I have this Autoencoder Model which converges fine using the MSELoss (as I have numbers between -1 and 1).
class AutoEncoder(nn.Module):

    def __init__(self):
        super().__init__()
        self._encoder = nn.Sequential(
            nn.Conv2d(1, 16, 3, padding=1), 
            nn.LeakyReLU(),
            nn.MaxPool2d(2, 2),              
            nn.Conv2d(16, 4, 3, padding=1),
            nn.LeakyReLU(),
            nn.MaxPool2d(2, 2),
            
            nn.Conv2d(4, 1, 3, padding=1),
            nn.LeakyReLU(),
            nn.MaxPool2d(2, 2),
            
            nn.Flatten()            
        )
        
        self._decoder = nn.Sequential(            
            Reshape(1, 2, 2),
            
            nn.Upsample(scale_factor=2, mode='nearest'),
            nn.ConvTranspose2d(1, 4, 3, padding=1),
            nn.LeakyReLU(),
            
            nn.Upsample(scale_factor=2, mode='nearest'),
            nn.ConvTranspose2d(4, 16, 3, padding=1),
            nn.LeakyReLU(),
            nn.Upsample(scale_factor=2, mode='nearest'),
            nn.ConvTranspose2d(16, 1, 3, padding=1),
            nn.Tanh()
        )
        
    def forward(self, x):
        _x = x
        _x = self._encoder(_x)
        _x = self._decoder(_x)
        return _x

Here you can see the original and the reconstruction. I use a Gramian Angular Field to convert time series data into a 2d matrix and back.

Now I would like to turn this into Variational Autoencoder but I can’t get it to converge any more.
# custom loss function used for training
class KLDivergence(nn.Module):
    
    def __init__(self, criterion=nn.MSELoss()):
        super().__init__()
        self.criterion = criterion
        
    def forward(self, y_hat, y):
        y_hat, x, mu, logvar = y_hat
        
        bce = self.criterion(y_hat, x).mean()
        #bce = t.nn.functional.binary_cross_entropy(y_hat * 0.5 + 0.5, x * 0.5 + 0.5)
        #bce = t.nn.functional.nll_loss(y_hat.view(y.shape[0], -1) + 1, x.view(y.shape[0], -1) + 1)
        kld = -0.5 * t.sum(1 + logvar - mu.pow(2) - logvar.exp())
        
        # kld /= x.shape[0] * x.shape[1]
        return bce + kld 


class VARAutoEncoder(AutoEncoder):
    
    def __init__(self):
        super().__init__()
        self.mu = nn.Linear(4, 4)
        self.sigma = nn.Linear(4, 4)
        self.unpack = lambda x: x # nn.Linear(4, 4)

    def forward(self, x):
        mu, logvar = self._encode(x)
        
        if self.training:
            z = self._reparam(mu, logvar)
            return self._decode(z), x, mu, logvar
        else:
            return self._decode(mu)
        
    def _encode(self, x):
        x = self._encoder(x)
        return self.mu(x), self.sigma(x)
    
    def _decode(self, x):
        return self._decoder(self.unpack(x))
    
    def _reparam(self, mu, logvar):
        std = logvar.mul(0.5).exp_()
        eps = Variable(std.data.new(std.size()).normal_())
        return eps.mul(std).add_(mu)

As a new user I can only put one image into the post but both reconstructions are now just kind of a straight horizontal line. If I remove the kld term from the loss and only return the bce it reconstructs as nicely as before (I just doubt that the bottle neck follows a normal distribution then - right?).