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diff --git a/tensorflow/python/kernel_tests/distributions/laplace_test.py b/tensorflow/python/kernel_tests/distributions/laplace_test.py
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+++ b/tensorflow/python/kernel_tests/distributions/laplace_test.py
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+# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ==============================================================================
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import importlib
+
+import numpy as np
+
+from tensorflow.python.client import session
+from tensorflow.python.framework import constant_op
+from tensorflow.python.framework import tensor_shape
+from tensorflow.python.ops import nn_ops
+from tensorflow.python.ops.distributions import laplace as laplace_lib
+from tensorflow.python.platform import test
+
+from tensorflow.python.platform import tf_logging
+
+
+def try_import(name):  # pylint: disable=invalid-name
+  module = None
+  try:
+    module = importlib.import_module(name)
+  except ImportError as e:
+    tf_logging.warning("Could not import %s: %s" % (name, str(e)))
+  return module
+
+
+stats = try_import("scipy.stats")
+
+
+class LaplaceTest(test.TestCase):
+
+  def testLaplaceShape(self):
+    with self.test_session():
+      loc = constant_op.constant([3.0] * 5)
+      scale = constant_op.constant(11.0)
+      laplace = laplace_lib.Laplace(loc=loc, scale=scale)
+
+      self.assertEqual(laplace.batch_shape_tensor().eval(), (5,))
+      self.assertEqual(laplace.batch_shape, tensor_shape.TensorShape([5]))
+      self.assertAllEqual(laplace.event_shape_tensor().eval(), [])
+      self.assertEqual(laplace.event_shape, tensor_shape.TensorShape([]))
+
+  def testLaplaceLogPDF(self):
+    with self.test_session():
+      batch_size = 6
+      loc = constant_op.constant([2.0] * batch_size)
+      scale = constant_op.constant([3.0] * batch_size)
+      loc_v = 2.0
+      scale_v = 3.0
+      x = np.array([2.5, 2.5, 4.0, 0.1, 1.0, 2.0], dtype=np.float32)
+      laplace = laplace_lib.Laplace(loc=loc, scale=scale)
+      log_pdf = laplace.log_prob(x)
+      self.assertEqual(log_pdf.get_shape(), (6,))
+      if not stats:
+        return
+      expected_log_pdf = stats.laplace.logpdf(x, loc_v, scale=scale_v)
+      self.assertAllClose(log_pdf.eval(), expected_log_pdf)
+
+      pdf = laplace.prob(x)
+      self.assertEqual(pdf.get_shape(), (6,))
+      self.assertAllClose(pdf.eval(), np.exp(expected_log_pdf))
+
+  def testLaplaceLogPDFMultidimensional(self):
+    with self.test_session():
+      batch_size = 6
+      loc = constant_op.constant([[2.0, 4.0]] * batch_size)
+      scale = constant_op.constant([[3.0, 4.0]] * batch_size)
+      loc_v = np.array([2.0, 4.0])
+      scale_v = np.array([3.0, 4.0])
+      x = np.array([[2.5, 2.5, 4.0, 0.1, 1.0, 2.0]], dtype=np.float32).T
+      laplace = laplace_lib.Laplace(loc=loc, scale=scale)
+      log_pdf = laplace.log_prob(x)
+      log_pdf_values = log_pdf.eval()
+      self.assertEqual(log_pdf.get_shape(), (6, 2))
+
+      pdf = laplace.prob(x)
+      pdf_values = pdf.eval()
+      self.assertEqual(pdf.get_shape(), (6, 2))
+      if not stats:
+        return
+      expected_log_pdf = stats.laplace.logpdf(x, loc_v, scale=scale_v)
+      self.assertAllClose(log_pdf_values, expected_log_pdf)
+      self.assertAllClose(pdf_values, np.exp(expected_log_pdf))
+
+  def testLaplaceLogPDFMultidimensionalBroadcasting(self):
+    with self.test_session():
+      batch_size = 6
+      loc = constant_op.constant([[2.0, 4.0]] * batch_size)
+      scale = constant_op.constant(3.0)
+      loc_v = np.array([2.0, 4.0])
+      scale_v = 3.0
+      x = np.array([[2.5, 2.5, 4.0, 0.1, 1.0, 2.0]], dtype=np.float32).T
+      laplace = laplace_lib.Laplace(loc=loc, scale=scale)
+      log_pdf = laplace.log_prob(x)
+      log_pdf_values = log_pdf.eval()
+      self.assertEqual(log_pdf.get_shape(), (6, 2))
+
+      pdf = laplace.prob(x)
+      pdf_values = pdf.eval()
+      self.assertEqual(pdf.get_shape(), (6, 2))
+      if not stats:
+        return
+      expected_log_pdf = stats.laplace.logpdf(x, loc_v, scale=scale_v)
+      self.assertAllClose(log_pdf_values, expected_log_pdf)
+      self.assertAllClose(pdf_values, np.exp(expected_log_pdf))
+
+  def testLaplaceCDF(self):
+    with self.test_session():
+      batch_size = 6
+      loc = constant_op.constant([2.0] * batch_size)
+      scale = constant_op.constant([3.0] * batch_size)
+      loc_v = 2.0
+      scale_v = 3.0
+      x = np.array([2.5, 2.5, 4.0, 0.1, 1.0, 2.0], dtype=np.float32)
+
+      laplace = laplace_lib.Laplace(loc=loc, scale=scale)
+
+      cdf = laplace.cdf(x)
+      self.assertEqual(cdf.get_shape(), (6,))
+      if not stats:
+        return
+      expected_cdf = stats.laplace.cdf(x, loc_v, scale=scale_v)
+      self.assertAllClose(cdf.eval(), expected_cdf)
+
+  def testLaplaceLogCDF(self):
+    with self.test_session():
+      batch_size = 6
+      loc = constant_op.constant([2.0] * batch_size)
+      scale = constant_op.constant([3.0] * batch_size)
+      loc_v = 2.0
+      scale_v = 3.0
+      x = np.array([-2.5, 2.5, -4.0, 0.1, 1.0, 2.0], dtype=np.float32)
+
+      laplace = laplace_lib.Laplace(loc=loc, scale=scale)
+
+      cdf = laplace.log_cdf(x)
+      self.assertEqual(cdf.get_shape(), (6,))
+      if not stats:
+        return
+      expected_cdf = stats.laplace.logcdf(x, loc_v, scale=scale_v)
+      self.assertAllClose(cdf.eval(), expected_cdf)
+
+  def testLaplaceLogSurvivalFunction(self):
+    with self.test_session():
+      batch_size = 6
+      loc = constant_op.constant([2.0] * batch_size)
+      scale = constant_op.constant([3.0] * batch_size)
+      loc_v = 2.0
+      scale_v = 3.0
+      x = np.array([-2.5, 2.5, -4.0, 0.1, 1.0, 2.0], dtype=np.float32)
+
+      laplace = laplace_lib.Laplace(loc=loc, scale=scale)
+
+      sf = laplace.log_survival_function(x)
+      self.assertEqual(sf.get_shape(), (6,))
+      if not stats:
+        return
+      expected_sf = stats.laplace.logsf(x, loc_v, scale=scale_v)
+      self.assertAllClose(sf.eval(), expected_sf)
+
+  def testLaplaceMean(self):
+    with self.test_session():
+      loc_v = np.array([1.0, 3.0, 2.5])
+      scale_v = np.array([1.0, 4.0, 5.0])
+      laplace = laplace_lib.Laplace(loc=loc_v, scale=scale_v)
+      self.assertEqual(laplace.mean().get_shape(), (3,))
+      if not stats:
+        return
+      expected_means = stats.laplace.mean(loc_v, scale=scale_v)
+      self.assertAllClose(laplace.mean().eval(), expected_means)
+
+  def testLaplaceMode(self):
+    with self.test_session():
+      loc_v = np.array([0.5, 3.0, 2.5])
+      scale_v = np.array([1.0, 4.0, 5.0])
+      laplace = laplace_lib.Laplace(loc=loc_v, scale=scale_v)
+      self.assertEqual(laplace.mode().get_shape(), (3,))
+      self.assertAllClose(laplace.mode().eval(), loc_v)
+
+  def testLaplaceVariance(self):
+    with self.test_session():
+      loc_v = np.array([1.0, 3.0, 2.5])
+      scale_v = np.array([1.0, 4.0, 5.0])
+      laplace = laplace_lib.Laplace(loc=loc_v, scale=scale_v)
+      self.assertEqual(laplace.variance().get_shape(), (3,))
+      if not stats:
+        return
+      expected_variances = stats.laplace.var(loc_v, scale=scale_v)
+      self.assertAllClose(laplace.variance().eval(), expected_variances)
+
+  def testLaplaceStd(self):
+    with self.test_session():
+      loc_v = np.array([1.0, 3.0, 2.5])
+      scale_v = np.array([1.0, 4.0, 5.0])
+      laplace = laplace_lib.Laplace(loc=loc_v, scale=scale_v)
+      self.assertEqual(laplace.stddev().get_shape(), (3,))
+      if not stats:
+        return
+      expected_stddev = stats.laplace.std(loc_v, scale=scale_v)
+      self.assertAllClose(laplace.stddev().eval(), expected_stddev)
+
+  def testLaplaceEntropy(self):
+    with self.test_session():
+      loc_v = np.array([1.0, 3.0, 2.5])
+      scale_v = np.array([1.0, 4.0, 5.0])
+      laplace = laplace_lib.Laplace(loc=loc_v, scale=scale_v)
+      self.assertEqual(laplace.entropy().get_shape(), (3,))
+      if not stats:
+        return
+      expected_entropy = stats.laplace.entropy(loc_v, scale=scale_v)
+      self.assertAllClose(laplace.entropy().eval(), expected_entropy)
+
+  def testLaplaceSample(self):
+    with session.Session():
+      loc_v = 4.0
+      scale_v = 3.0
+      loc = constant_op.constant(loc_v)
+      scale = constant_op.constant(scale_v)
+      n = 100000
+      laplace = laplace_lib.Laplace(loc=loc, scale=scale)
+      samples = laplace.sample(n, seed=137)
+      sample_values = samples.eval()
+      self.assertEqual(samples.get_shape(), (n,))
+      self.assertEqual(sample_values.shape, (n,))
+      if not stats:
+        return
+      self.assertAllClose(
+          sample_values.mean(),
+          stats.laplace.mean(
+              loc_v, scale=scale_v),
+          rtol=0.05,
+          atol=0.)
+      self.assertAllClose(
+          sample_values.var(),
+          stats.laplace.var(loc_v, scale=scale_v),
+          rtol=0.05,
+          atol=0.)
+      self.assertTrue(self._kstest(loc_v, scale_v, sample_values))
+
+  def testLaplaceSampleMultiDimensional(self):
+    with session.Session():
+      loc_v = np.array([np.arange(1, 101, dtype=np.float32)])  # 1 x 100
+      scale_v = np.array([np.arange(1, 11, dtype=np.float32)]).T  # 10 x 1
+      laplace = laplace_lib.Laplace(loc=loc_v, scale=scale_v)
+      n = 10000
+      samples = laplace.sample(n, seed=137)
+      sample_values = samples.eval()
+      self.assertEqual(samples.get_shape(), (n, 10, 100))
+      self.assertEqual(sample_values.shape, (n, 10, 100))
+      zeros = np.zeros_like(loc_v + scale_v)  # 10 x 100
+      loc_bc = loc_v + zeros
+      scale_bc = scale_v + zeros
+      if not stats:
+        return
+      self.assertAllClose(
+          sample_values.mean(axis=0),
+          stats.laplace.mean(
+              loc_bc, scale=scale_bc),
+          rtol=0.35,
+          atol=0.)
+      self.assertAllClose(
+          sample_values.var(axis=0),
+          stats.laplace.var(loc_bc, scale=scale_bc),
+          rtol=0.10,
+          atol=0.)
+      fails = 0
+      trials = 0
+      for ai, a in enumerate(np.reshape(loc_v, [-1])):
+        for bi, b in enumerate(np.reshape(scale_v, [-1])):
+          s = sample_values[:, bi, ai]
+          trials += 1
+          fails += 0 if self._kstest(a, b, s) else 1
+      self.assertLess(fails, trials * 0.03)
+
+  def _kstest(self, loc, scale, samples):
+    # Uses the Kolmogorov-Smirnov test for goodness of fit.
+    if not stats:
+      return True  # If scipy isn't available, return "True" for passing
+    ks, _ = stats.kstest(samples, stats.laplace(loc, scale=scale).cdf)
+    # Return True when the test passes.
+    return ks < 0.02
+
+  def testLaplacePdfOfSampleMultiDims(self):
+    with session.Session() as sess:
+      laplace = laplace_lib.Laplace(loc=[7., 11.], scale=[[5.], [6.]])
+      num = 50000
+      samples = laplace.sample(num, seed=137)
+      pdfs = laplace.prob(samples)
+      sample_vals, pdf_vals = sess.run([samples, pdfs])
+      self.assertEqual(samples.get_shape(), (num, 2, 2))
+      self.assertEqual(pdfs.get_shape(), (num, 2, 2))
+      self._assertIntegral(sample_vals[:, 0, 0], pdf_vals[:, 0, 0], err=0.02)
+      self._assertIntegral(sample_vals[:, 0, 1], pdf_vals[:, 0, 1], err=0.02)
+      self._assertIntegral(sample_vals[:, 1, 0], pdf_vals[:, 1, 0], err=0.02)
+      self._assertIntegral(sample_vals[:, 1, 1], pdf_vals[:, 1, 1], err=0.02)
+      if not stats:
+        return
+      self.assertAllClose(
+          stats.laplace.mean(
+              [[7., 11.], [7., 11.]], scale=np.array([[5., 5.], [6., 6.]])),
+          sample_vals.mean(axis=0),
+          rtol=0.05,
+          atol=0.)
+      self.assertAllClose(
+          stats.laplace.var([[7., 11.], [7., 11.]],
+                            scale=np.array([[5., 5.], [6., 6.]])),
+          sample_vals.var(axis=0),
+          rtol=0.05,
+          atol=0.)
+
+  def _assertIntegral(self, sample_vals, pdf_vals, err=1e-3):
+    s_p = zip(sample_vals, pdf_vals)
+    prev = (0, 0)
+    total = 0
+    for k in sorted(s_p, key=lambda x: x[0]):
+      pair_pdf = (k[1] + prev[1]) / 2
+      total += (k[0] - prev[0]) * pair_pdf
+      prev = k
+    self.assertNear(1., total, err=err)
+
+  def testLaplaceNonPositiveInitializationParamsRaises(self):
+    with self.test_session():
+      loc_v = constant_op.constant(0.0, name="loc")
+      scale_v = constant_op.constant(-1.0, name="scale")
+      laplace = laplace_lib.Laplace(
+          loc=loc_v, scale=scale_v, validate_args=True)
+      with self.assertRaisesOpError("scale"):
+        laplace.mean().eval()
+      loc_v = constant_op.constant(1.0, name="loc")
+      scale_v = constant_op.constant(0.0, name="scale")
+      laplace = laplace_lib.Laplace(
+          loc=loc_v, scale=scale_v, validate_args=True)
+      with self.assertRaisesOpError("scale"):
+        laplace.mean().eval()
+
+  def testLaplaceWithSoftplusScale(self):
+    with self.test_session():
+      loc_v = constant_op.constant([0.0, 1.0], name="loc")
+      scale_v = constant_op.constant([-1.0, 2.0], name="scale")
+      laplace = laplace_lib.LaplaceWithSoftplusScale(loc=loc_v, scale=scale_v)
+      self.assertAllClose(nn_ops.softplus(scale_v).eval(), laplace.scale.eval())
+      self.assertAllClose(loc_v.eval(), laplace.loc.eval())
+
+
+if __name__ == "__main__":
+  test.main()