diff --git a/tensorflow/contrib/distributions/python/kernel_tests/bijectors/scale_tril_test.py b/tensorflow/contrib/distributions/python/kernel_tests/bijectors/scale_tril_test.py
index d5b3367f9a3..1b88c1d130a 100644
--- a/tensorflow/contrib/distributions/python/kernel_tests/bijectors/scale_tril_test.py
+++ b/tensorflow/contrib/distributions/python/kernel_tests/bijectors/scale_tril_test.py
@@ -41,10 +41,10 @@ class ScaleTriLBijectorTest(test.TestCase):
                             diag_shift=shift)
 
     y_ = self.evaluate(b.forward(x))
-    self.assertAllClose(y, y_)
+    self.assertAllClose(y, y_, rtol=1e-4)
 
     x_ = self.evaluate(b.inverse(y))
-    self.assertAllClose(x, x_)
+    self.assertAllClose(x, x_, rtol=1e-4)
 
   @test_util.run_in_graph_and_eager_modes
   def testInvertible(self):
@@ -52,18 +52,18 @@ class ScaleTriLBijectorTest(test.TestCase):
     # Generate random inputs from an unconstrained space, with
     # event size 6 to specify 3x3 triangular matrices.
     batch_shape = [2, 1]
-    x = np.float32(np.random.randn(*(batch_shape + [6])))
+    x = np.float32(self._rng.randn(*(batch_shape + [6])))
     b = bijectors.ScaleTriL(diag_bijector=bijectors.Softplus(),
                             diag_shift=3.14159)
     y = self.evaluate(b.forward(x))
     self.assertAllEqual(y.shape, batch_shape + [3, 3])
 
     x_ = self.evaluate(b.inverse(y))
-    self.assertAllClose(x, x_)
+    self.assertAllClose(x, x_, rtol=1e-4)
 
     fldj = self.evaluate(b.forward_log_det_jacobian(x, event_ndims=1))
     ildj = self.evaluate(b.inverse_log_det_jacobian(y, event_ndims=2))
-    self.assertAllClose(fldj, -ildj)
+    self.assertAllClose(fldj, -ildj, rtol=1e-4)
 
 if __name__ == "__main__":
   test.main()