Much effort has been put into developing samplers with specific properties, such as producing blue noise, low-discrepancy, lattice or Poisson disk samples. These samplers can be slow if they rely on optimization processes, may rely on a wide range of numerical methods, are not always differentiable. The success of recent diffusion models for image generation suggests that these models could be appropriate for learning how to generate point sets from examples. However, their convolutional nature makes these methods impractical for dealing with scattered data such as point sets. We propose a generic way to produce 2-d point sets imitating existing samplers from observed point sets using a diffusion model. We address the problem of convolutional layers by leveraging neighborhood information from an optimal transport matching to a uniform grid, that allows us to benefit from fast convolutions on grids, and to support the example-based learning of non-uniform sampling patterns. We demonstrate how the differentiability of our approach can be used to optimize point sets to enforce properties.

翻译：为开发具有特定性质的采样器已投入大量努力，例如生成蓝噪声、低差异、晶格或泊松圆盘样本。这些采样器若依赖优化过程可能运行缓慢，需借助多种数值方法，且通常不具备可微性。近期扩散模型在图像生成领域的成功表明，此类模型或可适用于从样本中学习点集生成方法。然而，其卷积特性使得这些方法难以处理点集等散乱数据。我们提出一种通用方法，通过扩散模型从观测点集中模仿现有采样器生成二维点集。通过利用最优传输匹配将邻域信息映射至均匀网格，我们解决了卷积层的问题，既能受益于网格上的快速卷积，又能支持基于样本的非均匀采样模式学习。我们还展示了该方法可微性如何用于优化点集以强制执行特定属性。