diff --git a/tensorflow_probability/python/distributions/transformed_distribution.py b/tensorflow_probability/python/distributions/transformed_distribution.py
index 8d05d607bc..9f496cd28f 100644
--- a/tensorflow_probability/python/distributions/transformed_distribution.py
+++ b/tensorflow_probability/python/distributions/transformed_distribution.py
@@ -747,6 +747,10 @@ def _kl_transformed_transformed(a, b, name=None):
   """
   with tf.name_scope(name or 'kl_transformed_transformed'):
     if a.bijector == b.bijector:
+      if not a.bijector._is_injective:  # pylint: disable=protected-access
+        raise NotImplementedError(
+            'Unable to calculate KL divergence between {} and {} because '
+            'their bijector {} is not injective.'.format(a, b, a.bijector))
       return kullback_leibler.kl_divergence(a.distribution, b.distribution)
   raise NotImplementedError(
       'Unable to calculate KL divergence between {} and {} because '
diff --git a/tensorflow_probability/python/distributions/transformed_distribution_test.py b/tensorflow_probability/python/distributions/transformed_distribution_test.py
index cbc02404a2..7fe0947cc0 100644
--- a/tensorflow_probability/python/distributions/transformed_distribution_test.py
+++ b/tensorflow_probability/python/distributions/transformed_distribution_test.py
@@ -577,6 +577,21 @@ def testTransformedKLDifferentBijectorFails(self):
         NotImplementedError, r'their bijectors are not equal'):
       kullback_leibler.kl_divergence(d1, d2)
 
+  def testTransformedKLNonInjectiveBijectorFails(self):
+    # |X| has the same law for X ~ N(-1, 1) and X ~ N(1, 1), while the KL of
+    # the base distributions is 2, so the base KL must not be returned when
+    # the shared bijector is not injective.
+    d1 = transformed_distribution.TransformedDistribution(
+        normal_lib.Normal(loc=-1., scale=1.),
+        bijector=absolute_value.AbsoluteValue(),
+        validate_args=True)
+    d2 = transformed_distribution.TransformedDistribution(
+        normal_lib.Normal(loc=1., scale=1.),
+        bijector=absolute_value.AbsoluteValue(),
+        validate_args=True)
+    with self.assertRaisesRegex(NotImplementedError, r'is not injective'):
+      kullback_leibler.kl_divergence(d1, d2)
+
   def testTransformedNormalNormalKL(self):
     batch_size = 6
     mu_a = np.array([3.0] * batch_size).astype(np.float32)