diff --git a/tests/infer/reparam/test_split.py b/tests/infer/reparam/test_split.py
index 6337069ea0..0167f5778d 100644
--- a/tests/infer/reparam/test_split.py
+++ b/tests/infer/reparam/test_split.py
@@ -13,8 +13,7 @@
 
 from .util import check_init_reparam
 
-
-@pytest.mark.parametrize(
+event_shape_splits_dim = pytest.mark.parametrize(
     "event_shape,splits,dim",
     [
         ((6,), [2, 1, 3], -1),
@@ -31,7 +30,13 @@
     ],
     ids=str,
 )
-@pytest.mark.parametrize("batch_shape", [(), (4,), (3, 2)], ids=str)
+
+
+batch_shape = pytest.mark.parametrize("batch_shape", [(), (4,), (3, 2)], ids=str)
+
+
+@event_shape_splits_dim
+@batch_shape
 def test_normal(batch_shape, event_shape, splits, dim):
     shape = batch_shape + event_shape
     loc = torch.empty(shape).uniform_(-1.0, 1.0).requires_grad_()
@@ -72,24 +77,8 @@ def model():
     assert_close(actual_grads, expected_grads)
 
 
-@pytest.mark.parametrize(
-    "event_shape,splits,dim",
-    [
-        ((6,), [2, 1, 3], -1),
-        (
-            (
-                2,
-                5,
-            ),
-            [2, 3],
-            -1,
-        ),
-        ((4, 2), [1, 3], -2),
-        ((2, 3, 1), [1, 2], -2),
-    ],
-    ids=str,
-)
-@pytest.mark.parametrize("batch_shape", [(), (4,), (3, 2)], ids=str)
+@event_shape_splits_dim
+@batch_shape
 def test_init(batch_shape, event_shape, splits, dim):
     shape = batch_shape + event_shape
     loc = torch.empty(shape).uniform_(-1.0, 1.0)
@@ -100,3 +89,53 @@ def model():
             return pyro.sample("x", dist.Normal(loc, scale).to_event(len(event_shape)))
 
     check_init_reparam(model, SplitReparam(splits, dim))
+
+
+@batch_shape
+def test_transformed_distribution(batch_shape):
+    num_samples = 10
+
+    transform = dist.transforms.StackTransform(
+        [
+            dist.transforms.OrderedTransform(),
+            dist.transforms.DiscreteCosineTransform(),
+            dist.transforms.HaarTransform(),
+        ],
+        dim=-1,
+    )
+
+    num_transforms = len(transform.transforms)
+
+    def model():
+        scale_tril = pyro.sample("scale_tril", dist.LKJCholesky(num_transforms, 1))
+        with pyro.plate_stack("plates", batch_shape):
+            x_dist = dist.TransformedDistribution(
+                dist.MultivariateNormal(
+                    torch.zeros(num_samples, num_transforms), scale_tril=scale_tril
+                ).to_event(1),
+                [transform],
+            )
+            return pyro.sample("x", x_dist)
+
+    assert model().shape == batch_shape + (num_samples, num_transforms)
+
+    pyro.clear_param_store()
+    guide = pyro.infer.autoguide.AutoMultivariateNormal(model)
+    guide_sites = guide()
+
+    assert guide_sites["x"].shape == batch_shape + (num_samples, num_transforms)
+
+    for sections in [[1, 1, 1], [1, 2], [2, 1]]:
+        split_model = pyro.poutine.reparam(
+            model, config={"x": SplitReparam(sections, -1)}
+        )
+
+        pyro.clear_param_store()
+        guide = pyro.infer.autoguide.AutoMultivariateNormal(split_model)
+        guide_sites = guide()
+
+        for n, section in enumerate(sections):
+            assert guide_sites[f"x_split_{n}"].shape == batch_shape + (
+                num_samples,
+                section,
+            )