SOL: Measuring Gaps between Text Distributions by Double Sliced Wasserstein Metrics

arXiv:2610.06513v1 Announce Type: cross Abstract: Evaluating text generation requires measuring how well the generated distribution matches the data distribution. For autoregressive models, this is done by the perplexity. Diffusion and flow-based language models can only provide a likelihood bound, whose tightness differs between model families. Sample-based substitutes such as generative perplexity with entropy do not consider the distribution fit. We propose SOL, a distance between text distributions. Each sequence is represented by the empirical measure of its hidden states under a fixed transformer and the distributions of these measures are compared by the double sliced Wasserstein distance. We prove that SOL is a metric if the transformer is injective. Experiments show that SOL detects distributional failures, recovers expected model trends, and provides stable sample-based estimates. We put forward SOL to fill the gap in the current evaluation protocol used for non auto-regressive models. As a first step we use SOL to re-evaluate a variety of models trained on OpenWebText.

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Source: arXiv cs.LG | 2026-10-06