  Recent CLIP-guided 3D generation methods have achieved promising results but
struggle with generating faithful 3D shapes that conform with input text due to
the gap between text and image embeddings. To this end, this paper proposes
HOTS3D which makes the first attempt to effectively bridge this gap by aligning
text features to the image features with spherical optimal transport (SOT).
However, in high-dimensional situations, solving the SOT remains a challenge.
To obtain the SOT map for high-dimensional features obtained from CLIP encoding
of two modalities, we mathematically formulate and derive the solution based on
Villani's theorem, which can directly align two hyper-sphere distributions
without manifold exponential maps. Furthermore, we implement it by leveraging
input convex neural networks (ICNNs) for the optimal Kantorovich potential.
With the optimally mapped features, a diffusion-based generator and a
Nerf-based decoder are subsequently utilized to transform them into 3D shapes.
Extensive qualitative and qualitative comparisons with state-of-the-arts
demonstrate the superiority of the proposed HOTS3D for 3D shape generation,
especially on the consistency with text semantics.
