diff --git a/tensorflow_probability/python/bijectors/bijector.py b/tensorflow_probability/python/bijectors/bijector.py
index 4de390e18c..46106fd288 100644
--- a/tensorflow_probability/python/bijectors/bijector.py
+++ b/tensorflow_probability/python/bijectors/bijector.py
@@ -511,6 +511,7 @@ def __init__(self,
     name = name_util.strip_invalid_chars(name)
     super(Bijector, self).__init__(name=name)
     self._name = name
+    # TODO(b/176242804): Infer `parameters` if not specified by the child class.
     self._parameters = self._no_dependency(parameters)
 
     self._graph_parents = self._no_dependency(graph_parents or [])
@@ -648,6 +649,8 @@ def parameters(self):
     # Remove "self", "__class__", or other special variables. These can appear
     # if the subclass used:
     # `parameters = dict(locals())`.
+    if self._parameters is None:
+      return None
     return {k: v for k, v in self._parameters.items()
             if not k.startswith('__') and k != 'self'}
 
@@ -689,6 +692,11 @@ def __eq__(self, other):
     return True
 
   def _get_parameterization(self):
+    if self.parameters is None:
+      # If a user-written bijector doesn't specify `parameters`, we must assume
+      # that all instances are unique.
+      # TODO(b/176242804): this can be removed if we always infer `parameters`.
+      return id(self)
     return self.parameters
 
   def __call__(self, value, name=None, **kwargs):
diff --git a/tensorflow_probability/python/bijectors/bijector_test.py b/tensorflow_probability/python/bijectors/bijector_test.py
index ab48289fef..c982da4655 100644
--- a/tensorflow_probability/python/bijectors/bijector_test.py
+++ b/tensorflow_probability/python/bijectors/bijector_test.py
@@ -280,6 +280,24 @@ def _get_parameterization(self):
     return id(self)
 
 
+class UnspecifiedParameters(tfb.Bijector):
+  """A bijector that fails to pass `parameters` to the base class."""
+
+  def __init__(self, loc):
+    self._loc = loc
+    super(UnspecifiedParameters, self).__init__(
+        validate_args=False,
+        is_constant_jacobian=True,
+        forward_min_event_ndims=0,
+        name='unspecified_parameters')
+
+  def _forward(self, x):
+    return x + self._loc
+
+  def _forward_log_det_jacobian(self, x):
+    return tf.constant(0., x.dtype)
+
+
 @test_util.test_all_tf_execution_regimes
 class BijectorTestEventNdims(test_util.TestCase):
 
@@ -440,6 +458,18 @@ def testUniqueCacheKey(self):
     self.assertLen(bijector_1._cache.weak_keys(direction='forward'), 1)
     self.assertLen(bijector_2._cache.weak_keys(direction='forward'), 1)
 
+  def testBijectorsWithUnspecifiedParametersDoNotShareCache(self):
+    bijector_1 = UnspecifiedParameters(loc=tf.constant(1., dtype=tf.float32))
+    bijector_2 = UnspecifiedParameters(loc=tf.constant(2., dtype=tf.float32))
+
+    x = tf.constant(3., dtype=tf.float32)
+    y_1 = bijector_1.forward(x)
+    y_2 = bijector_2.forward(x)
+
+    self.assertIsNot(y_1, y_2)
+    self.assertLen(bijector_1._cache.weak_keys(direction='forward'), 1)
+    self.assertLen(bijector_2._cache.weak_keys(direction='forward'), 1)
+
   def testInstanceCache(self):
     instance_cache_bijector = tfb.Exp()
     instance_cache_bijector._cache = cache_util.BijectorCache(
diff --git a/tensorflow_probability/python/version.py b/tensorflow_probability/python/version.py
index e18bcad27d..75fe14f9f7 100644
--- a/tensorflow_probability/python/version.py
+++ b/tensorflow_probability/python/version.py
@@ -17,7 +17,7 @@
 # We follow Semantic Versioning (https://semver.org/)
 _MAJOR_VERSION = '0'
 _MINOR_VERSION = '12'
-_PATCH_VERSION = '0'
+_PATCH_VERSION = '1'
 
 # When building releases, we can update this value on the release branch to
 # reflect the current release candidate ('rc0', 'rc1') or, finally, the official