UDifi is a 3D diffusion model designed to generate textured 3D shapes with open surfaces from text conditions or unconditionally. The key innovation is the use of an optimal wavelet transformation in the spatial-frequency domain to represent unsigned distance fields (UDFs), which allows for a compact and efficient representation space. The model learns the optimal wavelet filter through data-driven optimization, minimizing unsigned distance errors during self-reconstruction. This approach preserves geometric details and reduces information loss compared to manually selected wavelet filters. The model is evaluated on the DeepFashion3D and ShapeNet datasets, demonstrating superior performance in generating shapes with both open and closed surfaces compared to state-of-the-art methods. The contributions include the introduction of UDifi, the optimal wavelet transformation, and the evaluation of its effectiveness in generating diverse 3D content.UDifi is a 3D diffusion model designed to generate textured 3D shapes with open surfaces from text conditions or unconditionally. The key innovation is the use of an optimal wavelet transformation in the spatial-frequency domain to represent unsigned distance fields (UDFs), which allows for a compact and efficient representation space. The model learns the optimal wavelet filter through data-driven optimization, minimizing unsigned distance errors during self-reconstruction. This approach preserves geometric details and reduces information loss compared to manually selected wavelet filters. The model is evaluated on the DeepFashion3D and ShapeNet datasets, demonstrating superior performance in generating shapes with both open and closed surfaces compared to state-of-the-art methods. The contributions include the introduction of UDifi, the optimal wavelet transformation, and the evaluation of its effectiveness in generating diverse 3D content.