My question is mainly related to the seminal paper by Song et al.: "Score-Based Generative Modeling through Stochastic Differential Equations". I would like to leverage their framework in order to build a strong prior that can accurately estimate the score function (gradient of the log probability density) of some data distribution (i.e., I'm not interest in data generation whatsoever).
Suppose I perform score matching by training a neural network using equation (7) in the paper and get a trained model $s_\theta(x, t)$. My question is whether we can do something a little more clever than naively using $s_\theta(x_0, t=0)$,in order to estimate the true score function of some data point $x_0$? For example, can we leverage the SDE itself or other time periods- perhaps something along the lines of equation (39) that has been derived for exact likelihood estimation?
Much thanks!
