diff --git a/mindspore/nn/probability/bijector/__init__.py b/mindspore/nn/probability/bijector/__init__.py
index d6eb8c175e..0a90856f82 100644
--- a/mindspore/nn/probability/bijector/__init__.py
+++ b/mindspore/nn/probability/bijector/__init__.py
@@ -21,6 +21,8 @@ from .power_transform import PowerTransform
 from .exp import Exp
 from .scalar_affine import ScalarAffine
 from .softplus import Softplus
+from .gumbel_cdf import GumbelCDF
+from .invert import Invert
 
 __all__ = [
     'Bijector',
@@ -28,4 +30,6 @@ __all__ = [
     'Exp',
     'ScalarAffine',
     'Softplus',
+    'GumbelCDF',
+    'Invert',
 ]
diff --git a/mindspore/nn/probability/bijector/gumbel_cdf.py b/mindspore/nn/probability/bijector/gumbel_cdf.py
new file mode 100644
index 0000000000..b15fff9bdc
--- /dev/null
+++ b/mindspore/nn/probability/bijector/gumbel_cdf.py
@@ -0,0 +1,107 @@
+# Copyright 2020 Huawei Technologies Co., Ltd
+#
+# 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.
+# ============================================================================
+"""GumbelCDF Bijector"""
+from mindspore.common import dtype as mstype
+from ..distribution._utils.utils import cast_to_tensor, check_greater_zero, set_param_type
+from ..distribution._utils.custom_ops import exp_generic, log_generic
+from .bijector import Bijector
+
+
+class GumbelCDF(Bijector):
+    r"""
+    GumbelCDF Bijector.
+    This Bijector performs the operation:
+
+    .. math::
+        Y = \exp(-\exp(\frac{-(X - loc)}{scale}))
+
+    Note:
+        For `reverse` and `reverse_log_jacobian`, input should be in range of (0, 1).
+
+    Args:
+        loc (int, float, list, numpy.ndarray, Tensor): The location. Default: 0..
+        scale (int, float, list, numpy.ndarray, Tensor): The scale. Default: 1.0.
+        name (str): The name of the Bijector. Default: 'Gumbel_CDF'.
+
+    Examples:
+        >>> # To initialize a GumbelCDF bijector of loc 0.0, and scale 1.0.
+        >>> import mindspore.nn.probability.bijector as msb
+        >>> gum = msb.GumbelCDF(0.0, 1.0)
+        >>>
+        >>> # To use GumbelCDF bijector in a network.
+        >>> class net(Cell):
+        >>>     def __init__(self):
+        >>>         super(net, self).__init__():
+        >>>         self.gum = msb.GumbelCDF(0.0, 1.0)
+        >>>
+        >>>     def construct(self, value):
+        >>>         # Similar calls can be made to other functions
+        >>>         # by replacing 'forward' by the name of the function.
+        >>>         ans1 = self.gum.forward(value)
+        >>>         ans2 = self.gum.inverse(value)
+        >>>         ans3 = self.gum.forward_log_jacobian(value)
+        >>>         ans4 = self.gum.inverse_log_jacobian(value)
+    """
+
+    def __init__(self,
+                 loc=0.0,
+                 scale=1.0,
+                 name='GumbelCDF'):
+        """
+        Constructor of GumbelCDF Bijector.
+        """
+        param = dict(locals())
+        parameter_type = set_param_type({'loc': loc, "scale": scale}, mstype.float32)
+        super(GumbelCDF, self).__init__(name=name, dtype=parameter_type, param=param)
+        self._loc = cast_to_tensor(loc, parameter_type)
+        self._scale = cast_to_tensor(scale, parameter_type)
+        check_greater_zero(self._scale, "scale")
+
+        self.exp = exp_generic
+        self.log = log_generic
+
+
+    @property
+    def loc(self):
+        return self._loc
+
+    @property
+    def scale(self):
+        return self._scale
+
+    def extend_repr(self):
+        str_info = f'loc = {self.loc}, scale = {self.scale}'
+        return str_info
+
+    def shape_mapping(self, shape):
+        return shape
+
+    def _forward(self, x):
+        x = self._check_value(x, 'value')
+        z = (x - self.loc) / self.scale
+        return self.exp(-self.exp(-z))
+
+    def _inverse(self, y):
+        y = self._check_value(y, 'value')
+        return self.loc - self.scale * self.log(-self.log(y))
+
+    def _forward_log_jacobian(self, x):
+        x = self._check_value(x, 'value')
+        z = (x - self.loc) / self.scale
+        return -z - self.exp(-z) - self.log(self.scale)
+
+    def _inverse_log_jacobian(self, y):
+        y = self._check_value(y, 'value')
+        return self.log(self.scale / (-y * self.log(y)))
diff --git a/mindspore/nn/probability/bijector/invert.py b/mindspore/nn/probability/bijector/invert.py
new file mode 100644
index 0000000000..efb47a51f4
--- /dev/null
+++ b/mindspore/nn/probability/bijector/invert.py
@@ -0,0 +1,75 @@
+# Copyright 2020 Huawei Technologies Co., Ltd
+#
+# 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.
+# ============================================================================
+"""Invert Bijector"""
+from mindspore._checkparam import Validator as validator
+from .bijector import Bijector
+
+
+class Invert(Bijector):
+    r"""
+    Invert Bijector.
+
+    Args:
+        bijector (Bijector): Base Bijector.
+        name (str): The name of the Bijector. Default: Invert.
+
+    Examples:
+        >>> # To initialize an Invert bijector.
+        >>> import mindspore.nn.probability.bijector as msb
+        >>> n = msb.Invert()
+        >>>
+        >>> # To use an Invert bijector in a network.
+        >>> class net(Cell):
+        >>>     def __init__(self):
+        >>>         super(net, self).__init__():
+        >>>         self.inv = msb.Invert(msb.Exp())
+        >>>
+        >>>     def construct(self, value):
+        >>>         # Similar calls can be made to other functions
+        >>>         # by replacing `forward` by the name of the function.
+        >>>         ans1 = self.inv.forward(value)
+        >>>         ans2 = self.inv.inverse(value)
+        >>>         ans3 = self.inv.forward_log_jacobian(value)
+        >>>         ans4 = self.inv.inverse_log_jacobian(value)
+    """
+
+    def __init__(self,
+                 bijector,
+                 name='Invert'):
+        param = dict(locals())
+        validator.check_value_type('bijector', bijector, [Bijector], "Invert")
+        name = (name + bijector.name) if name == 'Invert' else name
+        super(Invert, self).__init__(is_constant_jacobian=bijector.is_constant_jacobian,
+                                     is_injective=bijector.is_injective,
+                                     dtype=bijector.dtype,
+                                     name=name,
+                                     param=param)
+        self._bijector = bijector
+
+    @property
+    def bijector(self):
+        return self._bijector
+
+    def inverse(self, y):
+        return self.bijector("forward", y)
+
+    def forward(self, x):
+        return self.bijector("inverse", x)
+
+    def inverse_log_jacobian(self, y):
+        return self.bijector("forward_log_jacobian", y)
+
+    def forward_log_jacobian(self, x):
+        return self.bijector("inverse_log_jacobian", x)
diff --git a/tests/st/probability/bijector/test_gumbel_cdf.py b/tests/st/probability/bijector/test_gumbel_cdf.py
new file mode 100644
index 0000000000..d43a5d8c36
--- /dev/null
+++ b/tests/st/probability/bijector/test_gumbel_cdf.py
@@ -0,0 +1,108 @@
+# Copyright 2019 Huawei Technologies Co., Ltd
+#
+# 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.
+# ============================================================================
+"""test cases for gumbel_cdf"""
+import numpy as np
+import mindspore.context as context
+import mindspore.nn as nn
+import mindspore.nn.probability.bijector as msb
+from mindspore import Tensor
+from mindspore import dtype
+
+context.set_context(mode=context.GRAPH_MODE, device_target="Ascend")
+
+class Net(nn.Cell):
+    """
+    Test class: forward pass of bijector.
+    """
+    def __init__(self, loc, scale):
+        super(Net, self).__init__()
+        self.bijector = msb.GumbelCDF(loc, scale)
+
+    def construct(self, x_):
+        return self.bijector.forward(x_)
+
+def test_forward():
+    loc = np.array([0.0])
+    scale = np.array([[1.0], [2.0]])
+    forward = Net(loc, scale)
+    x = np.array([-2., -1., 0., 1., 2.]).astype(np.float32)
+    ans = forward(Tensor(x, dtype=dtype.float32))
+    tol = 1e-6
+    expected = np.exp(-np.exp(-(x - loc)/scale))
+    assert (np.abs(ans.asnumpy() - expected) < tol).all()
+
+class Net1(nn.Cell):
+    """
+    Test class: backward pass of bijector.
+    """
+    def __init__(self, loc, scale):
+        super(Net1, self).__init__()
+        self.bijector = msb.GumbelCDF(loc, scale)
+
+    def construct(self, x_):
+        return self.bijector.inverse(x_)
+
+def test_backward():
+    loc = np.array([0.0])
+    scale = np.array([[1.0], [2.0]])
+    backward = Net1(loc, scale)
+    x = np.array([0.1, 0.25, 0.5, 0.75, 0.9]).astype(np.float32)
+    ans = backward(Tensor(x, dtype=dtype.float32))
+    tol = 1e-6
+    expected = loc - scale * np.log(-np.log(x))
+    assert (np.abs(ans.asnumpy() - expected) < tol).all()
+
+class Net2(nn.Cell):
+    """
+    Test class: Forward Jacobian.
+    """
+    def __init__(self, loc, scale):
+        super(Net2, self).__init__()
+        self.bijector = msb.GumbelCDF(loc, scale)
+
+    def construct(self, x_):
+        return self.bijector.forward_log_jacobian(x_)
+
+def test_forward_jacobian():
+    loc = np.array([0.0])
+    scale = np.array([[1.0], [2.0]])
+    forward_jacobian = Net2(loc, scale)
+    x = np.array([-2., -1., 0., 1., 2.]).astype(np.float32)
+    ans = forward_jacobian(Tensor(x))
+    z = (x - loc) / scale
+    expected = -z - np.exp(-z) - np.log(scale)
+    tol = 1e-6
+    assert (np.abs(ans.asnumpy() - expected) < tol).all()
+
+class Net3(nn.Cell):
+    """
+    Test class: Backward Jacobian.
+    """
+    def __init__(self, loc, scale):
+        super(Net3, self).__init__()
+        self.bijector = msb.GumbelCDF(loc, scale)
+
+    def construct(self, x_):
+        return self.bijector.inverse_log_jacobian(x_)
+
+def test_backward_jacobian():
+    loc = np.array([0.0])
+    scale = np.array([[1.0], [2.0]])
+    backward_jacobian = Net3(loc, scale)
+    x = np.array([0.1, 0.2, 0.5, 0.75, 0.9]).astype(np.float32)
+    ans = backward_jacobian(Tensor(x))
+    expected = np.log(scale / (-x * np.log(x)))
+    tol = 1e-6
+    assert (np.abs(ans.asnumpy() - expected) < tol).all()
diff --git a/tests/st/probability/bijector/test_invert.py b/tests/st/probability/bijector/test_invert.py
new file mode 100644
index 0000000000..bf511b41b6
--- /dev/null
+++ b/tests/st/probability/bijector/test_invert.py
@@ -0,0 +1,101 @@
+# Copyright 2019 Huawei Technologies Co., Ltd
+#
+# 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.
+# ============================================================================
+"""test cases for invert"""
+import numpy as np
+import mindspore.context as context
+import mindspore.nn as nn
+import mindspore.nn.probability.bijector as msb
+from mindspore import Tensor
+from mindspore import dtype
+
+context.set_context(mode=context.GRAPH_MODE, device_target="Ascend")
+
+class Net(nn.Cell):
+    """
+    Test class: forward pass of bijector.
+    """
+    def __init__(self):
+        super(Net, self).__init__()
+        self.origin = msb.ScalarAffine(scale=2.0, shift=1.0)
+        self.invert = msb.Invert(self.origin)
+
+    def construct(self, x_):
+        return self.invert.forward(x_), self.origin.inverse(x_)
+
+def test_forward():
+    forward = Net()
+    x = np.array([2.0, 3.0, 4.0, 5.0]).astype(np.float32)
+    ans, ans2 = forward(Tensor(x, dtype=dtype.float32))
+    tol = 1e-6
+    assert (np.abs(ans.asnumpy() - ans2.asnumpy()) < tol).all()
+
+class Net1(nn.Cell):
+    """
+    Test class: backward pass of bijector.
+    """
+    def __init__(self):
+        super(Net1, self).__init__()
+        self.origin = msb.ScalarAffine(scale=2.0, shift=1.0)
+        self.invert = msb.Invert(self.origin)
+
+    def construct(self, x_):
+        return self.invert.inverse(x_), self.origin.forward(x_)
+
+def test_backward():
+    backward = Net1()
+    x = np.array([2.0, 3.0, 4.0, 5.0]).astype(np.float32)
+    ans, ans2 = backward(Tensor(x, dtype=dtype.float32))
+    tol = 1e-6
+    assert (np.abs(ans.asnumpy() - ans2.asnumpy()) < tol).all()
+
+class Net2(nn.Cell):
+    """
+    Test class: Forward Jacobian.
+    """
+    def __init__(self):
+        super(Net2, self).__init__()
+        self.origin = msb.ScalarAffine(scale=2.0, shift=1.0)
+        self.invert = msb.Invert(self.origin)
+
+    def construct(self, x_):
+        return self.invert.forward_log_jacobian(x_),\
+               self.origin.inverse_log_jacobian(x_)
+
+def test_forward_jacobian():
+    forward_jacobian = Net2()
+    x = Tensor([2.0, 3.0, 4.0, 5.0], dtype=dtype.float32)
+    ans, ans2 = forward_jacobian(x)
+    tol = 1e-6
+    assert (np.abs(ans.asnumpy() - ans2.asnumpy()) < tol).all()
+
+class Net3(nn.Cell):
+    """
+    Test class: Backward Jacobian.
+    """
+    def __init__(self):
+        super(Net3, self).__init__()
+        self.origin = msb.ScalarAffine(scale=2.0, shift=1.0)
+        self.invert = msb.Invert(self.origin)
+
+    def construct(self, x_):
+        return self.invert.inverse_log_jacobian(x_),\
+               self.origin.forward_log_jacobian(x_)
+
+def test_backward_jacobian():
+    backward_jacobian = Net3()
+    x = Tensor([2.0, 3.0, 4.0, 5.0], dtype=dtype.float32)
+    ans, ans2 = backward_jacobian(x)
+    tol = 1e-6
+    assert (np.abs(ans.asnumpy() - ans2.asnumpy()) < tol).all()
diff --git a/tests/ut/python/nn/probability/bijector/test_gumbel_cdf.py b/tests/ut/python/nn/probability/bijector/test_gumbel_cdf.py
new file mode 100644
index 0000000000..7d9d8da4da
--- /dev/null
+++ b/tests/ut/python/nn/probability/bijector/test_gumbel_cdf.py
@@ -0,0 +1,148 @@
+# Copyright 2019 Huawei Technologies Co., Ltd
+#
+# 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.
+# ============================================================================
+"""test cases for gumbel_cdf"""
+import pytest
+import mindspore.nn as nn
+import mindspore.nn.probability.bijector as msb
+from mindspore import Tensor
+from mindspore import dtype
+
+def test_init():
+    """
+    Test initializations.
+    """
+    b = msb.GumbelCDF()
+    assert isinstance(b, msb.Bijector)
+    b = msb.GumbelCDF(scale=1.0)
+    assert isinstance(b, msb.Bijector)
+    b = msb.GumbelCDF(loc=0.0)
+    assert isinstance(b, msb.Bijector)
+    b = msb.GumbelCDF(3.0, 4.0)
+    assert isinstance(b, msb.Bijector)
+
+def test_type():
+    with pytest.raises(TypeError):
+        msb.GumbelCDF(scale='scale')
+    with pytest.raises(TypeError):
+        msb.GumbelCDF(loc='loc')
+    with pytest.raises(TypeError):
+        msb.GumbelCDF(name=0.1)
+
+def test_invalid_scale():
+    """
+    Test invalid scale.
+    """
+    with pytest.raises(ValueError):
+        msb.GumbelCDF(scale=0.0)
+    with pytest.raises(ValueError):
+        msb.GumbelCDF(scale=-1.0)
+
+class ForwardBackward(nn.Cell):
+    """
+    Test class: forward and backward pass.
+    """
+    def __init__(self):
+        super(ForwardBackward, self).__init__()
+        self.b1 = msb.GumbelCDF(1.0, 2.0)
+        self.b2 = msb.GumbelCDF()
+
+    def construct(self, x_):
+        ans1 = self.b1.inverse(self.b1.forward(x_))
+        ans2 = self.b2.inverse(self.b2.forward(x_))
+        return ans1 + ans2
+
+def test_forward_and_backward_pass():
+    """
+    Test forward and backward pass of ScalarAffine bijector.
+    """
+    net = ForwardBackward()
+    x = Tensor([-2.0, -1.0, 0.0, 1.0, 2.0], dtype=dtype.float32)
+    ans = net(x)
+    assert isinstance(ans, Tensor)
+
+class ForwardJacobian(nn.Cell):
+    """
+    Test class: Forward log Jacobian.
+    """
+    def __init__(self):
+        super(ForwardJacobian, self).__init__()
+        self.b1 = msb.GumbelCDF(1.0, 2.0)
+        self.b2 = msb.GumbelCDF()
+
+    def construct(self, x_):
+        ans1 = self.b1.forward_log_jacobian(x_)
+        ans2 = self.b2.forward_log_jacobian(x_)
+        return ans1 + ans2
+
+def test_forward_jacobian():
+    """
+    Test forward log jacobian of ScalarAffine bijector.
+    """
+    net = ForwardJacobian()
+    x = Tensor([-2.0, -1.0, 0.0, 1.0, 2.0], dtype=dtype.float32)
+    ans = net(x)
+    assert isinstance(ans, Tensor)
+
+
+class BackwardJacobian(nn.Cell):
+    """
+    Test class: Backward log Jacobian.
+    """
+    def __init__(self):
+        super(BackwardJacobian, self).__init__()
+        self.b1 = msb.GumbelCDF(1.0, 2.0)
+        self.b2 = msb.GumbelCDF()
+
+    def construct(self, x_):
+        ans1 = self.b1.inverse_log_jacobian(x_)
+        ans2 = self.b2.inverse_log_jacobian(x_)
+        return ans1 + ans2
+
+def test_backward_jacobian():
+    """
+    Test backward log jacobian of ScalarAffine bijector.
+    """
+    net = BackwardJacobian()
+    x = Tensor([-2.0, -1.0, 0.0, 1.0, 2.0], dtype=dtype.float32)
+    ans = net(x)
+    assert isinstance(ans, Tensor)
+
+
+class Net(nn.Cell):
+    """
+    Test class: function calls going through construct.
+    """
+    def __init__(self):
+        super(Net, self).__init__()
+        self.b1 = msb.GumbelCDF(1.0, 2.0)
+        self.b2 = msb.GumbelCDF()
+
+    def construct(self, x_):
+        ans1 = self.b1('inverse', self.b1('forward', x_))
+        ans2 = self.b2('inverse', self.b2('forward', x_))
+        ans3 = self.b1('forward_log_jacobian', x_)
+        ans4 = self.b2('forward_log_jacobian', x_)
+        ans5 = self.b1('inverse_log_jacobian', x_)
+        ans6 = self.b2('inverse_log_jacobian', x_)
+        return ans1 - ans2 + ans3 -ans4 + ans5 - ans6
+
+def test_old_api():
+    """
+    Test old api which goes through construct.
+    """
+    net = Net()
+    x = Tensor([-2.0, -1.0, 0.0, 1.0, 2.0], dtype=dtype.float32)
+    ans = net(x)
+    assert isinstance(ans, Tensor)
diff --git a/tests/ut/python/nn/probability/bijector/test_invert.py b/tests/ut/python/nn/probability/bijector/test_invert.py
new file mode 100644
index 0000000000..7eb49ea646
--- /dev/null
+++ b/tests/ut/python/nn/probability/bijector/test_invert.py
@@ -0,0 +1,136 @@
+# Copyright 2019 Huawei Technologies Co., Ltd
+#
+# 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.
+# ============================================================================
+"""test cases for invert"""
+import pytest
+import mindspore.nn as nn
+import mindspore.nn.probability.bijector as msb
+from mindspore import Tensor
+from mindspore import dtype
+
+def test_init():
+    """
+    Test initializations.
+    """
+    b = msb.Invert(msb.ScalarAffine(scale=1.0))
+    assert isinstance(b, msb.Bijector)
+    b = msb.Invert(msb.Exp())
+    assert isinstance(b, msb.Bijector)
+
+
+def test_type():
+    with pytest.raises(TypeError):
+        msb.Invert(msb.Exp(), name=0.1)
+    with pytest.raises(TypeError):
+        msb.Invert(0.1)
+
+def test_name():
+    b = msb.Invert(msb.ScalarAffine(scale=1.0))
+    assert b.name == 'InvertScalarAffine'
+
+class ForwardBackward(nn.Cell):
+    """
+    Test class: forward and backward pass.
+    """
+    def __init__(self):
+        super(ForwardBackward, self).__init__()
+        self.inv1 = msb.Invert(msb.Exp())
+        self.inv2 = msb.Invert(msb.ScalarAffine())
+
+    def construct(self, x_):
+        ans1 = self.inv1.inverse(x_) + self.inv1.inverse(x_)
+        ans2 = self.inv2.inverse(x_) + self.inv2.forward(x_)
+        return ans1 + ans2
+
+def test_forward_and_backward_pass():
+    """
+    Test forward and backward pass of ScalarAffine bijector.
+    """
+    net = ForwardBackward()
+    x = Tensor([2.0, 3.0, 4.0, 5.0], dtype=dtype.float32)
+    ans = net(x)
+    assert isinstance(ans, Tensor)
+
+class ForwardJacobian(nn.Cell):
+    """
+    Test class: Forward log Jacobian.
+    """
+    def __init__(self):
+        super(ForwardJacobian, self).__init__()
+        self.inv1 = msb.Invert(msb.Exp())
+        self.inv2 = msb.Invert(msb.ScalarAffine())
+
+
+    def construct(self, x_):
+        ans1 = self.inv1.forward_log_jacobian(x_)
+        ans2 = self.inv2.forward_log_jacobian(x_)
+        return ans1 + ans2
+
+def test_forward_jacobian():
+    """
+    Test forward log jacobian of ScalarAffine bijector.
+    """
+    net = ForwardJacobian()
+    x = Tensor([2.0, 3.0, 4.0, 5.0], dtype=dtype.float32)
+    ans = net(x)
+    assert isinstance(ans, Tensor)
+
+
+class BackwardJacobian(nn.Cell):
+    """
+    Test class: Backward log Jacobian.
+    """
+    def __init__(self):
+        super(BackwardJacobian, self).__init__()
+        self.inv1 = msb.Invert(msb.Exp())
+        self.inv2 = msb.Invert(msb.ScalarAffine())
+
+    def construct(self, x_):
+        ans1 = self.inv1.inverse_log_jacobian(x_)
+        ans2 = self.inv2.inverse_log_jacobian(x_)
+        return ans1 + ans2
+
+def test_backward_jacobian():
+    """
+    Test backward log jacobian of ScalarAffine bijector.
+    """
+    net = BackwardJacobian()
+    x = Tensor([2.0, 3.0, 4.0, 5.0], dtype=dtype.float32)
+    ans = net(x)
+    assert isinstance(ans, Tensor)
+
+
+class Net(nn.Cell):
+    """
+    Test class: function calls going through construct.
+    """
+    def __init__(self):
+        super(Net, self).__init__()
+        self.b1 = msb.ScalarAffine(2.0, 1.0)
+        self.inv = msb.Invert(self.b1)
+
+    def construct(self, x_):
+        ans1 = self.inv('inverse', self.inv('forward', x_))
+        ans2 = self.inv('forward_log_jacobian', x_)
+        ans3 = self.inv('inverse_log_jacobian', x_)
+        return ans1 + ans2 + ans3
+
+def test_old_api():
+    """
+    Test old api which goes through construct.
+    """
+    net = Net()
+    x = Tensor([2.0, 3.0, 4.0, 5.0], dtype=dtype.float32)
+    ans = net(x)
+    assert isinstance(ans, Tensor)