diff --git a/pyro/ops/provenance.py b/pyro/ops/provenance.py
index ff5e64ad7f..bf67d0d15a 100644
--- a/pyro/ops/provenance.py
+++ b/pyro/ops/provenance.py
@@ -10,6 +10,13 @@
 _Tensor = TypeVar("_Tensor", bound=torch.Tensor)
 
 
+def _is_size(x: object) -> bool:
+    # ``torch.Size`` subclasses ``tuple``, so the pytree helpers below would
+    # otherwise flatten it and rebuild it as a plain tuple. Treating it as a
+    # leaf keeps the type intact.
+    return isinstance(x, torch.Size)
+
+
 class ProvenanceTensor(torch.Tensor):
     """
     Provenance tracking implementation in Pytorch.
@@ -85,6 +92,13 @@ def track_provenance(x, provenance: frozenset):
 track_provenance.register(torch.Tensor)(ProvenanceTensor)
 
 
+@track_provenance.register(torch.Size)
+def _track_provenance_size(x, provenance: frozenset):
+    # A torch.Size holds plain ints, so there is no provenance to add; return
+    # it unchanged rather than letting the tuple handler rebuild it.
+    return x
+
+
 @track_provenance.register(frozenset)
 @track_provenance.register(set)
 def _track_provenance_set(x, provenance: frozenset):
@@ -95,7 +109,9 @@ def _track_provenance_set(x, provenance: frozenset):
 @track_provenance.register(tuple)
 @track_provenance.register(dict)
 def _track_provenance_pytree(x, provenance: frozenset):
-    return tree_map(partial(track_provenance, provenance=provenance), x)
+    return tree_map(
+        partial(track_provenance, provenance=provenance), x, is_leaf=_is_size
+    )
 
 
 @track_provenance.register
@@ -123,6 +139,11 @@ def _extract_provenance_tensor(x):
     return x._t, x._provenance
 
 
+@extract_provenance.register(torch.Size)
+def _extract_provenance_size(x):
+    return x, frozenset()
+
+
 @extract_provenance.register(frozenset)
 @extract_provenance.register(set)
 def _extract_provenance_set(x):
@@ -140,7 +161,7 @@ def _extract_provenance_set(x):
 @extract_provenance.register(tuple)
 @extract_provenance.register(dict)
 def _extract_provenance_pytree(x):
-    flat_args, spec = tree_flatten(x)
+    flat_args, spec = tree_flatten(x, is_leaf=_is_size)
     xs = []
     provenance = frozenset()
     for x, p in map(extract_provenance, flat_args):
diff --git a/tests/ops/test_provenance.py b/tests/ops/test_provenance.py
index 478ae27f05..05e70646fb 100644
--- a/tests/ops/test_provenance.py
+++ b/tests/ops/test_provenance.py
@@ -4,7 +4,16 @@
 import pytest
 import torch
 
-from pyro.ops.provenance import ProvenanceTensor, get_provenance, track_provenance
+import pyro
+import pyro.distributions as dist
+from pyro.infer.inspect import get_model_relations
+from pyro.ops.provenance import (
+    ProvenanceTensor,
+    detach_provenance,
+    extract_provenance,
+    get_provenance,
+    track_provenance,
+)
 from tests.common import assert_equal, requires_cuda
 
 
@@ -66,3 +75,53 @@ def test_track_provenance(x):
     old_provenance = get_provenance(x)
     provenance = old_provenance | new_provenance
     assert provenance == get_provenance(track_provenance(x, new_provenance))
+
+
+@pytest.mark.parametrize(
+    "x",
+    [
+        torch.Size([3]),
+        torch.Size([2, 5]),
+        torch.Size([]),
+        [(torch.Size([3]),), {}],
+        [(), {"shape": torch.Size([2, 5])}],
+        [(torch.zeros(2), torch.Size([3])), {}],
+    ],
+    ids=["size", "size_2d", "size_empty", "in_args", "in_kwargs", "mixed_with_tensor"],
+)
+def test_provenance_preserves_torch_size(x):
+    """torch.Size subclasses tuple, so it must not be rebuilt as a plain tuple."""
+
+    def assert_sizes_intact(original, result):
+        if isinstance(original, torch.Tensor):
+            return  # tensors are legitimately wrapped/unwrapped
+        assert type(original) is type(result)
+        if isinstance(original, torch.Size):
+            assert result == original
+        elif isinstance(original, (list, tuple)):
+            for a, b in zip(original, result):
+                assert_sizes_intact(a, b)
+        elif isinstance(original, dict):
+            for key in original:
+                assert_sizes_intact(original[key], result[key])
+
+    assert_sizes_intact(x, track_provenance(x, frozenset({"a"})))
+    assert_sizes_intact(x, extract_provenance(x)[0])
+    assert_sizes_intact(x, detach_provenance(x))
+
+
+def test_multinomial_render_model():
+    """https://github.com/pyro-ppl/pyro/issues/3436"""
+
+    def model():
+        probs = pyro.param("probs", torch.tensor([0.1, 0.2, 0.7]))
+        return pyro.sample("y", dist.Multinomial(total_count=10, probs=probs))
+
+    relations = get_model_relations(model)
+    assert "y" in relations["sample_sample"] or "y" in relations["sample_param"]
+
+
+def test_provenance_tensor_new_with_size():
+    """Tensor.new() reads a torch.Size as a shape but a tuple as data."""
+    x = ProvenanceTensor(torch.zeros(4, dtype=torch.long), frozenset({"x"}))
+    assert tuple(x.new(torch.Size([3])).shape) == (3,)