diff --git a/src/systems/diffeqs/sdesystem.jl b/src/systems/diffeqs/sdesystem.jl
index 09bea2d152..412d308c87 100644
--- a/src/systems/diffeqs/sdesystem.jl
+++ b/src/systems/diffeqs/sdesystem.jl
@@ -231,6 +231,9 @@ function generate_diffusion_function(sys::SDESystem, dvs = unknowns(sys),
     if isdde
         eqs = delay_to_function(sys, eqs)
     end
+    if eqs isa AbstractMatrix && isdiag(eqs)
+        eqs = diag(eqs)
+    end
     u = map(x -> time_varying_as_func(value(x), sys), dvs)
     p = if has_index_cache(sys) && get_index_cache(sys) !== nothing
         reorder_parameters(get_index_cache(sys), ps)
@@ -403,14 +406,14 @@ function Girsanov_transform(sys::SDESystem, u; θ0 = 1.0)
         checks = false)
 end
 
-function DiffEqBase.SDEFunction{iip}(sys::SDESystem, dvs = unknowns(sys),
+function DiffEqBase.SDEFunction{iip, specialize}(sys::SDESystem, dvs = unknowns(sys),
         ps = parameters(sys),
         u0 = nothing;
         version = nothing, tgrad = false, sparse = false,
         jac = false, Wfact = false, eval_expression = false,
         eval_module = @__MODULE__,
         checkbounds = false,
-        kwargs...) where {iip}
+        kwargs...) where {iip, specialize}
     if !iscomplete(sys)
         error("A completed `SDESystem` is required. Call `complete` or `structural_simplify` on the system before creating an `SDEFunction`")
     end
@@ -480,7 +483,7 @@ function DiffEqBase.SDEFunction{iip}(sys::SDESystem, dvs = unknowns(sys),
 
     observedfun = ObservedFunctionCache(sys; eval_expression, eval_module)
 
-    SDEFunction{iip}(f, g,
+    SDEFunction{iip, specialize}(f, g,
         sys = sys,
         jac = _jac === nothing ? nothing : _jac,
         tgrad = _tgrad === nothing ? nothing : _tgrad,
@@ -505,6 +508,16 @@ function DiffEqBase.SDEFunction(sys::SDESystem, args...; kwargs...)
     SDEFunction{true}(sys, args...; kwargs...)
 end
 
+function DiffEqBase.SDEFunction{true}(sys::SDESystem, args...;
+        kwargs...)
+    SDEFunction{true, SciMLBase.AutoSpecialize}(sys, args...; kwargs...)
+end
+
+function DiffEqBase.SDEFunction{false}(sys::SDESystem, args...;
+        kwargs...)
+    SDEFunction{false, SciMLBase.FullSpecialize}(sys, args...; kwargs...)
+end
+
 """
 ```julia
 DiffEqBase.SDEFunctionExpr{iip}(sys::AbstractODESystem, dvs = unknowns(sys),
@@ -583,14 +596,16 @@ function SDEFunctionExpr(sys::SDESystem, args...; kwargs...)
     SDEFunctionExpr{true}(sys, args...; kwargs...)
 end
 
-function DiffEqBase.SDEProblem{iip}(sys::SDESystem, u0map = [], tspan = get_tspan(sys),
+function DiffEqBase.SDEProblem{iip, specialize}(
+        sys::SDESystem, u0map = [], tspan = get_tspan(sys),
         parammap = DiffEqBase.NullParameters();
         sparsenoise = nothing, check_length = true,
-        callback = nothing, kwargs...) where {iip}
+        callback = nothing, kwargs...) where {iip, specialize}
     if !iscomplete(sys)
         error("A completed `SDESystem` is required. Call `complete` or `structural_simplify` on the system before creating an `SDEProblem`")
     end
-    f, u0, p = process_DEProblem(SDEFunction{iip}, sys, u0map, parammap; check_length,
+    f, u0, p = process_DEProblem(
+        SDEFunction{iip, specialize}, sys, u0map, parammap; check_length,
         kwargs...)
     cbs = process_events(sys; callback, kwargs...)
     sparsenoise === nothing && (sparsenoise = get(kwargs, :sparse, false))
@@ -628,6 +643,21 @@ function DiffEqBase.SDEProblem(sys::SDESystem, args...; kwargs...)
     SDEProblem{true}(sys, args...; kwargs...)
 end
 
+function DiffEqBase.SDEProblem(sys::SDESystem,
+        u0map::StaticArray,
+        args...;
+        kwargs...)
+    SDEProblem{false, SciMLBase.FullSpecialize}(sys, u0map, args...; kwargs...)
+end
+
+function DiffEqBase.SDEProblem{true}(sys::SDESystem, args...; kwargs...)
+    SDEProblem{true, SciMLBase.AutoSpecialize}(sys, args...; kwargs...)
+end
+
+function DiffEqBase.SDEProblem{false}(sys::SDESystem, args...; kwargs...)
+    SDEProblem{false, SciMLBase.FullSpecialize}(sys, args...; kwargs...)
+end
+
 """
 ```julia
 DiffEqBase.SDEProblemExpr{iip}(sys::AbstractODESystem, u0map, tspan,
diff --git a/test/sdesystem.jl b/test/sdesystem.jl
index b18ab648e7..b1786aa721 100644
--- a/test/sdesystem.jl
+++ b/test/sdesystem.jl
@@ -614,3 +614,31 @@ sys2 = complete(sys2)
 prob = SDEProblem(sys1, sts .=> [1.0, 0.0, 0.0],
     (0.0, 100.0), ps .=> (10.0, 26.0))
 solve(prob, LambaEulerHeun(), seed = 1)
+
+# SDEProblem construction with StaticArrays
+# Issue#2814
+@parameters p d
+@variables x(tt)
+@brownian a
+eqs = [D(x) ~ p - d * x + a * sqrt(p)]
+@mtkbuild sys = System(eqs, tt)
+u0 = @SVector[x => 10.0]
+tspan = (0.0, 10.0)
+ps = @SVector[p => 5.0, d => 0.5]
+sprob = SDEProblem(sys, u0, tspan, ps)
+@test !isinplace(sprob)
+@test !isinplace(sprob.f)
+@test_nowarn solve(sprob, ImplicitEM())
+
+# Ensure diagonal noise generates vector noise function
+@variables y(tt)
+@brownian b
+eqs = [D(x) ~ p - d * x + a * sqrt(p)
+       D(y) ~ p - d * y + b * sqrt(d)]
+@mtkbuild sys = System(eqs, tt)
+u0 = @SVector[x => 10.0, y => 20.0]
+tspan = (0.0, 10.0)
+ps = @SVector[p => 5.0, d => 0.5]
+sprob = SDEProblem(sys, u0, tspan, ps)
+@test sprob.f.g(sprob.u0, sprob.p, sprob.tspan[1]) isa SVector{2, Float64}
+@test_nowarn solve(sprob, ImplicitEM())