diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceFiniteDiffExt/onearg.jl b/DifferentiationInterface/ext/DifferentiationInterfaceFiniteDiffExt/onearg.jl
index 82b769ef6..4a3712c0f 100644
--- a/DifferentiationInterface/ext/DifferentiationInterfaceFiniteDiffExt/onearg.jl
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceFiniteDiffExt/onearg.jl
@@ -14,7 +14,7 @@ function DI.prepare_pushforward_nokwarg(
     _sig = DI.signature(f, backend, x, tx, contexts...; strict)
     fc = DI.fix_tail(f, map(DI.unwrap, contexts)...)
     y = fc(x)
-    cache = if x isa Number || y isa Number
+    cache = if x isa Number || y isa Number || (! DI.ismutable_array(x)) || (! DI.ismutable_array(y))
         nothing
     else
         JVPCache(similar(x), y, fdtype(backend))
@@ -130,7 +130,7 @@ function DI.prepare_derivative_nokwarg(
     _sig = DI.signature(f, backend, x, contexts...; strict)
     fc = DI.fix_tail(f, map(DI.unwrap, contexts)...)
     y = fc(x)
-    cache = if y isa Number
+    cache = if y isa Number || (! DI.ismutable_array(y))
         nothing
     elseif y isa AbstractArray
         df = similar(y)
diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceFiniteDiffExt/twoarg.jl b/DifferentiationInterface/ext/DifferentiationInterfaceFiniteDiffExt/twoarg.jl
index e30ba1ec7..90c789f81 100644
--- a/DifferentiationInterface/ext/DifferentiationInterfaceFiniteDiffExt/twoarg.jl
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceFiniteDiffExt/twoarg.jl
@@ -18,7 +18,7 @@ function DI.prepare_pushforward_nokwarg(
         contexts::Vararg{DI.Context, C}
     ) where {C}
     _sig = DI.signature(f!, y, backend, x, tx, contexts...; strict)
-    cache = if x isa Number
+    cache = if x isa Number || (! DI.ismutable_array(x))
         nothing
     else
         JVPCache(similar(x), similar(y), fdtype(backend))