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New papers explore theory for generative models on manifolds and PDEs

By PulseAugur Editorial · Summary by gemini-2.5-flash-lite from 5 sources

Two new research papers explore theoretical underpinnings of generative models. One paper details intrinsic Wasserstein rates for score-based generative models operating on smooth manifolds, offering a theoretical bound on their sample complexity. The second paper develops a framework for understanding the regularity and generalization of one-step Wasserstein-guided generative models, particularly for probability measures induced by partial differential equations. AI

Summary written by gemini-2.5-flash-lite from 5 sources. How we write summaries →

IMPACT These papers contribute to the theoretical understanding of generative models, potentially leading to more robust and accurate models for complex data distributions and scientific applications.

RANK_REASON Two academic papers published on arXiv detailing theoretical advancements in generative models.

Read on arXiv cs.LG →

New papers explore theory for generative models on manifolds and PDEs

COVERAGE [5]

  1. Hugging Face Daily Papers TIER_1 ·

    On the Regularity and Generalization of One-Step Wasserstein-guided Generative Models for PDE-Induced Measures

    Despite the remarkable empirical success of generative models, the available theory on their statistical accuracy in scientific computing remains largely pessimistic. This paper develops a theoretical framework for understanding the regularity of transport maps and the generaliza…

  2. arXiv cs.LG TIER_1 · Atsushi Nitanda ·

    Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds

    Score-based generative models are trained in high-dimensional ambient spaces, yet many data distributions are supported on low-dimensional nonlinear structures. We prove that, for compact $d$-dimensional smooth manifolds $\mathcal{M} \subset [0,1]^D$ with $d > 2$ and $β$-Hölder d…

  3. arXiv stat.ML TIER_1 · Likun Lin, Zhongjian Wang, Jack Xin, Zhiwen Zhang ·

    On the Regularity and Generalization of One-Step Wasserstein-guided Generative Models for PDE-Induced Measures

    arXiv:2605.21388v1 Announce Type: cross Abstract: Despite the remarkable empirical success of generative models, the available theory on their statistical accuracy in scientific computing remains largely pessimistic. This paper develops a theoretical framework for understanding t…

  4. arXiv stat.ML TIER_1 · Zhiwen Zhang ·

    On the Regularity and Generalization of One-Step Wasserstein-guided Generative Models for PDE-Induced Measures

    Despite the remarkable empirical success of generative models, the available theory on their statistical accuracy in scientific computing remains largely pessimistic. This paper develops a theoretical framework for understanding the regularity of transport maps and the generaliza…

  5. arXiv stat.ML TIER_1 · Guoji Fu, Taiji Suzuki, Wee Sun Lee, Atsushi Nitanda ·

    Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds

    arXiv:2605.15822v1 Announce Type: cross Abstract: Score-based generative models are trained in high-dimensional ambient spaces, yet many data distributions are supported on low-dimensional nonlinear structures. We prove that, for compact $d$-dimensional smooth manifolds $\mathcal…

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