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MIND: Monge Inception Distance for Generative Models Evaluation

NeurIPS 2026 · Learning theory and algorithms › Optimal transport · approach: Wasserstein losses for generative models · 0 citations (OpenAlex)

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Proposes MIND, a sliced-Wasserstein-based inception distance computed by sorting 1D projections, claiming it matches FID-50k with 5k samples, is ~100x faster, and is more robust to moment-matching hacking.

Problem

FID for evaluating generative models needs ~50k samples, is expensive to compute, and is not a proper distance, so it can be gamed by matching first two moments.

Approach

Replace FID's Gaussian fit with an average of squared 1D Wasserstein distances over random unit projections of Inception features, computed exactly via sorting; a scaling factor alpha=3d aligns its magnitude with FID.

Key results

• MIND with 5k samples separates generated from real data once n>=5,000, whereas FID needs more than 10k samples.
• Under moment-matching attack, FID retains 11.2% of its value while MIND retains 31.1%.
• Computing MIND at 5k samples is more than 2 orders of magnitude faster than FID on TPUv4, and uses over 10x less peak memory.

Surprising findings

• Sliced FID and mean FID are even less robust than standard FID under moment matching (2.6% and 4.2% remaining).

Limitations

• Scaling factor alpha=3d is chosen empirically on ImageNet-64 and only loosely justified
• Adversarial robustness is shown only for moment-matching, and MIND is still affected (31.1% remaining)
• Experiments limited to Inception-v3 features and ImageNet-64 diffusion model

Experimental setup

Datasets: ImageNet-64 CelebA

Benchmarks: ImageNet-64

Metrics: probability of error in ranking hypothesis-testing error walltime peak memory moment-matching robustness ratio

Baselines: FID mean FID sliced FID MMD Sinkhorn divergence

Builds on: Fréchet Inception Distance sliced Wasserstein distance maximum mean discrepancy Sinkhorn divergence

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