# MIND: Monge Inception Distance for Generative Models Evaluation

arXiv: https://arxiv.org/abs/2605.06797 · HTML: https://mlsanity.com/paper/2605.06797/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 19 of 19)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Rethinking FID: Towards a Better Evaluation Metric for Image Generation](https://mlsanity.com/paper/2401.09603/) (2023)
- [Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models](https://mlsanity.com/paper/2306.04675/) (2023)
- [Effectively Unbiased FID and Inception Score and where to find them](https://mlsanity.com/paper/1911.07023/) (2019)
- [Statistical and Topological Properties of Sliced Probability Divergences](https://mlsanity.com/paper/2003.05783/) (2020)
- [Representation Fr'echet Loss for Visual Generation](https://mlsanity.com/paper/2604.28190/) (2026)

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

- [Improved Baselines with Representation Autoencoders](https://mlsanity.com/paper/2605.18324/) (2026)
- [Representation Distribution Matching for One-Step Visual Generation](https://mlsanity.com/paper/2607.02375/) (2026)
- [DiffusionBench: On Holistic Evaluation of Diffusion Transformers](https://mlsanity.com/paper/2606.24888/) (2026)
- [AdvFD: Boosting Visual Generation via Adversarial Fr'echet Distance Loss](https://mlsanity.com/paper/2608.11205/) (2026)
- [Adaptive Second-Order Solvers for Fast Stochastic Diffusion Sampling](https://mlsanity.com/paper/2610.03034/) (2026)
- [LOB-ID: Evaluating Synthetic Market Data by Inception Distances](https://mlsanity.com/paper/2608.13082/) (2026)
- [What FID Hides: Detecting, Ranking, and Diagnosing Deviations in Generative Evaluation](https://mlsanity.com/paper/2608.24881/) (2026)
- [Sliced Orlicz-Wasserstein](https://mlsanity.com/paper/2609.32847/) (2026)
- [Debias Anything: Fairness with Diversity without Supervision in Diffusion Models](https://mlsanity.com/paper/2610.01815/) (2026)
- [SOL: Measuring Gaps between Text Distributions by Double Sliced Wasserstein Metrics](https://mlsanity.com/paper/2610.06513/) (2026)

## Abstract (arXiv)

We propose the Monge Inception Distance (MIND), a metric for evaluating generative models that addresses key limitations of the widely adopted Fr'echet Inception Distance (FID). The MIND metric leverages the sliced Wasserstein distance to compare distributions by averaging one-dimensional optimal transport distances, efficiently computed via sorting. This approach circumvents the estimation of high-dimensional means and covariance matrices, which underlie FID's poor sample complexity and vulnerability to adversarial attacks. We empirically demonstrate three primary advantages: (i) it is more sample-efficient by one order of magnitude, (ii) it is faster to compute by two orders of magnitude, (iii) it is more robust to adversarial attacks such as moment-matching. We show that MIND with 5k samples can replace the evaluation performance of FID with 50k samples, providing high correlation with this standard benchmark and superior discriminative performance. We further demonstrate that even smaller sample sizes (e.g., 1k or 2k) remain highly informative for rapid model iteration.