Used in https://towardsdatascience.com/variational-autoencoders-explained-in-detail-d585327c660a

vae loss.py

# the loss is composed of how well we can reconstruct the image
loss_reconstruction = -tf.reduce_sum(
    tf.contrib.distributions.Normal(
        decoded_images,
        params['decoder_std']
    ).log_prob(images),
    axis=1
)

# and how off the distribution over the latent space is from the prior.
# Given the prior is a standard Gaussian and the inferred distribution
# is a Gaussian with a diagonal covariance matrix, the KL-divergence
# becomes analytically solvable, and we get
loss_prior = -0.5 * tf.reduce_sum(
    1 + tf.log(encoder_var) - encoder_mu ** 2 - encoder_var,
    axis=1
)

loss_auto_encode = tf.reduce_mean(
    loss_reconstruction + loss_prior,
    axis=0
)

# digit_classification_weight is used to weight between the two losses,
# since there's a tension between them
loss_digit_classifier = params['digit_classification_weight'] * tf.reduce_mean(
    tf.nn.sparse_softmax_cross_entropy_with_logits(labels=digits,
                                                   logits=digit_logits),
    axis=0
)

loss = loss_auto_encode + loss_digit_classifier

train_op = tf.train.AdamOptimizer(params['learning_rate']).minimize(loss)