About KL Divergence loss

[ylzz1997]

About KL Divergence loss in losses.py

def kl_loss(z_p, logs_q, m_p, logs_p, z_mask):
  z_p = z_p.float()
  logs_q = logs_q.float()
  m_p = m_p.float()
  logs_p = logs_p.float()
  z_mask = z_mask.float()

  kl = logs_p - logs_q - 0.5
  kl += 0.5 * ((z_p - m_p)**2) * torch.exp(-2. * logs_p)
  kl = torch.sum(kl * z_mask)
  l = kl / torch.sum(z_mask)
  return l

KL Loss:

kl = logs_p - logs_q - 0.5
kl += 0.5 * ((z_p - m_p)**2) * torch.exp(-2. * logs_p)

The formula for calculating Gaussian divergence is:

But the code is:

loss in code $σ_1^2$

May I ask why $σ_1^2$ is missing?

Question quoted in

https://github.com/RVC-Project/Retrieval-based-Voice-Conversion-WebUI/issues/469

[nshmyrev]

Same as https://github.com/jaywalnut310/vits/issues/6#issuecomment-861903556