MIND: Monge Inception Distance for Generative Models Evaluation

Authors: Quentin Berthet, Yu-Han Wu, Clement Crepy et al.

arXiv · PDF

Summary

The authors introduce MIND (Monge Inception Distance), a new metric for evaluating generative models that fixes major problems with the widely used FID (Fréchet Inception Distance). MIND uses sliced Wasserstein distance—averaging many one-dimensional optimal transport problems—instead of comparing high-dimensional Gaussian statistics, which makes it much more sample-efficient, faster to compute, and robust to adversarial attacks like moment-matching.

Main takeaways:

• FID estimates high-dimensional means and covariances, which requires tons of samples and is fragile; MIND avoids this by using sliced optimal transport (sorting in 1D).
• MIND with 5,000 samples performs as well as FID with 50,000 samples, a 10× improvement in sample efficiency.
• MIND is two orders of magnitude faster to compute than FID.
• Even at 1,000–2,000 samples, MIND remains highly informative for rapid model iteration, and it correlates well with FID while being more discriminative and attack-resistant.

Relevance

Not relevant to my work on persona installation or conditional behavior in language models — this is a generative-model evaluation metric for images or other modalities, not a tool for understanding LLM fine-tuning or behavioral steering.

Abstract

arXiv:2605.06797v1 Announce Type: new Abstract: 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.