How to make torch.distributions.MultivariateNormal accept zero values on the diagonal of covariance matrix?

Question

I use torch.normal to generate (1,n)-dimensional samples with an std vector that includes zero values. This doesn't generate any errors (when std[k] is zero the corresponding mean[k] is sampled).

However, torch.distributions.MultivariateNormal doesn't accept diagonal covariance matrix whose diagonal values are std[k]**2

I need the MultivariateNormal object to compute log_prob of the generated sample for which i used torch.normal

Code:

import torch
mean = torch.Tensor([1.00000,1.00000,1.00000,1.00000,1.00000,-1.00000,-1.00000,-1.00000,-1.00000])
std = torch.Tensor([17708.14062,68.16734,0.00000,0.00000,5917.79932,15390.00488, 0.00000,10070.79395,4994.94434])
x = torch.normal(mean, std)
torch.distributions.MultivariateNormal(loc=mean, covariance_matrix=torch.Tensor(np.diag(np.array(std)**2))).log_prob(x)

Error:

ValueError: Expected parameter covariance_matrix (Tensor of shape (9, 9)) of distribution MultivariateNormal(loc: torch.Size([9]), covariance_matrix: torch.Size([9, 9])) to satisfy the constraint PositiveDefinite(), but found invalid values

I don't get why torch.normal doesn't mind zero values in the std but normal.distributions.MultivariateNormal does.

I tried to look up special parameters that can be passed to the constructor to ignore this, like the 'allow_singular' parameter in the scipy library, but there seems to be none.

from scipy.stats import multivariate_normal
pi = multivariate_normal(mean=mean, cov=np.diag(np.array(std)**2),  allow_singular=True).pdf(
    np.array(action))