Improved Score Function Estimation and Hessian Estimation

This paper investigates methods for estimating the score function (gradient of the log-density) of a data distribution, crucial for generative models like diffusion models. It combines implicit score matching and denoising score matching, demonstrating improved convergence rates and the ability to estimate log-density Hessians (second derivatives) without suffering from the curse of dimensionality. This is significant because accurate score function estimation is vital for the performance of generative models, and efficient Hessian estimation supports the convergence of ODE-based samplers used in these models.