Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

翻译：三维数据的神经表示已在多种应用中广泛采用，特别是在近期利用基于坐标的网络对标量场或矢量场进行建模的研究中。然而，这些方法面临固有挑战，例如处理薄壁结构与非水密几何体，这限制了其灵活性与准确性。相比之下，我们提出了一种新颖的几何数据表示方法，将几何建模为分布——这是一种强大的表示形式，无需对曲面亏格、连通性或边界条件作任何假设。我们的方法采用扩散模型与新型网络架构来学习表面点分布，从而捕捉细粒度几何细节。我们在多种物体类型上对提出的表示进行了定性与定量评估，证明了其在实现高几何保真度方面的有效性。此外，我们探索了基于该表示的应用，例如纹理网格表示、神经表面压缩、动态物体建模与渲染，彰显了其在推进三维几何学习方面的潜力。