diff --git a/test/test_input_output_aliases.py b/test/test_input_output_aliases.py
index c7c04f781c3..b2c5fc50b21 100644
--- a/test/test_input_output_aliases.py
+++ b/test/test_input_output_aliases.py
@@ -38,6 +38,50 @@ def test_aliasing_with_cloned(self):
     torch.allclose(t1 - 1, t1_cloned)
     self.assertEqual(met.metric_data("InputOutputAliasCount")[1], 1.0)
 
+  def test_aliasing_across_mark_step(self):
+    xla_device = xm.xla_device()
+    met.clear_all()
+    t1 = torch.randn(4, 5).to(xla_device)
+    t1 += 1
+    xm.mark_step()
+    self.assertEqual(met.metric_data("InputOutputAliasCount")[1], 1.0)
+    t1 *= 100
+    xm.mark_step()
+    self.assertEqual(met.metric_data("InputOutputAliasCount")[1], 2.0)
+
+  def test_aliasing_with_multiple_inplace_update(self):
+    BATCH_SIZE = 1
+    SEQ_LEN = 128
+    NUM_KV_HEADS = 16
+    HEAD_SIZE = 256
+    BLOCK_SIZE = 16
+    DTYPE = torch.bfloat16
+    num_blocks = 1024
+    device = xm.xla_device()
+    key = torch.randn(
+        BATCH_SIZE * SEQ_LEN,
+        NUM_KV_HEADS,
+        HEAD_SIZE,
+        device=device,
+        dtype=DTYPE)
+    k_cache = torch.randn(
+        num_blocks * BLOCK_SIZE,
+        NUM_KV_HEADS,
+        HEAD_SIZE,
+        device=device,
+        dtype=DTYPE)
+    slot_mapping = torch.randint(
+        0, num_blocks, (BATCH_SIZE, SEQ_LEN), device=device, dtype=torch.int64)
+    # materalize k_cache to device data
+    xm.mark_step()
+    met.clear_all()
+    for _ in range(10):
+      k_cache.index_copy_(0, slot_mapping.flatten(), key)
+    xm.mark_step()
+    xm.wait_device_ops()
+    self.assertEqual(met.metric_data("InputOutputAliasCount")[1], 1.0)
+    torch.allclose(k_cache[slot_mapping[0][0]].cpu(), key[0].cpu())
+
 
 if __name__ == '__main__':
   test = unittest.main()
diff --git a/test/tpu/run_tests.sh b/test/tpu/run_tests.sh
index b2a8fff33dc..a0eddebc3d5 100755
--- a/test/tpu/run_tests.sh
+++ b/test/tpu/run_tests.sh
@@ -21,6 +21,7 @@ python3 test/pjrt/test_dtypes.py
 python3 test/pjrt/test_dynamic_plugin_tpu.py
 python3 test/test_fori_loop_with_while_loop_simple_add_dispatch_in_torch.py
 python3 test/test_pallas.py
+python3 test/test_input_output_aliases.py
 python3 test/torch_distributed/test_torch_distributed_all_gather_xla_backend.py
 python3 test/torch_distributed/test_torch_distributed_all_reduce_xla_backend.py
 python3 test/torch_distributed/test_torch_distributed_multi_all_reduce_xla_backend.py
diff --git a/torch_xla/csrc/aten_xla_type.cpp b/torch_xla/csrc/aten_xla_type.cpp
index 8464d1320c2..12a49a91ad9 100644
--- a/torch_xla/csrc/aten_xla_type.cpp
+++ b/torch_xla/csrc/aten_xla_type.cpp
@@ -29,6 +29,7 @@
 #include "torch_xla/csrc/helpers.h"
 #include "torch_xla/csrc/ops/as_strided.h"
 #include "torch_xla/csrc/ops/as_strided_view_update.h"
+#include "torch_xla/csrc/ops/device_data.h"
 #include "torch_xla/csrc/ops/diagonal_view_update.h"
 #include "torch_xla/csrc/ops/einsum_utilities.h"
 #include "torch_xla/csrc/ops/index_ops.h"
@@ -2538,7 +2539,38 @@ void XLANativeFunctions::_propagate_xla_data(const at::Tensor& input,
   // 1) Aid XLA's InputOutputAlias.
   auto input_tensor = bridge::GetXlaTensor(input);
   auto output_tensor = bridge::GetXlaTensor(output);
-  output_tensor->data()->alias_id = input_tensor->GetUniqueId();
+  if (input_tensor->CurrentDataHandle() != nullptr ||
+      (input_tensor->CurrentIrValue().node != nullptr &&
+       torch_xla::DeviceData::Cast(
+           input_tensor->CurrentIrValue().node.get()))) {
+    /*
+    if input has a XLAData or holds a devicedata node, set alias_id to
+    tensor_id. Consider the case.
+
+    // x.tensor_id = 1, x.alias_id = 1
+    x = torch.randn(5,5).to(xla_device())
+    // x.tensor_id = 2, x.alias_id should be 1
+    x += 1
+    xm.mark_step()
+    // x.tensor_id =3, x.alias_id should be 2 since input tensor id will be 2
+    // for this graph
+    x *= 1 of 1
+    */
+    output_tensor->data()->alias_id = input_tensor->GetUniqueId();
+  } else {
+    /*
+    Consider the case
+
+    // x.tensor_id = 1, x.alias_id = 1
+    x = torch.randn(5,5).to(xla_device())
+    // x.tensor_id = 2, x.alias_id should be 1
+    x += 1
+    // x.tensor_id = 3, x.alias_id should still be 1
+    x * = 2
+    xm.mark_step()
+    */
+    output_tensor->data()->alias_id = input_tensor->data()->alias_id;
+  }
 
   // 2) Aid SPMD.
   XLATensor::ShardingSpecPtr sharding = input_tensor->sharding_spec();