Example-Based Sampling with Diffusion Models

TL;DR

This paper introduces a diffusion model-based method for generating 2D point sets that imitate existing samplers, leveraging optimal transport to handle scattered data and enable property optimization.

Contribution

It presents a novel diffusion model approach for example-based point set sampling, overcoming convolutional limitations via optimal transport matching.

Findings

Successfully imitates various sampling patterns

Supports optimization of point set properties

Efficiently handles scattered data with grid-based convolutions

Abstract

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.