Abstract: A broad range of cross-$m$-domain generation researches boil down to matching a joint distribution by deep generative models (DGMs). Hitherto algorithms excel in pairwise domains while as $m$ increases, remain struggling to scale themselves to fit a joint distribution. In this paper, we propose a domain-scalable DGM, i.e., MMI-ALI for $m$-domain joint distribution matching. As an $m$-domain ensemble model of ALIs (Dumoulin et al., 2016), MMI-ALI is adversarially trained with maximizing Multivariate Mutual Information (MMI) w.r.t. joint variables of each pair of domains and their shared feature. The negative MMIs are upper bounded by a series of feasible losses provably leading to matching $m$-domain joint distributions. MMI-ALI linearly scales as $m$ increases and thus, strikes a right balance between efficacy and scalability. We evaluate MMI-ALI in diverse challenging $m$-domain scenarios and verify its superiority.