<ul><li>Euclidean diffusion models have been successful in generative modeling, with recent advancements focusing on manifold data.</li><li>A study explores the challenges posed by the singularity of the score function in manifold-constrained data when using Euclidean diffusion models.</li><li>Two novel methods, Niso-DM and Tango-DM, are proposed to mitigate the singularity and improve sampling accuracy by addressing scale discrepancies and training only the tangential component of the score function.</li><li>Numerical experiments demonstrate that these methods outperform existing approaches on distributions over complex geometries in manifold data.</li></ul>

Improving the Euclidean Diffusion Generation of Manifold Data by Mitigating Score Function Singularity

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