  Maximum Mutual information (MMI), which models the bidirectional dependency
between responses ($y$) and contexts ($x$), i.e., the forward probability $\log
p(y|x)$ and the backward probability $\log p(x|y)$, has been widely used as the
objective in the \sts model to address the dull-response issue in open-domain
dialog generation. Unfortunately, under the framework of the \sts model, direct
decoding from $\log p(y|x) + \log p(x|y)$ is infeasible since the second part
(i.e., $p(x|y)$) requires the completion of target generation before it can be
computed, and the search space for $y$ is enormous. Empirically, an N-best list
is first generated given $p(y|x)$, and $p(x|y)$ is then used to rerank the
N-best list, which inevitably results in non-globally-optimal solutions. In
this paper, we propose to use non-autoregressive (non-AR) generation model to
address this non-global optimality issue. Since target tokens are generated
independently in non-AR generation, $p(x|y)$ for each target word can be
computed as soon as it's generated, and does not have to wait for the
completion of the whole sequence. This naturally resolves the non-global
optimal issue in decoding. Experimental results demonstrate that the proposed
non-AR strategy produces more diverse, coherent, and appropriate responses,
yielding substantive gains in BLEU scores and in human evaluations.
