diff --git a/starlette/datastructures.py b/starlette/datastructures.py
index 40806246f..243f9a894 100644
--- a/starlette/datastructures.py
+++ b/starlette/datastructures.py
@@ -237,10 +237,12 @@ def __str__(self) -> str:
 class ImmutableMultiDict(typing.Mapping):
     def __init__(
         self,
-        *args: typing.Union[
-            "ImmutableMultiDict",
-            typing.Mapping,
-            typing.List[typing.Tuple[typing.Any, typing.Any]],
+        *args: typing.Optional[
+            typing.Union[
+                "ImmutableMultiDict",
+                typing.Mapping,
+                typing.List[typing.Tuple[typing.Any, typing.Any]],
+            ]
         ],
         **kwargs: typing.Any,
     ) -> None:
@@ -364,10 +366,12 @@ def append(self, key: typing.Any, value: typing.Any) -> None:
 
     def update(
         self,
-        *args: typing.Union[
-            "MultiDict",
-            typing.Mapping,
-            typing.List[typing.Tuple[typing.Any, typing.Any]],
+        *args: typing.Optional[
+            typing.Union[
+                "MultiDict",
+                typing.Mapping,
+                typing.List[typing.Tuple[typing.Any, typing.Any]],
+            ]
         ],
         **kwargs: typing.Any,
     ) -> None: