diff --git a/doc/release/1.16.0-notes.rst b/doc/release/1.16.0-notes.rst
index 2b84bb90a311..6a73ed3548da 100644
--- a/doc/release/1.16.0-notes.rst
+++ b/doc/release/1.16.0-notes.rst
@@ -107,6 +107,12 @@ Previously, a ``LinAlgError`` would be raised when an empty matrix/empty
 matrices (with zero rows and/or columns) is/are passed in. Now outputs of
 appropriate shapes are returned.
 
+``np.diff`` Added kwargs prepend and append
+-------------------------------------------
+Add kwargs prepend and append, allowing for values to be inserted
+on either end of the differences.  Similar to options for ediff1d.
+Allows for the inverse of cumsum easily via prepend=0
+
 ARM support updated
 -------------------
 Support for ARM CPUs has been updated to accommodate 32 and 64 bit targets,
diff --git a/numpy/lib/function_base.py b/numpy/lib/function_base.py
index 2992e92bb056..704e56514973 100644
--- a/numpy/lib/function_base.py
+++ b/numpy/lib/function_base.py
@@ -1090,7 +1090,7 @@ def gradient(f, *varargs, **kwargs):
         return outvals
 
 
-def diff(a, n=1, axis=-1):
+def diff(a, n=1, axis=-1, prepend=np._NoValue, append=np._NoValue):
     """
     Calculate the n-th discrete difference along the given axis.
 
@@ -1108,6 +1108,12 @@ def diff(a, n=1, axis=-1):
     axis : int, optional
         The axis along which the difference is taken, default is the
         last axis.
+    prepend, append : array_like, optional
+        Values to prepend or append to "a" along axis prior to
+        performing the difference.  Scalar values are expanded to
+        arrays with length 1 in the direction of axis and the shape
+        of the input array in along all other axes.  Otherwise the
+        dimension and shape must match "a" except along axis.
 
     Returns
     -------
@@ -1176,6 +1182,28 @@ def diff(a, n=1, axis=-1):
     nd = a.ndim
     axis = normalize_axis_index(axis, nd)
 
+    combined = []
+    if prepend is not np._NoValue:
+        prepend = np.asanyarray(prepend)
+        if prepend.ndim == 0:
+            shape = list(a.shape)
+            shape[axis] = 1
+            prepend = np.broadcast_to(prepend, tuple(shape))
+        combined.append(prepend)
+
+    combined.append(a)
+
+    if append is not np._NoValue:
+        append = np.asanyarray(append)
+        if append.ndim == 0:
+            shape = list(a.shape)
+            shape[axis] = 1
+            append = np.broadcast_to(append, tuple(shape))
+        combined.append(append)
+
+    if len(combined) > 1:
+        a = np.concatenate(combined, axis)
+
     slice1 = [slice(None)] * nd
     slice2 = [slice(None)] * nd
     slice1[axis] = slice(1, None)
diff --git a/numpy/lib/tests/test_function_base.py b/numpy/lib/tests/test_function_base.py
index d5faed6aea49..40cca1dbb4bb 100644
--- a/numpy/lib/tests/test_function_base.py
+++ b/numpy/lib/tests/test_function_base.py
@@ -734,6 +734,58 @@ def test_subclass(self):
         assert_array_equal(out3.mask, [[], [], [], [], []])
         assert_(type(out3) is type(x))
 
+    def test_prepend(self):
+        x = np.arange(5) + 1
+        assert_array_equal(diff(x, prepend=0), np.ones(5))
+        assert_array_equal(diff(x, prepend=[0]), np.ones(5))
+        assert_array_equal(np.cumsum(np.diff(x, prepend=0)), x)
+        assert_array_equal(diff(x, prepend=[-1, 0]), np.ones(6))
+
+        x = np.arange(4).reshape(2, 2)
+        result = np.diff(x, axis=1, prepend=0)
+        expected = [[0, 1], [2, 1]]
+        assert_array_equal(result, expected)
+        result = np.diff(x, axis=1, prepend=[[0], [0]])
+        assert_array_equal(result, expected)
+
+        result = np.diff(x, axis=0, prepend=0)
+        expected = [[0, 1], [2, 2]]
+        assert_array_equal(result, expected)
+        result = np.diff(x, axis=0, prepend=[[0, 0]])
+        assert_array_equal(result, expected)
+
+        assert_raises(ValueError, np.diff, x, prepend=np.zeros((3,3)))
+
+        assert_raises(np.AxisError, diff, x, prepend=0, axis=3)
+
+    def test_append(self):
+        x = np.arange(5)
+        result = diff(x, append=0)
+        expected = [1, 1, 1, 1, -4]
+        assert_array_equal(result, expected)
+        result = diff(x, append=[0])
+        assert_array_equal(result, expected)
+        result = diff(x, append=[0, 2])
+        expected = expected + [2]
+        assert_array_equal(result, expected)
+
+        x = np.arange(4).reshape(2, 2)
+        result = np.diff(x, axis=1, append=0)
+        expected = [[1, -1], [1, -3]]
+        assert_array_equal(result, expected)
+        result = np.diff(x, axis=1, append=[[0], [0]])
+        assert_array_equal(result, expected)
+
+        result = np.diff(x, axis=0, append=0)
+        expected = [[2, 2], [-2, -3]]
+        assert_array_equal(result, expected)
+        result = np.diff(x, axis=0, append=[[0, 0]])
+        assert_array_equal(result, expected)
+
+        assert_raises(ValueError, np.diff, x, append=np.zeros((3,3)))
+
+        assert_raises(np.AxisError, diff, x, append=0, axis=3)
+
 
 class TestDelete(object):