The paper introduces SOL, a new metric for measuring gaps between text distributions using double sliced Wasserstein distances. It represents each sequence as an empirical measure of hidden states from a fixed transformer and compares these measures across distributions. The authors prove SOL is a metric when the transformer is injective and demonstrate its effectiveness in detecting distributional failures and recovering expected model trends in experiments on OpenWebText models.
arXiv:2606. 08417v1 Announce Type: cross Abstract: Diffusion and continuous flow-based language models have emerged as the leading non-autoregressive alternatives to language modeling.
The paper critiques generative perplexity (gen‑PPL) as an unreliable metric for evaluating unconditional text generation, showing that it can be minimized by trivial, non‑diverse outputs. The authors demonstrate this by constructing simple samplers that achieve low gen‑PPL yet produce incoherent text, and they propose alternative evaluation tools—including distributional discrepancies, diversity diagnostics, and a compression‑based KL divergence measure—to better assess generative language models. They argue that future progress in diffusion language models should rely on a suite of metrics that capture diverse aspects of generated text quality.
arXiv:2510.24574v3 Announce Type: replace-cross Abstract: Training time-series forecasting models requires aligning the conditional distribution of model forecasts with that of the label sequence. Th...
arXiv:2610. 20743v1 Announce Type: new Abstract: Many modern learning problems require comparing probability distributions whose individual observations are themselves probability measures, naturally giving rise to meta-measures in $\mathcal{P}(\mathcal{P}(\Omega))$.
arXiv:2605.07786v4 Announce Type: replace-cross Abstract: As generative models achieve unprecedented visual quality, the gold standard for image evaluation remains traditional feature-distribution me...
arXiv:2606. 30310v1 Announce Type: cross Abstract: The Sliced Wasserstein (SW) distance has emerged as a computationally attractive alternative to the Wasserstein distance by leveraging one-dimensional optimal transport along random projections.
The paper develops a statistical framework showing that empirical score matching can achieve minimax optimal performance for diffusion generative models when data lie on a low‑dimensional manifold. It establishes convergence rates for empirical risk minimization over constrained Sobolev classes and demonstrates that the resulting score estimators yield minimax optimal Wasserstein‑1 rates for the generated distribution, up to logarithmic factors. The analysis reveals that the statistical rates depend on the intrinsic dimension of the data manifold rather than its ambient dimension, providing conditions under which score‑based generative modeling generalizes rather than overfits.
arXiv:2605. 09916v2 Announce Type: replace-cross Abstract: We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal transport in large-scale, non-Euclidean datasets.
arXiv:2606. 09159v1 Announce Type: cross Abstract: Diffusion Language Models (DLMs) enable parallel text generation by iteratively denoising a full sequence, offering attractive flexibility compared to auto-regressive (AR) decoding.
arXiv:2610.07706v1 Announce Type: cross Abstract: Autoregressive large language models (LLMs) have rapidly advanced in capability, but their increasing scale comes with substantial computational and...
The paper introduces Wasserstein Exponential Smoothing (WES), a single‑parameter recursive method for forecasting distributional time series on ℝ. WES updates forecast distributions along Wasserstein geodesics, allowing direct application to empirical distributions without parametric modeling. In high‑frequency equity‑index return and household electricity‑demand data, WES achieves the lowest one‑step‑ahead Wasserstein prediction error among existing benchmarks and is retained in the 90% model confidence set for all 20 series examined.
arXiv:2606. 29665v1 Announce Type: cross Abstract: This paper examines how metric adjustments to Multidimensional Scaling (MDS) can enhance its effectiveness as a visual tool for pattern recognition.