Reading a paper and I cannot see why the following gives the diagonal covariance matrix. If we have two matrices $\theta$ and its mean over timesteps $\bar{\theta}$. Then according to this paper (section 3.3) the diagonal covariance can be calculated like this...
$$ diag(\theta^2 - \bar{\theta}^2) $$
But I cannot explain why this would be the case. Can someone explain why this is true?