Here is the pseudocode:

1. $v \sim MultiVariateGaussian(\mu,\sigma I)$
2. $v = \frac{v}{ \| v \| }$

In pytorch:

v = MultivariateNormal(torch.zeros(10000), torch.eye(10000))
v = v/v.norm(10000)

Here is the pseudocode:

1. $v \sim MultiVariateGaussian(\mu,\sigma I)$
2. $v = \frac{v}{ \| v \| }$

In pytorch:

v = MultivariateNormal(torch.zeros(10000), torch.eye(10000))
v = v/v.norm(2)

I don't understand this well enough but I've been told by whuber that:

v = torch.normal(torch.zeros(10000), torch.eye(10000))
v = v/v.norm(2)

is also correct i.e. sampling from a univariate normal for each coordinate.

In pytorch:

v = MultivariateNormal(torch.zeros(10000), torch.eye(10000))
v = v/v.norm(10000)

Here is the pseudocode:

1. $v \sim MultiVariateGaussian(\mu,\sigma I)$
2. $v = \frac{v}{ \| v \| }$

In pytorch:

v = MultivariateNormal(torch.zeros(10000), torch.eye(10000))
v = v/v.norm(10000)