How to generate large scale multivariate data in MATLAB without any specific covariance matrix?

I want to data with non-linear relationships to show that deep neural networks can detect them in comparison to steep ones. So I want relationships that rely on correlations of multiple variables but no need for any specific covariance matrix. And I want that for that for many variables (~50000) which turns out slow iwhth mvnrnd. Is there any faster solution?