diff --git a/pyro/ops/provenance.py b/pyro/ops/provenance.py
index 02a515c7e5..5058e66414 100644
--- a/pyro/ops/provenance.py
+++ b/pyro/ops/provenance.py
@@ -46,14 +46,15 @@ def __new__(cls, data: torch.Tensor, provenance=frozenset(), **kwargs):
         assert not isinstance(data, ProvenanceTensor)
         if not provenance:
             return data
-        return super().__new__(cls)
+        ret = data.as_subclass(cls)
+        ret._t = data  # this makes sure that detach_provenance always
+        # returns the same object. This is important when
+        # using the tensor as key in a dict, e.g. the global
+        # param store
+        return ret
 
     def __init__(self, data, provenance=frozenset()):
         assert isinstance(provenance, frozenset)
-        if isinstance(data, ProvenanceTensor):
-            provenance |= data._provenance
-            data = data._t
-        self._t = data
         self._provenance = provenance
 
     def __repr__(self):
diff --git a/tests/ops/test_provenance.py b/tests/ops/test_provenance.py
new file mode 100644
index 0000000000..818d9d83ca
--- /dev/null
+++ b/tests/ops/test_provenance.py
@@ -0,0 +1,45 @@
+# Copyright Contributors to the Pyro project.
+# SPDX-License-Identifier: Apache-2.0
+
+import pytest
+import torch
+
+from pyro.ops.provenance import ProvenanceTensor
+from tests.common import assert_equal, requires_cuda
+
+
+@requires_cuda
+@pytest.mark.parametrize(
+    "dtype1",
+    [
+        torch.float16,
+        torch.float32,
+        torch.float64,
+        torch.int8,
+        torch.int16,
+        torch.int32,
+        torch.int64,
+        torch.uint8,
+    ],
+)
+@pytest.mark.parametrize(
+    "dtype2",
+    [
+        torch.float16,
+        torch.float32,
+        torch.float64,
+        torch.int8,
+        torch.int16,
+        torch.int32,
+        torch.int64,
+        torch.uint8,
+    ],
+)
+def test_provenance_tensor(dtype1, dtype2):
+    device = torch.device("cuda")
+    x = torch.tensor([1, 2, 3], dtype=dtype1)
+    y = ProvenanceTensor(x, frozenset(["x"]))
+    z = torch.as_tensor(y, device=device, dtype=dtype2)
+
+    assert x.shape == y.shape == z.shape
+    assert_equal(x, z.cpu())