diff --git a/tensorflow/python/framework/convert_to_constants.py b/tensorflow/python/framework/convert_to_constants.py
index 929b7aeeec8..c6efc853b1b 100644
--- a/tensorflow/python/framework/convert_to_constants.py
+++ b/tensorflow/python/framework/convert_to_constants.py
@@ -29,6 +29,7 @@ from tensorflow.python.framework import dtypes
 from tensorflow.python.framework import tensor_util
 from tensorflow.python.grappler import tf_optimizer
 from tensorflow.python.ops import array_ops
+from tensorflow.python.util import object_identity
 from tensorflow.python.training.saver import export_meta_graph
 
 
@@ -177,10 +178,12 @@ def _get_tensor_data(func):
     Dict
   """
   tensor_data = {}
-  map_index_to_variable = {
-      func.captured_inputs.index(var.handle): var
-      for var in func.graph.variables
-  }
+  map_index_to_variable = {}
+  for var in func.graph.variables:
+    for idx, captured_input in enumerate(func.captured_inputs):
+      if var.handle is captured_input:  # pylint: disable=protected-access
+        map_index_to_variable[idx] = var
+        break
 
   # Iterates through all captures which are represented as Placeholders.
   for idx, (val_tensor, name_tensor) in enumerate(func.graph.captures):
@@ -353,9 +356,10 @@ def _construct_concrete_function(func, output_graph_def,
   """
   # Create a ConcreteFunction from the new GraphDef.
   input_tensors = func.graph.internal_captures
-  converted_inputs = set(
+  converted_inputs = object_identity.ObjectIdentitySet(
       [input_tensors[index] for index in converted_input_indices])
-  not_converted_inputs = set(func.inputs).difference(converted_inputs)
+  not_converted_inputs = object_identity.ObjectIdentitySet(
+      func.inputs).difference(converted_inputs)
   not_converted_inputs_map = {
       tensor.name: tensor for tensor in not_converted_inputs
   }
diff --git a/tensorflow/python/util/object_identity.py b/tensorflow/python/util/object_identity.py
index ba134965752..2f913ddad87 100644
--- a/tensorflow/python/util/object_identity.py
+++ b/tensorflow/python/util/object_identity.py
@@ -156,6 +156,12 @@ class ObjectIdentitySet(collections_abc.MutableSet):
   def __init__(self, *args):
     self._storage = set([self._wrap_key(obj) for obj in list(*args)])
 
+  @staticmethod
+  def _from_storage(storage):
+    result = ObjectIdentitySet()
+    result._storage = storage  # pylint: disable=protected-access
+    return result
+
   def _wrap_key(self, key):
     return _ObjectIdentityWrapper(key)
 
@@ -174,6 +180,10 @@ class ObjectIdentitySet(collections_abc.MutableSet):
   def intersection(self, items):
     return self._storage.intersection([self._wrap_key(item) for item in items])
 
+  def difference(self, items):
+    return ObjectIdentitySet._from_storage(
+        self._storage.difference([self._wrap_key(item) for item in items]))
+
   def __len__(self):
     return len(self._storage)
 
diff --git a/tensorflow/python/util/object_identity_test.py b/tensorflow/python/util/object_identity_test.py
index 8290473be2d..5dc8be1a25d 100644
--- a/tensorflow/python/util/object_identity_test.py
+++ b/tensorflow/python/util/object_identity_test.py
@@ -30,5 +30,23 @@ class ObjectIdentityWrapperTest(test.TestCase):
     self.assertNotEqual(object_identity._ObjectIdentityWrapper(o), o)
 
 
+class ObjectIdentitySetTest(test.TestCase):
+
+  def testDifference(self):
+
+    class Element(object):
+      pass
+
+    a = Element()
+    b = Element()
+    c = Element()
+    set1 = object_identity.ObjectIdentitySet([a, b])
+    set2 = object_identity.ObjectIdentitySet([b, c])
+    diff_set = set1.difference(set2)
+    self.assertIn(a, diff_set)
+    self.assertNotIn(b, diff_set)
+    self.assertNotIn(c, diff_set)
+
+
 if __name__ == '__main__':
   test.main()