  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 \cite{dumoulin2016adversarially},
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 that provably lead 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.
