Score-based Diffusion Models in Function Space

Understand

Diffusion models have recently emerged as a powerful framework for generative modeling.

• They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate samples by denoising.
• Despite their tremendous success, they are mostly formulated on finite-dimensional spaces, e.g., Euclidean, limiting their applications to many domains where the data has a functional form, such as in scientific computing and 3D geometric data analysis.
• This work introduces a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space.