  Diffusion models have shown remarkable results for image generation, editing
and inpainting. Recent works explore diffusion models for 3D shape generation
with neural implicit functions, i.e., signed distance function and occupancy
function. However, they are limited to shapes with closed surfaces, which
prevents them from generating diverse 3D real-world contents containing open
surfaces. In this work, we present UDiFF, a 3D diffusion model for unsigned
distance fields (UDFs) which is capable to generate textured 3D shapes with
open surfaces from text conditions or unconditionally. Our key idea is to
generate UDFs in spatial-frequency domain with an optimal wavelet
transformation, which produces a compact representation space for UDF
generation. Specifically, instead of selecting an appropriate wavelet
transformation which requires expensive manual efforts and still leads to large
information loss, we propose a data-driven approach to learn the optimal
wavelet transformation for UDFs. We evaluate UDiFF to show our advantages by
numerical and visual comparisons with the latest methods on widely used
benchmarks. Page: https://weiqi-zhang.github.io/UDiFF.
