Reproduce “Trivialized Momentum Facilitates Diffusion Generative Modeling on Lie Groups” on OpenResearch

About this paper

Yuchen Zhu, Tianrong Chen, Lingkai Kong, Evangelos A. Theodorou, Molei Tao

The Trivialized Diffusion Model (TDM) from Georgia Tech introduces a method using "trivialized momentum" to enable highly effective and scalable generative modeling on Lie groups. This approach overcomes limitations of prior manifold diffusion models by eliminating approximations, achieving state-of-the-art performance on challenging datasets including high-dimensional SO(n) and U(n).

Key insights

• Trivializing the momentum variable allows the complex task of learning score functions on a curved manifold to be transformed into learning in a fixed Euclidean vector space, greatly simplifying the problem.
• Eliminating projection steps during both training and sampling, combined with the high-accuracy OSI, drastically reduces numerical errors and ensures that generated samples adhere exactly to the underlying geometric structure.
• The approach effectively transfers the full effectiveness of Euclidean diffusion models to general Lie groups in an exact and analytical fashion, overcoming limitations of prior approximation-heavy methods.

Summary by alphaXiv.