Domain　adaptation　proves　to　be　an　effective　solution　for　addressing　inadequate　translation　performance　within　specific　domains.　However,　the　straightforward　approach　of　mixing　data　from　multiple　domains　to　obtain　the　multi-domain　neural　machine　translation　(NMT)　model　can　give　rise　to　the　parameter　interference　between　domains　problem,　resulting　in　a　degradation　of　overall　performance.　To　address　this,　we　introduce　a　multi-domain　adaptive　NMT　method　aimed　at　learning　domain　specific　sub-layer　latent　variable　and　employ　the　Gumbel-Softmax　reparameterization　technique　to　concurrently　train　both　model　parameters　and　domain　specific　sub-layer　latent　variable.　This　approach　facilitates　learning　private　domain-specific　knowledge　while　sharing　common　domain-invariant　knowledge,　effectively　mitigating　the　parameter　interference　problem.　The　experimental　results　show　that　our　proposed　method　significantly　improved　by　up　to　7.68　and　3.71　BLEU　compared　with　the　baseline　model　in　English-German　and　Chinese-English　public　multi-domain　datasets,　respectively.　Copyright　©　2024　held　by　the　owner/author(s).　Publication　rights　licensed　to　ACM.