diff --git a/shark_turbine/aot/support/procedural/exported_program.py b/shark_turbine/aot/support/procedural/exported_program.py
index 331a7345..bbc431ae 100644
--- a/shark_turbine/aot/support/procedural/exported_program.py
+++ b/shark_turbine/aot/support/procedural/exported_program.py
@@ -234,6 +234,8 @@ def store_produced_value(
             raise ValueError(f"Cannot store value to unmapped global for: {info}")
         logger.debug("Resolved  global for store %r", mapping)
         materialized_global: MaterializedGlobal = mapping.value  # type: ignore
+        assert isinstance(materialized_global.global_op, util_d.GlobalOp)
+        materialized_global.global_op.is_mutable = True
         converted_value = Operation.create(
             "torch_c.to_builtin_tensor",
             results=[materialized_global.ir_type],
@@ -251,7 +253,7 @@ def resolve_literal(
             return None
 
         # See if we know about it.
-        materialized_global = self._lift_tensor_to_global(literal)
+        materialized_global = self._lift_tensor_to_global(literal, info)
         if not materialized_global:
             # If it is unknown, just let the default importer take it on.
             return None
@@ -269,7 +271,7 @@ def resolve_literal(
         return converted_value
 
     def _lift_tensor_to_global(
-        self, literal: torch.Tensor
+        self, literal: torch.Tensor, info: InputInfo | None
     ) -> Optional[MaterializedGlobal]:
         module_builder = self.module_builder
         mapping = module_builder.global_ref_tracker.track(literal)
@@ -282,7 +284,7 @@ def _lift_tensor_to_global(
         # Policy check: Should we auto-import? Generally, we keep "small"
         # tensors as inline as they can be optimized.
         external_trait = ExternalTensorTrait.get(literal)
-        if not self._should_lift_tensor_to_global(literal, external_trait):
+        if not self._should_lift_tensor_to_global(literal, external_trait, info):
             return None
 
         # If it is a tensor we haven't seen yet, materialize it
@@ -304,8 +306,13 @@ def _lift_tensor_to_global(
         return materialized_global
 
     def _should_lift_tensor_to_global(
-        self, literal: torch.Tensor, external_trait: Optional[ExternalTensorTrait]
+        self,
+        literal: torch.Tensor,
+        external_trait: Optional[ExternalTensorTrait],
+        info: InputInfo | None,
     ) -> bool:
+        if info is not None and info.store_producer_node:
+            return True
         if external_trait is not None:
             return True
         volume = math.prod(literal.shape)
diff --git a/tests/aot/globals_test.py b/tests/aot/globals_test.py
index 26bab1a6..607382fd 100644
--- a/tests/aot/globals_test.py
+++ b/tests/aot/globals_test.py
@@ -425,6 +425,68 @@ def testUnsupportedCombinations(self):
             export_global(AbstractF32, external=True, uninitialized=True)
 
 
+class SimpleCache(torch.nn.Module):
+    def __init__(self, max_size, dtype=torch.float32):
+        super().__init__()
+        self.register_buffer("cache", torch.zeros(max_size, dtype=dtype))
+
+    def forward(self, input_pos, values):
+        # input_pos: [S], values: [S]
+        assert input_pos.shape[0] == values.shape[0]
+
+        # Writing the values to the buffer at the specified positions
+        cache = torch.ops.aten.index_put_(self.cache, [input_pos], values)
+
+        return cache
+
+
+class ReadWriteReadCache(torch.nn.Module):
+    def __init__(self, max_size, dtype=torch.float32):
+        super().__init__()
+        self.register_buffer("cache", torch.zeros(max_size, dtype=dtype))
+
+    def forward(self, input_pos, values):
+        # input_pos: [S], values: [S]
+        assert input_pos.shape[0] == values.shape[0]
+        cache_value_0 = self.cache[2].clone()
+        # Writing the values to the buffer at the specified positions
+        cache = torch.ops.aten.index_put_(self.cache, [input_pos], values)
+        cache_value_1 = cache[2].clone()
+        return cache, cache_value_0, cache_value_1
+
+
+class BufferTest(unittest.TestCase):
+    def testMutableBuffer(self):
+        max_size = 10
+        simple_cache = SimpleCache(max_size)
+
+        input_pos = torch.tensor([2, 5, 7])
+        values = torch.tensor([1.0, 2.0, 3.0])
+        simple_cache(input_pos, values)
+        exported_fx_graph = torch.export.export(simple_cache, args=(input_pos, values))
+        exported_programm = export(exported_fx_graph)
+        module_str = str(exported_programm.mlir_module)
+        self.assertIn(
+            "util.global private mutable @__auto.constant_10_torch.float32",
+            module_str,
+        )
+
+    def testReadWriteReadMutableBuffer(self):
+        max_size = 10
+        simple_cache = ReadWriteReadCache(max_size)
+
+        input_pos = torch.tensor([2, 5, 7])
+        values = torch.tensor([1.0, 2.0, 3.0])
+        simple_cache(input_pos, values)
+        exported_fx_graph = torch.export.export(simple_cache, args=(input_pos, values))
+        exported_programm = export(exported_fx_graph)
+        module_str = str(exported_programm.mlir_module)
+        self.assertIn(
+            "util.global private mutable @__auto.constant_10_torch.float32",
+            module_str,
+        )
+
+
 if __name__ == "__main__":
     logging.basicConfig(level=logging.DEBUG)
     unittest.main()