The　Steiner　minimum　tree　(SMT)　serves　as　an　optimal　connection　model　for　multiterminal　nets　in　very　large　scale　integration　(VLSI).　Constructing　both　rectilinear　SMT　(RSMT)　and　octilinear　SMT　(OSMT)　are　known　to　be　NP-hard　problems.　Simultaneously,　constructing　multiple　topologies　of　SMTs　for　a　given　net　holds　significant　importance　in　alleviating　routing　constraints　such　as　alleviating　congestion　and　ensuring　timing　convergence.　However,　existing　efforts　predominantly　focus　on　designing　specialized　methods　to　construct　a　specifically　structured　SMT　for　a　given　net,　making　it　challenging　to　extend　to　different　structures　or　topologies　of　SMTs,　while　also　exhibiting　insufficient　optimization　capabilities.　In　this　work,　we　propose　a　unified　approach　based　on　deep　reinforcement　learning　(DRL)　to　address　both　RSMT　and　OSMT　problems　while　generating　diverse　routing　topologies.　First,　we　design　an　edge　point　sequence　(EPS)　that　leverages　the　structural　characteristics　of　SMT　to　connect　the　output　of　the　deep　learning　model　with　the　SMT　structure.　Second,　we　propose　a　deep　learning　model　tailored　for　EPS,　employing　the　negative　wirelength　of　SMT　as　a　reward　to　train　the　model　using　DRL.　Third,　we　provide　a　corresponding　rapid　and　accurate　wirelength　computation　algorithm　for　evaluating　the　quality　of　the　construction　solution　to　expedite　model　training.　Finally,　we　leverage　the　stochastic　nature　of　machine　learning　to　construct　diverse　SMT　construction　solutions.　To　the　best　of　our　knowledge,　this　is　the　first　unified　approach　capable　of　simultaneously　addressing　both　RSMT　and　OSMT　problems　while　generating　diverse　solutions.　The　proposed　unified　approach　demonstrates　superior　solution　quality　and　higher　efficiency　compared　to　specifically　designed　algorithms.