Trivialized Momentum Facilitates Diffusion Generative Modeling on Lie Groups
CoRR(2024)
Abstract
The generative modeling of data on manifold is an important task, for which
diffusion models in flat spaces typically need nontrivial adaptations. This
article demonstrates how a technique called `trivialization' can transfer the
effectiveness of diffusion models in Euclidean spaces to Lie groups. In
particular, an auxiliary momentum variable was algorithmically introduced to
help transport the position variable between data distribution and a fixed,
easy-to-sample distribution. Normally, this would incur further difficulty for
manifold data because momentum lives in a space that changes with the position.
However, our trivialization technique creates to a new momentum variable that
stays in a simple fixed vector space. This design, together with a
manifold preserving integrator, simplifies implementation and avoids
inaccuracies created by approximations such as projections to tangent space and
manifold, which were typically used in prior work, hence facilitating
generation with high-fidelity and efficiency. The resulting method achieves
state-of-the-art performance on protein and RNA torsion angle generation and
sophisticated torus datasets. We also, arguably for the first time, tackle the
generation of data on high-dimensional Special Orthogonal and Unitary groups,
the latter essential for quantum problems.
MoreTranslated text
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined