Example-Based Sampling with Diffusion Models
This provides a faster, differentiable alternative to traditional optimization-based samplers for graphics and simulation applications, though it is incremental in adapting diffusion models to scattered data.
The paper tackles the problem of generating 2D point sets that mimic existing samplers, such as those producing blue noise or Poisson disk samples, by using a diffusion model to learn from examples, and demonstrates its differentiability for optimizing point set properties.
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.