diff --git a/tests/test_tilelang_copy_templates.py b/tests/test_tilelang_copy_templates.py
new file mode 100644
index 0000000..ed02bac
--- /dev/null
+++ b/tests/test_tilelang_copy_templates.py
@@ -0,0 +1,58 @@
+from __future__ import annotations
+
+import importlib.util
+
+import pytest
+import torch
+
+from operator_runtime.testing import require_cuda
+
+pytestmark = pytest.mark.skipif(
+    importlib.util.find_spec("tilelang") is None,
+    reason="tilelang is not installed",
+)
+
+
+@pytest.mark.parametrize(
+    ("copy_fn_name", "copy_out_fn_name", "module_name"),
+    [
+        ("copy_eager", "copy_eager_", "ops.common.tilelang.eager_copy"),
+        ("copy_lazy_out_idx", "copy_lazy_out_idx_", "ops.common.tilelang.lazy_out_idx_copy"),
+    ],
+)
+def test_tilelang_copy_templates_match_torch(copy_fn_name, copy_out_fn_name, module_name) -> None:
+    require_cuda()
+    module = __import__(module_name, fromlist=[copy_fn_name, copy_out_fn_name])
+    copy_fn = getattr(module, copy_fn_name)
+    copy_out_fn = getattr(module, copy_out_fn_name)
+
+    src = torch.randn((1024,), dtype=torch.float32, device="cuda")
+    out = copy_fn(src)
+    torch.testing.assert_close(out, src)
+
+    user_out = torch.empty_like(src)
+    returned = copy_out_fn(user_out, src)
+    assert returned is user_out
+    torch.testing.assert_close(user_out, src)
+
+
+@pytest.mark.parametrize(
+    ("copy_out_fn_name", "module_name", "message"),
+    [
+        ("copy_eager_", "ops.common.tilelang.eager_copy", "matching shapes"),
+        ("copy_lazy_out_idx_", "ops.common.tilelang.lazy_out_idx_copy", "matching shapes"),
+    ],
+)
+def test_tilelang_copy_templates_reject_mismatched_out(
+    copy_out_fn_name,
+    module_name,
+    message,
+) -> None:
+    require_cuda()
+    module = __import__(module_name, fromlist=[copy_out_fn_name])
+    copy_out_fn = getattr(module, copy_out_fn_name)
+
+    src = torch.randn((1024,), dtype=torch.float32, device="cuda")
+    out = torch.empty((512,), dtype=torch.float32, device="cuda")
+    with pytest.raises(ValueError, match=message):
+        copy_out_fn(out, src)