# Is Beta-VAE regularization equivalent to using a Gaussian prior with variance smaller than 1?

The Beta-VAE model offers the regularization over the -$$\beta$$ KL(q(z|x)||p(z)) term of the ELBO term in VAE formulation. Scaling this term up forces some latents to be distributed as unit Gaussians (given that p(z) is isotropic Gaussian). I wonder, is it possible to acquire the same regularization by only tuning the prior such as having a Gaussian with smaller std such as 0.01?

Beta VAE paper: https://openreview.net/forum?id=Sy2fzU9gl