log pθ(d|ctext) ≥

(cid:104)

Eqφ(u,ν|d,ctext)

log

pθ(d − u, ν|ctext)
qφ(u, ν|d, ctext)

(7)

(cid:105)

The training loss Ldur is then the negative variational lower
bound. We apply the stop gradient operator (van den Oord
et al., 2017), which prevents back-propagating the gradient
of inputs, to the input conditions so that the training of the
duration predictor does not affect that of other modules.
The sampling procedure is relatively simple; the phoneme
duration is sampled from random noise through the inverse
transformation of the stochastic duration predictor, and then
it is converted to integers.

2.3. Adversarial Training
ConditionalVariationalAutoencoderwithAdversarialLearningfor End-to-EndText-to-Speech