This topic has gone stale. Please, check the latest updates on this issue 103.
As a sneak peek, check this implementation that supports any tensor type:
def cov(tensor, rowvar=True, bias=False):
    """Estimate a covariance matrix (np.cov)
    https://gist.github.com/ModarTensai/5ab449acba9df1a26c12060240773110
    """
    tensor = tensor if rowvar else tensor.transpose(-1, -2)
    tensor = tensor - tensor.mean(dim=-1, keepdim=True)
    factor = 1 / (tensor.shape[-1] - int(not bool(bias)))
    return factor * tensor @ tensor.transpose(-1, -2).conj()