By unconditional sampling latent codes in latent space, Surf-D can produce high-quality and diverse shapes. We also calculate their average CD to each object in the training set to confirm that our model is capable of producing unique shapes. Given the category condition, Surf-D generates different categories of detailed 3D shapes with high-quality and diversity. We explore more applications that Surf-D can be applied to. As shown in the video, the clothes generated by Surf-D can be used for virtual try-on with high quality and fidelity. Imagine that you can just use sketches to generate whatever clothes you want, then put on your own avatar to try-on. Although it may sound crazy, this can be achieved with our proposed Surf-D! Given single-view images of objects, Surf-D can produce high-quality results faithfully aligned with input images. Give the text description of objects, Surf-D produces high-quality results aligned with input texts.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.