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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.