diff --git a/test/distribution/test_distribution_transform_static.py b/test/distribution/test_distribution_transform_static.py
index 3d128df5acb847..0306127261ed79 100644
--- a/test/distribution/test_distribution_transform_static.py
+++ b/test/distribution/test_distribution_transform_static.py
@@ -12,6 +12,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+import typing
 import unittest
 
 import numpy as np
@@ -1223,5 +1224,295 @@ def test_forward_log_det_jacobian(self):
         )
 
 
+def _np_softplus(x, beta=1.0, threshold=20.0):
+    if np.any(beta * x > threshold):
+        return x
+    return 1.0 / beta * np.log1p(np.exp(beta * x))
+
+
+class TestSigmoidTransform(unittest.TestCase):
+    def setUp(self):
+        self._t = transform.SigmoidTransform()
+
+    def test_is_injective(self):
+        self.assertTrue(self._t._is_injective())
+
+    def test_domain(self):
+        self.assertTrue(isinstance(self._t._domain, variable.Real))
+
+    def test_codomain(self):
+        self.assertTrue(isinstance(self._t._codomain, variable.Variable))
+
+    @param.param_func(
+        ((np.ones((5, 10)), 1 / (1 + np.exp(-np.ones((5, 10))))),)
+    )
+    @test_with_pir_api
+    def test_forward(self, input, expected):
+        with paddle.static.program_guard(paddle.static.Program()):
+            x = paddle.static.data('X', input.shape, input.dtype)
+            model = transform.SigmoidTransform()
+            out = model.forward(x)
+            place = (
+                paddle.CUDAPlace(0)
+                if paddle.core.is_compiled_with_cuda()
+                else paddle.CPUPlace()
+            )
+            exe = paddle.static.Executor(place)
+            (result,) = exe.run(feed={'X': input}, fetch_list=[out])
+        np.testing.assert_allclose(
+            result,
+            expected,
+            rtol=config.RTOL.get(str(input.dtype)),
+            atol=config.ATOL.get(str(input.dtype)),
+        )
+
+    @param.param_func(
+        ((np.ones(10), np.log(np.ones(10)) - np.log1p(-np.ones(10))),)
+    )
+    @test_with_pir_api
+    def test_inverse(self, input, expected):
+        with paddle.static.program_guard(paddle.static.Program()):
+            x = paddle.static.data('X', input.shape, input.dtype)
+            model = transform.SigmoidTransform()
+            out = model.inverse(x)
+            place = (
+                paddle.CUDAPlace(0)
+                if paddle.core.is_compiled_with_cuda()
+                else paddle.CPUPlace()
+            )
+            exe = paddle.static.Executor(place)
+            (result,) = exe.run(feed={'X': input}, fetch_list=[out])
+        np.testing.assert_allclose(
+            result,
+            expected,
+            rtol=config.RTOL.get(str(input.dtype)),
+            atol=config.ATOL.get(str(input.dtype)),
+        )
+
+    @param.param_func(
+        (
+            (
+                np.ones(10),
+                -_np_softplus(-np.ones(10)) - _np_softplus(np.ones(10)),
+            ),
+        )
+    )
+    @test_with_pir_api
+    def test_forward_log_det_jacobian(self, input, expected):
+        with paddle.static.program_guard(paddle.static.Program()):
+            x = paddle.static.data('X', input.shape, input.dtype)
+            model = transform.SigmoidTransform()
+            out = model.forward_log_det_jacobian(x)
+            place = (
+                paddle.CUDAPlace(0)
+                if paddle.core.is_compiled_with_cuda()
+                else paddle.CPUPlace()
+            )
+            exe = paddle.static.Executor(place)
+            (result,) = exe.run(feed={'X': input}, fetch_list=[out])
+        np.testing.assert_allclose(
+            result,
+            expected,
+            rtol=config.RTOL.get(str(input.dtype)),
+            atol=config.ATOL.get(str(input.dtype)),
+        )
+
+    @param.param_func([((), ()), ((2, 3, 5), (2, 3, 5))])
+    def test_forward_shape(self, shape, expected_shape):
+        self.assertEqual(self._t.forward_shape(shape), expected_shape)
+
+    @param.param_func([((), ()), ((2, 3, 5), (2, 3, 5))])
+    def test_inverse_shape(self, shape, expected_shape):
+        self.assertEqual(self._t.forward_shape(shape), expected_shape)
+
+    @param.param_func([(np.array(1.0), np.array(1.0))])
+    @test_with_pir_api
+    def test_zerodim(self, input, expected):
+        shape = ()
+        if paddle.framework.in_pir_mode():
+            shape = []
+        with paddle.static.program_guard(paddle.static.Program()):
+            x = paddle.static.data('X', input.shape, 'float32')
+            model = transform.SigmoidTransform()
+            self.assertEqual(model.forward(x).shape, shape)
+            self.assertEqual(model.inverse(x).shape, shape)
+            self.assertEqual(model.forward_log_det_jacobian(x).shape, shape)
+            self.assertEqual(model.inverse_log_det_jacobian(x).shape, shape)
+            self.assertEqual(model.forward_shape(x.shape), shape)
+            self.assertEqual(model.inverse_shape(x.shape), shape)
+
+
+class TestStickBreakingTransform(unittest.TestCase):
+    def setUp(self):
+        self._t = transform.StickBreakingTransform()
+
+    def test_is_injective(self):
+        self.assertTrue(self._t._is_injective())
+
+    def test_domain(self):
+        self.assertTrue(isinstance(self._t._domain, variable.Independent))
+
+    def test_codomain(self):
+        self.assertTrue(isinstance(self._t._codomain, variable.Variable))
+
+    @param.param_func(((np.random.random(10),),))
+    @test_with_pir_api
+    def test_forward(self, input):
+        with paddle.static.program_guard(paddle.static.Program()):
+            x = paddle.static.data('X', input.shape, input.dtype)
+            model = transform.StickBreakingTransform()
+            fwd = model.forward(x)
+            out = model.inverse(fwd)
+            place = (
+                paddle.CUDAPlace(0)
+                if paddle.core.is_compiled_with_cuda()
+                else paddle.CPUPlace()
+            )
+            exe = paddle.static.Executor(place)
+            (result,) = exe.run(feed={'X': input}, fetch_list=[out])
+        np.testing.assert_allclose(
+            result,
+            input,
+            rtol=config.RTOL.get(str(input.dtype)),
+            atol=config.ATOL.get(str(input.dtype)),
+        )
+
+    @param.param_func([((2, 3, 5), (2, 3, 6))])
+    def test_forward_shape(self, shape, expected_shape):
+        self.assertEqual(self._t.forward_shape(shape), expected_shape)
+
+    @param.param_func([((2, 3, 5), (2, 3, 4))])
+    def test_inverse_shape(self, shape, expected_shape):
+        self.assertEqual(self._t.inverse_shape(shape), expected_shape)
+
+    @param.param_func(((np.random.random(10),),))
+    @test_with_pir_api
+    def test_forward_log_det_jacobian(self, input):
+        with paddle.static.program_guard(paddle.static.Program()):
+            x = paddle.static.data('X', input.shape, input.dtype)
+            model = transform.StickBreakingTransform()
+            out = model.forward_log_det_jacobian(x)
+            place = (
+                paddle.CUDAPlace(0)
+                if paddle.core.is_compiled_with_cuda()
+                else paddle.CPUPlace()
+            )
+            exe = paddle.static.Executor(place)
+            (result,) = exe.run(feed={'X': input}, fetch_list=[out])
+        self.assertEqual(result.shape, ())
+
+
+@param.place(config.DEVICES)
+@param.param_cls(
+    (param.TEST_CASE_NAME, 'transforms', 'axis'),
+    [
+        ('simple_one_transform', [transform.ExpTransform()], 0),
+    ],
+)
+class TestStackTransform(unittest.TestCase):
+    def setUp(self):
+        self._t = transform.StackTransform(self.transforms, self.axis)
+
+    def test_is_injective(self):
+        self.assertTrue(self._t._is_injective())
+
+    def test_domain(self):
+        self.assertTrue(isinstance(self._t._domain, variable.Stack))
+
+    def test_codomain(self):
+        self.assertTrue(isinstance(self._t._codomain, variable.Stack))
+
+    @param.param_func(
+        [
+            (np.array([[0.0, 1.0, 2.0, 3.0]]),),
+            (np.array([[-5.0, 6.0, 7.0, 8.0]]),),
+        ]
+    )
+    @test_with_pir_api
+    def test_forward(self, input):
+        with paddle.static.program_guard(paddle.static.Program()):
+            x = paddle.static.data('X', input.shape, input.dtype)
+            model = transform.StackTransform(self.transforms, self.axis)
+            out = model.forward(x)
+            place = (
+                paddle.CUDAPlace(0)
+                if paddle.core.is_compiled_with_cuda()
+                else paddle.CPUPlace()
+            )
+            exe = paddle.static.Executor(place)
+            (result,) = exe.run(feed={'X': input}, fetch_list=[out])
+        self.assertEqual(tuple(result.shape), input.shape)
+
+    @param.param_func(
+        [
+            (np.array([[1.0, 2.0, 3.0]]),),
+            (
+                np.array(
+                    [[6.0, 7.0, 8.0]],
+                ),
+            ),
+        ]
+    )
+    @test_with_pir_api
+    def test_inverse(self, input):
+        with paddle.static.program_guard(paddle.static.Program()):
+            x = paddle.static.data('X', input.shape, input.dtype)
+            model = transform.StackTransform(self.transforms, self.axis)
+            out = model.inverse(x)
+            place = (
+                paddle.CUDAPlace(0)
+                if paddle.core.is_compiled_with_cuda()
+                else paddle.CPUPlace()
+            )
+            exe = paddle.static.Executor(place)
+            (result,) = exe.run(feed={'X': input}, fetch_list=[out])
+        self.assertEqual(tuple(result.shape), input.shape)
+
+    @param.param_func(
+        [(np.array([[1.0, 2.0, 3.0]]),), (np.array([[6.0, 7.0, 8.0]]),)]
+    )
+    @test_with_pir_api
+    def test_forward_log_det_jacobian(self, input):
+        with paddle.static.program_guard(paddle.static.Program()):
+            x = paddle.static.data('X', input.shape, input.dtype)
+            model = transform.StackTransform(self.transforms, self.axis)
+            out = model.forward_log_det_jacobian(x)
+            place = (
+                paddle.CUDAPlace(0)
+                if paddle.core.is_compiled_with_cuda()
+                else paddle.CPUPlace()
+            )
+            exe = paddle.static.Executor(place)
+            (result,) = exe.run(feed={'X': input}, fetch_list=[out])
+        self.assertEqual(tuple(result.shape), input.shape)
+
+    @param.param_func([((), ()), ((2, 3, 5), (2, 3, 5))])
+    def test_forward_shape(self, shape, expected_shape):
+        self.assertEqual(self._t.forward_shape(shape), expected_shape)
+
+    @param.param_func([((), ()), ((2, 3, 5), (2, 3, 5))])
+    def test_inverse_shape(self, shape, expected_shape):
+        self.assertEqual(self._t.forward_shape(shape), expected_shape)
+
+    def test_axis(self):
+        self.assertEqual(self._t.axis, self.axis)
+
+    @param.param_func(
+        [
+            (0, 0, TypeError),
+            ([0], 0, TypeError),
+            ([paddle.distribution.ExpTransform()], 'axis', TypeError),
+        ]
+    )
+    @test_with_pir_api
+    def test_init_exception(self, transforms, axis, exc):
+        with self.assertRaises(exc):
+            paddle.distribution.StackTransform(transforms, axis)
+
+    @test_with_pir_api
+    def test_transforms(self):
+        self.assertIsInstance((self._t.transforms), typing.Sequence)
+
+
 if __name__ == '__main__':
     unittest.main()