diff --git a/src/DifferentiableFlatten.jl b/src/DifferentiableFlatten.jl
index 50296a9..bea71d3 100644
--- a/src/DifferentiableFlatten.jl
+++ b/src/DifferentiableFlatten.jl
@@ -107,8 +107,12 @@ function ChainRulesCore.rrule(::typeof(_build_ordered_dict), vals, keys)
 end
 
 function flatten(x)
-    v, un = flatten(ntfromstruct(x))
-    return identity.(v), Unflatten(x, y -> structfromnt(typeof(x), un(y)))
+    if Base.issingletontype(typeof(x))
+        v, un = Union{}[], _ -> x
+    else
+        v, un = flatten(ntfromstruct(x))
+        return identity.(v), Unflatten(x, y -> structfromnt(typeof(x), un(y)))
+    end
 end
 
 function zygote_flatten(::Real, x::Real)
diff --git a/test/runtests.jl b/test/runtests.jl
index 90cd46a..979f3fa 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -110,4 +110,7 @@ MyStruct(a, b) = MyStruct{typeof(a), typeof(a), typeof(b)}(a, b)
 
     x = JuMP.Containers.DenseAxisArray(reshape(Float64[1.0, 1.0], (2,)), 1)
     @test zygote_flatten(x, (data = [1.0, 1.0],))[1] == [1.0, 1.0]
+
+    @test flatten(exp)[1] == Union{}[]
+    @test flatten(exp)[2]([]) === exp
 end