diff --git a/src/systems/systems.jl b/src/systems/systems.jl
index 3391e59369..a166ff8d8a 100644
--- a/src/systems/systems.jl
+++ b/src/systems/systems.jl
@@ -128,14 +128,16 @@ function __structural_simplify(sys::AbstractSystem, io = nothing; simplify = fal
             @views copyto!(sorted_g_rows[i, :], g[g_row, :])
         end
         # Fix for https://github.com/SciML/ModelingToolkit.jl/issues/2490
-        if isdiag(sorted_g_rows)
-            # If the noise matrix is diagonal, then we just give solver just takes a vector column of equations
+        if sorted_g_rows isa AbstractMatrix && size(sorted_g_rows, 2) == 1
+            # If there's only one brownian variable referenced across all the equations,
+            # we get a Nx1 matrix of noise equations, which is a special case known as scalar noise
+            noise_eqs = sorted_g_rows[:, 1]
+            is_scalar_noise = true
+        elseif isdiag(sorted_g_rows)
+            # If the noise matrix is diagonal, then the solver just takes a vector column of equations
             # and it interprets that as diagonal noise.
             noise_eqs = diag(sorted_g_rows)
             is_scalar_noise = false
-        elseif sorted_g_rows isa AbstractMatrix && size(sorted_g_rows, 2) == 1
-            noise_eqs = sorted_g_rows[:, 1]
-            is_scalar_noise = true
         else
             noise_eqs = sorted_g_rows
             is_scalar_noise = false