arXiv:2605.30153v1 Announce Type: new 
Abstract: Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their statistical efficiency remains limited. Existing theories typically rely on strong regularity assumptions, such as uniformly bounded densities or globally smooth score functions, which fail to capture such intrinsic structures. In this work, we study the sample complexity of diffusion models for learning distributions supported on a union of low-dimensional subspaces. Assuming that the data distribution within each subspace is subgaussian, we show that diffusion models require at most $\widetilde{O}(\varepsilon^{-k \vee 2})$ samples to achieve $\varepsilon$ error in 1-Wasserstein distance, where $k$ is the intrinsic dimension. This near-optimal convergence rate depends only on the intrinsic dimension and significantly improves upon prior theoretical guarantees that suffer from the curse of dimensionality. Notably, our analysis applies to a broad collection of distributions without imposing smoothness, bounded-density, or log-concavity assumptions. Overall, our results show that diffusion models can statistically adapt to intrinsic low-dimensional structure while naturally accommodating multi-modal data, offering a rigorous theoretical justification for their success in complex high-dimensional learning tasks.

توضح دراسة حديثة نُشرت على arXiv كفاءة النماذج القائمة على الانتشار في التعلم من التوزيعات متعددة الأبعاد ذات الأبعاد المنخفضة، حيث تُظهر أن هذه النماذج يمكن أن تحقق تعقيدًا عينيًا مثاليًا تحت ظروف معينة. تشير الأبحاث إلى أن نماذج الانتشار تحتاج إلى عدد أقل بكثير من العينات لتحقيق دقة مطلوبة في مسافة واسيترن 1، خاصة عندما تكون توزيعات البيانات تحت غاوسية.

Un estudio reciente publicado en arXiv destaca la eficiencia estadística de los modelos de difusión basados en puntajes para aprender distribuciones multimodales de baja dimensión, demostrando que estos modelos pueden lograr una complejidad de muestra óptima bajo ciertas condiciones. La investigación indica que los modelos de difusión requieren significativamente menos muestras para alcanzar una precisión deseada en la distancia de Wasserstein de 1, específicamente cuando las distribuciones de datos son subgaussianas.

Une étude récente publiée sur arXiv met en lumière l'efficacité statistique des modèles de diffusion basés sur le score pour apprendre des distributions multi-modales à faible dimension, montrant que ces modèles peuvent atteindre une complexité d'échantillonnage optimale dans certaines conditions. La recherche indique que les modèles de diffusion nécessitent significativement moins d'échantillons pour atteindre une précision souhaitée dans la distance de Wasserstein à 1, en particulier lorsque les distributions de données sont subgaussiennes.

A recent study published on arXiv highlights the statistical efficiency of score-based diffusion models in learning low-dimensional multi-modal distributions, demonstrating that these models can achieve optimal sample complexity under certain conditions. The research indicates that diffusion models require significantly fewer samples to achieve a desired accuracy in 1-Wasserstein distance, specifically when data distributions are subgaussian.