MIND用排序计算距离，评估生成模型更快更稳更省样本。
MIND: Monge Inception Distance for Generative Models Evaluation
- 用一维最优传输平均替代高维统计量估计，避免复杂计算。
- 5000样本即可达到FID 5万样本的评估效果，效率提升10倍。
- 对对抗攻击更鲁棒，适合快速迭代模型的场景。
我们提出蒙日启明距离（MIND），一种用于评估生成模型的新指标，解决广泛使用的弗雷谢启明距离（FID）的关键缺陷。MIND利用切片沃瑟斯坦距离，通过排序高效计算一维最优传输距离的平均值，从而规避了FID依赖的高维均值与协方差矩阵估计。实证表明，MIND具备三大优势：(i) 样本效率提升一个数量级；(ii) 计算速度加快两个数量级；(iii) 对如矩匹配等对抗攻击更具鲁棒性。结果显示，使用5000样本的MIND可替代FID使用50000样本的评估性能，且与标准基准高度相关，判别能力更优。即使仅用1000或2000样本，仍能提供高度信息量，适用于快速模型迭代。
原文摘要 · Abstract (English)
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.
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