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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.