Stochastic　optimization　has　experienced　significant　growth　in　recent　decades,　with　the　increasing　prevalence　of　variance　reduction　techniques　in　stochastic　optimization　algorithms　to　enhance　computational　efficiency.　In　this　paper,　we　introduce　two　projection-free　stochastic　approximation　algorithms　for　maximizing　diminishing　return　(DR)　submodular　functions　over　convex　constraints,　building　upon　the　Stochastic　Path　Integrated　Differential　EstimatoR　(SPIDER)　and　its　variants.　Firstly,　we　present　a　SPIDER　Continuous　Greedy　(SPIDER-CG)　algorithm　for　the　monotone　case　that　guarantees　a　(1-　e(-1))OPT-　epsilon　approximation　after　O(epsilon(-1))　iterations　and　O(epsilon(-2))　stochastic　gradient　computations　under　the　mean-squared　smoothness　assumption.　For　the　non-monotone　case,　we　develop　a　SPIDER　Frank-Wolfe　(SPIDER-FW)　algorithm　that　guarantees　a　1/4　(1-　minx　(x　is　an　element　of　C)||x||(infinity))OPT-　epsilon　approximation　withO(epsilon(-1))　iterations　and　O(epsilon　(-2))　stochastic　gradient　estimates.　To　address　the　practical　challenge　associated　with　a　large　number　of　samples　per　iteration,　we　introduce　a　modified　gradient　estimator　based　on　SPIDER,　leading　to　a　Hybrid　SPIDER-FW　(Hybrid　SPIDER-CG)　algorithm,　which　achieves　the　same　approximation　guarantee　as　SPIDER-FW　(SPIDER-CG)　algorithm　with　only　O(1)　samples　per　iteration.　Numerical　experiments　on　both　simulated　and　real　data　demonstrate　the　efficiency　of　the　proposed　methods.