diff --git a/tensorflow_probability/python/distributions/BUILD b/tensorflow_probability/python/distributions/BUILD
index 90cb00d01a..c42e793ebb 100644
--- a/tensorflow_probability/python/distributions/BUILD
+++ b/tensorflow_probability/python/distributions/BUILD
@@ -4540,6 +4540,7 @@ multi_substrate_py_test(
     tags = ["colab-smoke"],
     deps = [
         ":beta",
+        ":dirichlet",
         ":exponential",
         ":independent",
         ":joint_distribution_auto_batched",
@@ -4552,6 +4553,7 @@ multi_substrate_py_test(
         ":normal",
         ":sample",
         ":transformed_distribution",
+        ":uniform",
         # numpy dep,
         # scipy dep,
         # tensorflow dep,
diff --git a/tensorflow_probability/python/distributions/transformed_distribution.py b/tensorflow_probability/python/distributions/transformed_distribution.py
index 9e77d68506..8d05d607bc 100644
--- a/tensorflow_probability/python/distributions/transformed_distribution.py
+++ b/tensorflow_probability/python/distributions/transformed_distribution.py
@@ -388,7 +388,7 @@ def _log_prob(self, y, **kwargs):
     return tf.reduce_logsumexp(tf.stack(lp_on_fibers), axis=0)
 
   def _prob(self, y, **kwargs):
-    if not hasattr(self.distribution, '_prob'):
+    if not hasattr(self.distribution, '_prob') or self.bijector._is_injective:  # pylint: disable=protected-access
       return tf.exp(self._log_prob(y, **kwargs))
     distribution_kwargs, bijector_kwargs = self._kwargs_split_fn(kwargs)
 
@@ -400,9 +400,6 @@ def _prob(self, y, **kwargs):
         )
     ildj = self.bijector.inverse_log_det_jacobian(
         y, event_ndims=event_ndims, **bijector_kwargs)
-    if self.bijector._is_injective:  # pylint: disable=protected-access
-      base_prob = self.distribution.prob(x, **distribution_kwargs)
-      return base_prob * tf.exp(tf.cast(ildj, base_prob.dtype))
 
     # Compute prob on each element of the inverse image.
     prob_on_fibers = []
diff --git a/tensorflow_probability/python/distributions/transformed_distribution_test.py b/tensorflow_probability/python/distributions/transformed_distribution_test.py
index 53416a55ac..64e3294f3f 100644
--- a/tensorflow_probability/python/distributions/transformed_distribution_test.py
+++ b/tensorflow_probability/python/distributions/transformed_distribution_test.py
@@ -42,6 +42,7 @@
 from tensorflow_probability.python.bijectors import split
 from tensorflow_probability.python.bijectors import tanh
 from tensorflow_probability.python.distributions import beta
+from tensorflow_probability.python.distributions import dirichlet
 from tensorflow_probability.python.distributions import exponential
 from tensorflow_probability.python.distributions import independent
 from tensorflow_probability.python.distributions import joint_distribution_auto_batched as jdab
@@ -54,6 +55,7 @@
 from tensorflow_probability.python.distributions import normal as normal_lib
 from tensorflow_probability.python.distributions import sample as sample_lib
 from tensorflow_probability.python.distributions import transformed_distribution
+from tensorflow_probability.python.distributions import uniform
 from tensorflow_probability.python.internal import hypothesis_testlib as tfp_hps
 from tensorflow_probability.python.internal import prefer_static as ps
 from tensorflow_probability.python.internal import tensorshape_util
@@ -650,6 +652,26 @@ def testLogProbRatio(self):
     #     oracle_64, d0.log_prob(x0) - d1.log_prob(x1),
     #     rtol=0., atol=0.007)
 
+  @test_util.numpy_disable_test_missing_functionality('b/306384754')
+  def testLogProbMatchesProbDirichlet(self):
+    # This was https://github.com/tensorflow/probability/issues/1761
+    scaled_dir = transformed_distribution.TransformedDistribution(
+        distribution=dirichlet.Dirichlet([2.0, 3.0]),
+        bijector=scale_lib.Scale(2.0))
+    x = np.array([0.2, 1.8], dtype=np.float32)
+    self.assertAllClose(scaled_dir.prob(x),
+                        tf.exp(scaled_dir.log_prob(x)))
+
+  @test_util.numpy_disable_test_missing_functionality('b/306384754')
+  def testLogProbMatchesProbUniform(self):
+    # Uniform does not define _log_prob
+    scaled_uniform = transformed_distribution.TransformedDistribution(
+        distribution=uniform.Uniform(),
+        bijector=scale_lib.Scale(2.0))
+    x = np.array([0.2], dtype=np.float32)
+    self.assertAllClose(scaled_uniform.prob(x),
+                        tf.exp(scaled_uniform.log_prob(x)))
+
 
 @test_util.test_all_tf_execution_regimes
 class ScalarToMultiTest(test_util.TestCase):