  3D shape generation from text is a fundamental task in 3D representation
learning. The text-shape pairs exhibit a hierarchical structure, where a
general text like ``chair" covers all 3D shapes of the chair, while more
detailed prompts refer to more specific shapes. Furthermore, both text and 3D
shapes are inherently hierarchical structures. However, existing Text2Shape
methods, such as SDFusion, do not exploit that. In this work, we propose
HyperSDFusion, a dual-branch diffusion model that generates 3D shapes from a
given text. Since hyperbolic space is suitable for handling hierarchical data,
we propose to learn the hierarchical representations of text and 3D shapes in
hyperbolic space. First, we introduce a hyperbolic text-image encoder to learn
the sequential and multi-modal hierarchical features of text in hyperbolic
space. In addition, we design a hyperbolic text-graph convolution module to
learn the hierarchical features of text in hyperbolic space. In order to fully
utilize these text features, we introduce a dual-branch structure to embed text
features in 3D feature space. At last, to endow the generated 3D shapes with a
hierarchical structure, we devise a hyperbolic hierarchical loss. Our method is
the first to explore the hyperbolic hierarchical representation for
text-to-shape generation. Experimental results on the existing text-to-shape
paired dataset, Text2Shape, achieved state-of-the-art results. We release our
implementation under HyperSDFusion.github.io.
