Score matching is a method used to train probabilistic models without evaluating the intractable partition function $Z$ or its derivatives. This technique minimizes the expected squared difference between the score function (the gradient of the log density with respect to the input $x$) of the model and that of the true data distribution:

$L(x,\theta) = \frac{1}{2} \left\| \nabla_x \log p_{\text{model}}(x;\theta) - \nabla_x \log p_{\text{data}}(x) \right\|_{2}^{2}$

$J(\theta) = \mathbb{E}_{p_{\text{data}}(x)} [L(x,\theta)]$

$\theta^* = \arg\min_{\theta} J(\theta)$