The generative story of our model is as follows: (1) generate the dialogue act of the current dialogue turn conditioned on the previous dialogue act and the previous utterance P Θ Θ Θ (z t |z t−1 , y t−1 ); and (2) generate the current utterance conditioned on the previous utterance and the current dialogue act P Θ Θ Θ (y t |z t , y t−1 ).
p Θ Θ Θ (z 1:T , y 1:T ) is decomposed as: Furthermore, each utterance is generated by a sequential process whereby each token y t,n is conditioned on all the previously generated tokens y t,<n , as well as the external conditioning context consisting of the dialogue act z t and the previous turn's utterance y t−1 , i.e., (2) Importantly, the decomposition of the joint distribution in Equation 1 allows dynamic programming for exact decoding ( §2.2).