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In this paper, we present Surf-D, a novel method for generating high-quality3D shapes as Surfaces with arbitrary topologies using Diffusion models.Specifically, we adopt Unsigned Distance Field (UDF) as the surfacerepresentation, as it excels in handling arbitrary topologies, enabling thegeneration of complex shapes. While the prior methods explored shape generationwith different representations, they suffer from limited topologies andgeometry details. Moreover, it's non-trivial to directly extend prior diffusionmodels to UDF because they lack spatial continuity due to the discrete volumestructure. However, UDF requires accurate gradients for mesh extraction andlearning. To tackle the issues, we first leverage a point-based auto-encoder tolearn a compact latent space, which supports gradient querying for any inputpoint through differentiation to effectively capture intricate geometry at ahigh resolution. Since the learning difficulty for various shapes can differ, acurriculum learning strategy is employed to efficiently embed various surfaces,enhancing the whole embedding process. With pretrained shape latent space, weemploy a latent diffusion model to acquire the distribution of various shapes.Our approach demonstrates superior performance in shape generation acrossmultiple modalities and conducts extensive experiments in unconditionalgeneration, category conditional generation, 3D reconstruction from images, andtext-to-shape tasks.

Surf-D: High-Quality Surface Generation for Arbitrary Topologies using Diffusion Models