map that to the latent space that small that see that small amount of Gaussian noise that you added at the beginning will also be Gaussian it'll just have this twist there down covariance and that's given by how the flow behaves linearly and that's just the Jacobian so we know that if you take a multivariate Gaussian and you multiply by a matrix you also get a multivariate Gaussian so locally the the flow behaves like a linear transformation and that matrix is the Jacobian so that that's what that's where this comes from and the point is