MIND: Monge Inception Distance for Generative Models Evaluation

2026-05-07

AI Summary

This work addresses critical limitations of existing generative model evaluation metrics—such as the Fréchet Inception Distance (FID)—in sample complexity, computational efficiency, and robustness against adversarial attacks. The authors propose the Monge Inception Distance (MIND), which computes a one-dimensional optimal transport average of Inception features via sliced Wasserstein distance, thereby circumventing the need for high-dimensional mean and covariance estimation. MIND achieves evaluation performance comparable to FID with only 1k–5k samples, offering an order-of-magnitude improvement in sample efficiency and two orders of magnitude faster computation. Moreover, it demonstrates significantly enhanced robustness against adversarial manipulations such as moment matching. While maintaining high correlation with FID, MIND exhibits superior discriminative power, substantially facilitating efficient generative model development and iteration.

Abstract

We propose the Monge Inception Distance (MIND), a metric for evaluating generative models that addresses key limitations of the widely adopted Fréchet 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.

Problem

• generative models evaluation
• Fréchet Inception Distance
• sample complexity
• adversarial robustness
• distribution comparison

Innovation

• Monge Inception Distance
• sliced Wasserstein distance
• generative model evaluation
• sample efficiency
• adversarial robustness