diff --git a/pymc/logprob/transforms.py b/pymc/logprob/transforms.py
index 0b8d494276..5f751b5bf1 100644
--- a/pymc/logprob/transforms.py
+++ b/pymc/logprob/transforms.py
@@ -448,7 +448,8 @@ def measurable_transform_logcdf(op: MeasurableTransform, value, *inputs, **kwarg
 
     backward_value = op.transform_elemwise.backward(value, *other_inputs)
 
-    # Some transformations, like squaring may produce multiple backward values
+    # Fail if transformation is not injective
+    # A TensorVariable is returned in 1-to-1 inversions, and a tuple in 1-to-many
     if isinstance(backward_value, tuple):
         raise NotImplementedError
 
@@ -469,6 +470,11 @@ def measurable_transform_icdf(op: MeasurableTransform, value, *inputs, **kwargs)
     input_icdf = _icdf_helper(measurable_input, value)
     icdf = op.transform_elemwise.forward(input_icdf, *other_inputs)
 
+    # Fail if transformation is not injective
+    # A TensorVariable is returned in 1-to-1 inversions, and a tuple in 1-to-many
+    if isinstance(op.transform_elemwise.backward(icdf, *other_inputs), tuple):
+        raise NotImplementedError
+
     return icdf
 
 
diff --git a/tests/logprob/test_transforms.py b/tests/logprob/test_transforms.py
index 785e2599fb..9960dff948 100644
--- a/tests/logprob/test_transforms.py
+++ b/tests/logprob/test_transforms.py
@@ -49,7 +49,7 @@
 
 from pymc.distributions.transforms import _default_transform, log, logodds
 from pymc.logprob.abstract import MeasurableVariable, _logprob
-from pymc.logprob.basic import conditional_logp, logp
+from pymc.logprob.basic import conditional_logp, icdf, logcdf, logp
 from pymc.logprob.transforms import (
     ArccoshTransform,
     ArcsinhTransform,
@@ -1080,3 +1080,37 @@ def test_check_jac_det(transform):
         elemwise=True,
         rv_var=pt.random.normal(0.5, 1, name="base_rv"),
     )
+
+
+def test_logcdf_measurable_transform():
+    x = pt.exp(pt.random.uniform(0, 1))
+    value = x.type()
+    logcdf_fn = pytensor.function([value], logcdf(x, value))
+
+    assert logcdf_fn(0) == -np.inf
+    np.testing.assert_almost_equal(logcdf_fn(np.exp(0.5)), np.log(0.5))
+    np.testing.assert_almost_equal(logcdf_fn(5), 0)
+
+
+def test_logcdf_measurable_non_injective_fails():
+    x = pt.abs(pt.random.uniform(0, 1))
+    value = x.type()
+    with pytest.raises(NotImplementedError):
+        logcdf(x, value)
+
+
+def test_icdf_measurable_transform():
+    x = pt.exp(pt.random.uniform(0, 1))
+    value = x.type()
+    icdf_fn = pytensor.function([value], icdf(x, value))
+
+    np.testing.assert_almost_equal(icdf_fn(1e-16), 1)
+    np.testing.assert_almost_equal(icdf_fn(0.5), np.exp(0.5))
+    np.testing.assert_almost_equal(icdf_fn(1 - 1e-16), np.e)
+
+
+def test_icdf_measurable_non_injective_fails():
+    x = pt.abs(pt.random.uniform(0, 1))
+    value = x.type()
+    with pytest.raises(NotImplementedError):
+        icdf(x, value)