  We present Surf-D, a novel method for generating high-quality 3D shapes as
Surfaces with arbitrary topologies using Diffusion models. Previous methods
explored shape generation with different representations and they suffer from
limited topologies and poor geometry details. To generate high-quality surfaces
of arbitrary topologies, we use the Unsigned Distance Field (UDF) as our
surface representation to accommodate arbitrary topologies. Furthermore, we
propose a new pipeline that employs a point-based AutoEncoder to learn a
compact and continuous latent space for accurately encoding UDF and support
high-resolution mesh extraction. We further show that our new pipeline
significantly outperforms the prior approaches to learning the distance fields,
such as the grid-based AutoEncoder, which is not scalable and incapable of
learning accurate UDF. In addition, we adopt a curriculum learning strategy to
efficiently embed various surfaces. With the pretrained shape latent space, we
employ a latent diffusion model to acquire the distribution of various shapes.
Extensive experiments are presented on using Surf-D for unconditional
generation, category conditional generation, image conditional generation, and
text-to-shape tasks. The experiments demonstrate the superior performance of
Surf-D in shape generation across multiple modalities as conditions. Visit our
project page at https://yzmblog.github.io/projects/SurfD/.
