diff --git a/backends/vulkan/_passes/insert_prepack_nodes.py b/backends/vulkan/_passes/insert_prepack_nodes.py
index bf1fc28ba56..ed736438cbb 100644
--- a/backends/vulkan/_passes/insert_prepack_nodes.py
+++ b/backends/vulkan/_passes/insert_prepack_nodes.py
@@ -8,10 +8,6 @@
 
 from copy import deepcopy
 
-import executorch.backends.vulkan.custom_ops_lib  # noqa
-
-import torch
-
 from executorch.backends.vulkan.op_registry import handles_own_prepacking
 from executorch.backends.vulkan.utils import is_param_node
 
@@ -31,27 +27,27 @@ def insert_prepack_nodes(program: ExportedProgram) -> ExportedProgram:
     argument into the operator implementation.
     """
 
-    def prepack_not_required(node: torch.fx.Node) -> bool:
+    for node in program.graph_module.graph.nodes:
+        # Prepacking is only needed for constant tensors. Only nodes corresponding to
+        # constant tensors will proceed beyond this point.
         if not is_param_node(program, node):
-            return True
+            continue
 
-        # Annotate that this node is going to represented as a tensorref in the Vulkan
-        # compute graph. This will be useful for later graph passes.
+        # Mark that this node is going to be represented as a TensorRef type in the
+        # Vulkan compute graph. This annotation is used in later graph passes.
         node.meta["vkdg_tensorref"] = True
 
+        # Get the list of node users that do not handle their own prepacking
+        nodes_to_replace_input = []
         for user in node.users:
-            if user.op == "call_function" and handles_own_prepacking(
-                # pyre-ignore
-                user.target
-            ):
-                return True
+            if user.op == "call_function" and not handles_own_prepacking(user.target):
+                nodes_to_replace_input.append(user)
 
-        return False
-
-    for node in program.graph_module.graph.nodes:
-        if prepack_not_required(node):
+        if len(nodes_to_replace_input) == 0:
             continue
 
+        replace_all_uses = len(nodes_to_replace_input) == len(node.users)
+
         with program.graph_module.graph.inserting_after(node):
             prepack_node = program.graph_module.graph.create_node(
                 "call_function",
@@ -74,9 +70,14 @@ def prepack_not_required(node: torch.fx.Node) -> bool:
             # Set the mem_obj_id to -1 to indicate that this node requires a dedicated
             # memory object.
             prepack_node.meta["spec"].mem_obj_id = -1
-            node.replace_all_uses_with(
-                prepack_node, lambda x, y=prepack_node: (x != y and x.op != "output")
-            )
+            if replace_all_uses:
+                node.replace_all_uses_with(
+                    prepack_node,
+                    lambda x, y=prepack_node: (x != y and x.op != "output"),
+                )
+            else:
+                for user_node in nodes_to_replace_input:
+                    user_node.replace_input_with(node, prepack_node)
 
     program.graph.eliminate_dead_code()
     return program