Expected_log_prob in Gaussian likelihood for SVGP

[Sam4896]

Hi,
I am learning how to use the approximate GP in gpytorch. And while doing the example, I can accross the expected_log_prob function in Gaussian likelihood:
`def expected_log_prob(self, target: Tensor, input: MultivariateNormal, *params: Any, **kwargs: Any) -> Tensor:
mean, variance = input.mean, input.variance
num_event_dim = len(input.event_shape)

    noise = self._shaped_noise_covar(mean.shape, *params, **kwargs).diagonal(dim1=-1, dim2=-2)
    # Potentially reshape the noise to deal with the multitask case
    noise = noise.view(*noise.shape[:-1], *input.event_shape)

    res = ((target - mean).square() + variance) / noise + noise.log() + math.log(2 * math.pi)
    res = res.mul(-0.5)
    if num_event_dim > 1:  # Do appropriate summation for multitask Gaussian likelihoods
        res = res.sum(list(range(-1, -num_event_dim, -1)))
    return res`

The code suggests that the variance is added to the difference term and not with the noise term. Considering a homoscedastic noise, I thought that the variance should be in the Covariance matrix along with the diagonal noise matrix. So taking the log prob of the MVN
the code should be something like:

res = ((target - mean).square() / (noise +variance) + (variance+noise).log() + math.log(2 * math.pi)

Can someone please help me understand this, what is happening here?