2023)
- [Lower Bounds on the Total Variation Distance Between Mixtures of Two Gaussians](https://mlsanity.com/paper/2109.01064/) (2021)
- [Direct Density-Derivative Estimation and Its Application in KL-Divergence Approximation](https://mlsanity.com/paper/1406.7638/) (2014)

## Built on by (most cited first, 10 of 10)

- [A Comprehensive Survey of Synthetic Tabular Data Generation](https://mlsanity.com/paper/2504.16506/) (2025)
- [Data Plagiarism Index: Characterizing the Privacy Risk of Data-Copying in Tabular Generative Models](https://mlsanity.com/paper/2406.13012/) (2024)
- [Advancing Retail Data Science: Comprehensive Evaluation of Synthetic Data](https://mlsanity.com/paper/2406.13130/) (2024)
- [Cross-fluctuation phase transitions reveal sampling dynamics in diffusion models](https://mlsanity.com/paper/2511.00124/) (2025)
- [Weight Clipping for Robust Conformal Inference under Unbounded Covariate Shifts](https://mlsanity.com/paper/2605.02072/) (2026)
- [GReaTER: Generate Realistic Tabular data after data Enhancement and Reduction](https://mlsanity.com/paper/2503.15564/) (2025)
- [Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspective](https://mlsanity.com/paper/2601.15500/) (2026)
- [DEREC-SIMPRO: unlock Language Model benefits to advance Synthesis in Data Clean Room](https://mlsanity.com/paper/2411.00879/) (2024)
- [Reliable LLM-Based Edge-Cloud-Expert Cascades for Telecom Knowledge Systems](https://mlsanity.com/paper/2512.20012/) (2025)
- [Approximating the Total Variation Distance between Gaussians](https://mlsanity.com/paper/2503.11099/) (2025)

## Abstract (arXiv)

With the proliferation of generative AI and the increasing volume of generative data (also called as synthetic data), assessing the fidelity of generative data has become a critical concern. In this paper, we propose a discriminative approach to estimate the total variation (TV) distance between two distributions as an effective measure of generative data fidelity. Our method quantitatively characterizes the relation between the Bayes risk in classifying two distributions and their TV distance. Therefore, the estimation of total variation distance reduces to that of the Bayes risk. In particular, this paper establishes theoretical results regarding the convergence rate of the estimation error of TV distance between two Gaussian distributions. We demonstrate that, with a specific choice of hypothesis class in classification, a fast convergence rate in estimating the TV distance can be achieved. Specifically, the estimation accuracy of the TV distance is proven to inherently depend on the separation of two Gaussian distributions: smaller estimation errors are achieved when the two Gaussian distributions are farther apart. This phenomenon is also validated empirically through extensive simulations. In the end, we apply this discriminative estimation method to rank fidelity of synthetic image data using the MNIST dataset.