Abstract

In spatial statistics, classical statistical inference such as parameter estimation or spatial interpolation is computationally intensive or intractable for many spatial processes. This intractability often comes from the joint likelihood or the conditional distribution which are rarely available in closed form. A key objective in spatial statistics is to simulate from the conditional distribution—the distribution of the spatial process at unobserved locations given the observed locations—to enable spatial interpolation. In this talk, we propose using neural diffusion models for conditional simulation of complex spatial processes. Using a masking approach, we train a score-based diffusion model within a stochastic differential equation (SDE) framework to learn the conditional reverse process--a process which reverse-diffuses Gaussian noise into samples from conditional distributions. The masking approach involves modifying the diffusion model so that the partially observed field and mask indicating observed and unobserved locations are inputs to the neural network approximating the score. As a result, the diffusion model only requires unconditional samples from the spatial process during training and is amortized with respect to the mask, provided the mask pattern is similar to those used during training. Finally, we discuss methods for validating that the generated samples do indeed come from accurate approximations of the true conditional distributions.