diff --git a/sharktank/tests/export_test.py b/sharktank/tests/export_test.py
index 20b7de734..92992121b 100644
--- a/sharktank/tests/export_test.py
+++ b/sharktank/tests/export_test.py
@@ -4,6 +4,8 @@
 # See https://llvm.org/LICENSE.txt for license information.
 # SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 
+import pytest
+
 from sharktank.types import (
     ReplicatedTensor,
     SplitPrimitiveTensor,
@@ -70,6 +72,10 @@ def testGetFlatArgumentDeviceAffinities(self):
         }
         assert_dicts_equal(affinities, expected_affinities)
 
+    @pytest.mark.xfail(
+        torch.__version__ >= (2, 4),
+        reason="https://github.com/nod-ai/shark-ai/issues/685",
+    )
     def testExportWithArgumentDeviceAffinities(self):
         args = (ReplicatedTensor(ts=[torch.tensor([1])]), torch.tensor([[2]]))
 
diff --git a/sharktank/tests/layers/paged_llama_attention_block_test.py b/sharktank/tests/layers/paged_llama_attention_block_test.py
index 63251c5a9..d5cb6863d 100644
--- a/sharktank/tests/layers/paged_llama_attention_block_test.py
+++ b/sharktank/tests/layers/paged_llama_attention_block_test.py
@@ -4,6 +4,8 @@
 # See https://llvm.org/LICENSE.txt for license information.
 # SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 
+import pytest
+
 import logging
 
 logging.basicConfig(level=logging.DEBUG)
@@ -118,6 +120,10 @@ def forward(self, h, seq_block_ids, cache_state):
         asm = str(output.mlir_module)
         self.assertNotIn("scaled_dot_product_attention", asm)
 
+    @pytest.mark.xfail(
+        torch.__version__ >= (2, 4),
+        reason="https://github.com/nod-ai/shark-ai/issues/684",
+    )
     def testExportNondecomposed(self):
         dtype = torch.float32
 
diff --git a/sharktank/tests/layers/sharded_conv2d_with_iree_test.py b/sharktank/tests/layers/sharded_conv2d_with_iree_test.py
index 9b29e5761..f0153e25b 100644
--- a/sharktank/tests/layers/sharded_conv2d_with_iree_test.py
+++ b/sharktank/tests/layers/sharded_conv2d_with_iree_test.py
@@ -6,6 +6,8 @@
 # See https://llvm.org/LICENSE.txt for license information.
 # SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 
+import pytest
+
 from pathlib import Path
 import tempfile
 import torch
@@ -181,6 +183,9 @@ def run_test_sharded_conv2d_with_iree(
         )
 
 
+@pytest.mark.xfail(
+    torch.__version__ >= (2, 5), reason="https://github.com/nod-ai/shark-ai/issues/682"
+)
 def test_sharded_conv2d_with_iree(
     mlir_path: Optional[Path],
     module_path: Optional[Path],
diff --git a/sharktank/tests/models/punet/sharded_resnet_block_with_iree_test.py b/sharktank/tests/models/punet/sharded_resnet_block_with_iree_test.py
index 581584369..c24dc149e 100644
--- a/sharktank/tests/models/punet/sharded_resnet_block_with_iree_test.py
+++ b/sharktank/tests/models/punet/sharded_resnet_block_with_iree_test.py
@@ -228,6 +228,9 @@ def run_test_sharded_resnet_block_with_iree(
     strict=True,
     raises=AssertionError,
 )
+@pytest.mark.xfail(
+    torch.__version__ >= (2, 5), reason="https://github.com/nod-ai/shark-ai/issues/683"
+)
 def test_sharded_resnet_block_with_iree(
     mlir_path: Optional[Path],
     module_path: Optional[Path],