Wishart site sample violating PositiveDefinite()

Hello! I’m having a little trouble with Wishart sample sites, where error was raised about PositiveDefinite(). Theoretically, Wishart distribution should be a distribution over positive definite matrices. I was wondering whether this is a numerical issue or something else that I should be award. (Despite the drawbacks of using a Wishart for covariance/precision prior, I’m simply lured by its conjugacy properties)
The error message is sent when I tried to use Wishart samples as precision matrices. Is there any solution to this?

ValueError: Expected parameter precision_matrix (Tensor of shape (50, 1, 1, 64, 64)) of distribution MultivariateNormal(loc: torch.Size([50, 1, 1, 64]), precision_matrix: torch.Size([50, 1, 1, 64, 64])) to satisfy the constraint PositiveDefinite(), but found invalid values:

I tried to convert it to the lower Cholesky, but it seems that this won’t work either.

# not working ↓
tril = pyro.deterministic("tril", torch.tril(torch.linalg.inv(inv_Sigma)), event_dim=2)

Thanks for your time! Have a nice day!