diff --git a/_unittests/ut_export/test_jit.py b/_unittests/ut_export/test_jit.py
new file mode 100644
index 00000000..525eae01
--- /dev/null
+++ b/_unittests/ut_export/test_jit.py
@@ -0,0 +1,147 @@
+import inspect
+import unittest
+import torch
+from onnx_diagnostic.ext_test_case import (
+    ExtTestCase,
+    hide_stdout,
+    ignore_warnings,
+    requires_onnxscript,
+)
+from onnx_diagnostic.reference import ExtendedReferenceEvaluator
+from onnx_diagnostic.helpers.torch_test_helper import is_torchdynamo_exporting
+
+try:
+    from experimental_experiment.torch_interpreter import to_onnx
+except ImportError:
+    to_onnx = None
+
+
+has_scan_reverse = "reverse" in set(inspect.signature(torch.ops.higher_order.scan).parameters)
+
+
+@torch.jit.script_if_tracing
+def dummy_loop(padded: torch.Tensor, pos: torch.Tensor):
+    copy = torch.zeros(padded.shape)
+    for i in range(pos.shape[0]):
+        p = pos[i]
+        copy[i, :p] = padded[i, :p]
+    return copy
+
+
+def dummy_loop_with_scan(padded: torch.Tensor, pos: torch.Tensor):
+    def pad_row(padded, p):
+        row = torch.zeros((padded.shape[0],))
+        torch._check(p.item() > 0)
+        torch._check(p.item() < padded.shape[0])
+        # this check is not always true, we add it anyway to make this dimension >= 2
+        # and avoid raising an exception about dynamic dimension in {0, 1}
+        if is_torchdynamo_exporting():
+            torch._check(p.item() > 1)
+        row[: p.item()] = padded[: p.item()]
+        return (row,)
+
+    if has_scan_reverse:
+        # torch==2.6
+        return torch.ops.higher_order.scan(
+            pad_row, [], [padded, pos], additional_inputs=[], reverse=False, dim=0
+        )
+    return torch.ops.higher_order.scan(pad_row, [], [padded, pos], [])
+
+
+def select_when_exporting(f, f_scan):
+    return f_scan if is_torchdynamo_exporting() else f
+
+
+class TestJit(ExtTestCase):
+    def test_dummy_loop(self):
+        x = torch.randn((5, 6))
+        y = torch.arange(5, dtype=torch.int64) + 1
+        res = dummy_loop(x, y)
+        res_scan = dummy_loop_with_scan(x, y)
+        self.assertEqualArray(res, res_scan[0])
+
+    @hide_stdout()
+    @ignore_warnings(UserWarning)
+    @requires_onnxscript("0.4")
+    def test_export_loop_onnxscript(self):
+        class Model(torch.nn.Module):
+            def forward(self, images, position):
+                return select_when_exporting(dummy_loop, dummy_loop_with_scan)(
+                    images, position
+                )
+
+        model = Model()
+        x = torch.randn((5, 6))
+        y = torch.arange(5, dtype=torch.int64) + 1
+        expected = model(x, y)
+
+        name = self.get_dump_file("test_export_loop_onnxscript.onnx")
+        torch.onnx.export(
+            model,
+            (x, y),
+            name,
+            dynamic_axes={"images": {0: "batch", 1: "maxdim"}, "position": {0: "batch"}},
+            dynamo=False,
+        )
+        ref = ExtendedReferenceEvaluator(name)
+        feeds = dict(images=x.numpy(), position=y.numpy())
+        got = ref.run(None, feeds)[0]
+        self.assertEqualArray(expected, got)
+
+        DYN = torch.export.Dim.DYNAMIC
+        ep = torch.export.export(
+            model,
+            (x, y),
+            dynamic_shapes={"images": {0: DYN, 1: DYN}, "position": {0: DYN}},
+            strict=False,
+        )
+        self.assertNotEmpty(ep)
+
+        name2 = self.get_dump_file("test_export_loop_onnxscript.dynamo.onnx")
+        torch.onnx.export(
+            model,
+            (x, y),
+            name2,
+            dynamic_shapes={"images": {0: "batch", 1: "maxdim"}, "position": {0: "batch"}},
+            dynamo=True,
+            fallback=False,
+        )
+        import onnxruntime
+
+        ref = onnxruntime.InferenceSession(name2, providers=["CPUExecutionProvider"])
+        feeds = dict(images=x.numpy(), position=y.numpy())
+        got = ref.run(None, feeds)[0]
+        self.assertEqualArray(expected, got)
+
+    @hide_stdout()
+    @ignore_warnings(UserWarning)
+    @unittest.skipIf(to_onnx is None, "missing to_onnx")
+    def test_export_loop_custom(self):
+        class Model(torch.nn.Module):
+            def forward(self, images, position):
+                return select_when_exporting(dummy_loop, dummy_loop_with_scan)(
+                    images, position
+                )
+
+        model = Model()
+        x = torch.randn((5, 6))
+        y = torch.arange(5, dtype=torch.int64) + 1
+        expected = model(x, y)
+
+        name2 = self.get_dump_file("test_export_loop.custom.onnx")
+        to_onnx(
+            model,
+            (x, y),
+            filename=name2,
+            dynamic_shapes={"images": {0: "batch", 1: "maxdim"}, "position": {0: "batch"}},
+        )
+        import onnxruntime
+
+        ref = onnxruntime.InferenceSession(name2, providers=["CPUExecutionProvider"])
+        feeds = dict(images=x.numpy(), position=y.numpy())
+        got = ref.run(None, feeds)[0]
+        self.assertEqualArray(expected, got)
+
+
+if __name__ == "__main__":
+    unittest.main(verbosity=2)