  Recently, studies on machine learning have focused on methods that use
symmetry implicit in a specific manifold as an inductive bias. Grassmann
manifolds provide the ability to handle fundamental shapes represented as shape
spaces, enabling stable shape analysis. In this paper, we present a novel
approach in which we establish the theoretical foundations for learning
distributions on the Grassmann manifold via continuous normalization flows,
with the explicit goal of generating stable shapes. Our approach facilitates
more robust generation by effectively eliminating the influence of extraneous
transformations, such as rotations and inversions, through learning and
generating within a Grassmann manifold designed to accommodate the essential
shape information of the object. The experimental results indicated that the
proposed method could generate high-quality samples by capturing the data
structure. Furthermore, the proposed method significantly outperformed
state-of-the-art methods in terms of the log-likelihood or evidence lower
bound. The results obtained are expected to stimulate further research in this
field, leading to advances for stable shape generation and analysis.
