What does the notation, that is commonly used in diffusion models mean $\mathcal{N}(x_{t};\mu_{\theta},\Sigma_{\theta})$? Commonly used in diffusion models (https://arxiv.org/pdf/2006.11239.pdf), what does the notation, $\mathcal{N}(x_{t};\mu_{\theta},\Sigma_{\theta})$ mean? I get the parameterized by $\mu$ and $\sigma$ part, but I'm unclear exactly on the $x_t$ part.

It's Gaussian $\mathcal{N}$ probability density function parametrized by $\mu_\theta$ and $\Sigma_\theta$ evaluated at $x_t$ point.
