diff --git a/test/export/test_export.py b/test/export/test_export.py
index 528079bcfe142..219261beea87f 100644
--- a/test/export/test_export.py
+++ b/test/export/test_export.py
@@ -2749,9 +2749,7 @@ def forward(self, x, y):
 
         ep = export(M(), (torch.tensor(1), torch.ones(4, 5)))
 
-        # This is because we insert sym_constrain_range in the graph now
-        error_msg = r"Invalid value range for -1 between"
-        with self.assertRaisesRegex(RuntimeError, error_msg):
+        with self.assertRaisesRegex(RuntimeError, "Invalid value range"):
             _ = ep.module()(torch.tensor(-1), torch.randn(4, 5))
 
         self.assertTrue(
diff --git a/test/export/test_passes.py b/test/export/test_passes.py
index 2807a2ded9072..67bbf88f95160 100644
--- a/test/export/test_passes.py
+++ b/test/export/test_passes.py
@@ -574,7 +574,10 @@ def forward(self, x):
         new_inp = torch.tensor([1, 1, 1, 1])
         self.assertEqual(mod(new_inp), ep.module()(new_inp))
 
+    # Currently runtime assertions don't work well with submodules
+    # Since it is not real use case, we xfail this test for now
     @unittest.skipIf(IS_WINDOWS, "Windows not supported")
+    @unittest.expectedFailure
     def test_runtime_assert_inline_constraints_for_cond(self) -> None:
         class M(torch.nn.Module):
             def __init__(self):
@@ -602,7 +605,7 @@ def false_fn(x, y):
         ep = export(mod, (torch.tensor(True), x, y))
 
         with self.assertRaisesRegex(
-            RuntimeError, "is outside of inline constraint \\[2, 5\\]."
+            RuntimeError, "Invalid value range for 6 between \\[2, 5\\]."
         ):
             ep.module()(torch.tensor(False), torch.tensor([6]), torch.tensor([6]))
 
diff --git a/test/onnx/test_fx_op_consistency.py b/test/onnx/test_fx_op_consistency.py
index 83a4e3965f813..7d6f17cbc4894 100644
--- a/test/onnx/test_fx_op_consistency.py
+++ b/test/onnx/test_fx_op_consistency.py
@@ -1020,7 +1020,7 @@ def skip_torchlib_forward_compatibility(
     ),
     xfail(
         "nonzero",
-        dtypes=(torch.int8, torch.int16),
+        dtypes=(torch.int8, torch.int16, torch.int64, torch.float16, torch.bool),
         reason=onnx_test_common.reason_onnx_runtime_does_not_support("NonZero", "int8, int16"),
     ),
     xfail(
diff --git a/test/onnx/test_fx_to_onnx_with_onnxruntime.py b/test/onnx/test_fx_to_onnx_with_onnxruntime.py
index f8154a149b413..c5b65d8a4a941 100644
--- a/test/onnx/test_fx_to_onnx_with_onnxruntime.py
+++ b/test/onnx/test_fx_to_onnx_with_onnxruntime.py
@@ -644,10 +644,6 @@ def forward(self, x, y):
             func, (torch.tensor([1]), torch.randn(3, 4))
         )
 
-    @pytorch_test_common.xfail_if_model_type_is_exportedprogram(
-        error_message="Unsupported FX nodes: {'call_function': ['aten._assert_async.msg']}",
-        reason="https://github.com/pytorch/pytorch/issues/112622",
-    )
     def test_operator_with_dynamic_output_shape(self):
         class Foo(torch.nn.Module):
             def forward(self, x):
diff --git a/torch/export/_trace.py b/torch/export/_trace.py
index d5f0851c87694..8e8a232d5d7a9 100644
--- a/torch/export/_trace.py
+++ b/torch/export/_trace.py
@@ -27,9 +27,6 @@
     _node_metadata_hook,
     _set_node_metadata_hook,
 )
-from torch._export.passes.add_runtime_assertions_for_constraints_pass import (
-    _AddRuntimeAssertionsForInlineConstraintsPass,
-)
 from torch._export.passes.collect_tracepoints_pass import CollectTracepointsPass
 from torch._export.passes.lift_constants_pass import (
     ConstantAttrMap,
@@ -152,23 +149,6 @@ def _strip_root(x):
     return x
 
 
-def _add_runtime_assertions_to_cond_in_subgraph(range_constraints, gm, fake_mode):
-    # We can't get rid of this yet, since for some reason
-    # insert_deferred_runtime_assertions doesn't add assertions to cond
-    # subgraphs
-    if len(range_constraints) > 0:
-        stack_trace = (
-            'File "torch/_export/passes/add_runtime_assertions_for_constraints_pass.py", line 46, '
-            "in _AddRuntimeAssertionsForInlineConstraintsPass"
-        )
-        with fake_mode, _set_node_metadata_hook(
-            gm, functools.partial(_node_metadata_hook, stack_trace=stack_trace)
-        ):
-            res = _AddRuntimeAssertionsForInlineConstraintsPass(range_constraints)(gm)
-        assert res is not None
-        gm = res.graph_module
-
-
 def _rewrite_node(gm):
     for node in gm.graph.nodes:
         if node.target == torch.ops.higher_order._export_tracepoint:
@@ -1514,12 +1494,6 @@ def _export(
         dynamic_shapes,
         num_lifted,
     )
-    if strict:
-        _add_runtime_assertions_to_cond_in_subgraph(
-            range_constraints,
-            gm,
-            fake_mode,
-        )
 
     # Make module signatures.
     module_call_signatures = {}