diff --git a/python/paddle/__init__.py b/python/paddle/__init__.py
index 8404e82c544955732fd44040a9f57fd6eeb398bd..b61ea8ed679eef11202d5ce0c1179d627564d178 100644
--- a/python/paddle/__init__.py
+++ b/python/paddle/__init__.py
@@ -38,6 +38,7 @@ import paddle.compat
 import paddle.distributed
 import paddle.sysconfig
 import paddle.tensor
+import paddle.distribution
 import paddle.nn
 import paddle.distributed.fleet
 import paddle.optimizer
diff --git a/python/paddle/distribution.py b/python/paddle/distribution.py
index fff10c5b2a9ee497cccff94346314db2c8011eb5..ba4bfa8708b2ae3d8ae6643393e0f87cc9c6b360 100644
--- a/python/paddle/distribution.py
+++ b/python/paddle/distribution.py
@@ -18,3 +18,517 @@
 #            'Normal',
 #            'sampling_id',
 #            'Uniform']
+
+from __future__ import print_function
+
+from .fluid.layers import control_flow
+from .fluid.layers import tensor
+from .fluid.layers import ops
+from .fluid.layers import nn
+from .fluid.framework import in_dygraph_mode
+from .tensor.math import elementwise_mul, elementwise_div, elementwise_add, elementwise_sub
+import math
+import numpy as np
+import warnings
+
+from .fluid.data_feeder import convert_dtype, check_variable_and_dtype, check_type, check_dtype
+
+__all__ = ['Distribution', 'Uniform', 'Normal']
+
+
+class Distribution(object):
+    """
+    The abstract base class for probability distributions. Functions are 
+    implemented in specific distributions.
+    """
+
+    def __init__(self):
+        super(Distribution, self).__init__()
+
+    def sample(self):
+        """Sampling from the distribution."""
+        raise NotImplementedError
+
+    def entropy(self):
+        """The entropy of the distribution."""
+        raise NotImplementedError
+
+    def kl_divergence(self, other):
+        """The KL-divergence between self distributions and other."""
+        raise NotImplementedError
+
+    def log_prob(self, value):
+        """Log probability density/mass function."""
+        raise NotImplementedError
+
+    def probs(self, value):
+        """Probability density/mass function."""
+        raise NotImplementedError
+
+    def _validate_args(self, *args):
+        """
+        Argument validation for distribution args
+        Args:
+            value (float, list, numpy.ndarray, Tensor)
+        Raises
+            ValueError: if one argument is Tensor, all arguments should be Tensor
+        """
+        is_variable = False
+        is_number = False
+        for arg in args:
+            if isinstance(arg, tensor.Variable):
+                is_variable = True
+            else:
+                is_number = True
+
+        if is_variable and is_number:
+            raise ValueError(
+                'if one argument is Tensor, all arguments should be Tensor')
+
+        return is_variable
+
+    def _to_variable(self, *args):
+        """
+        Argument convert args to Tensor
+
+        Args:
+            value (float, list, numpy.ndarray, Tensor)
+        Returns:
+            Tensor of args.
+        """
+        numpy_args = []
+        variable_args = []
+        tmp = 0.
+
+        for arg in args:
+            valid_arg = False
+            for cls in [float, list, np.ndarray, tensor.Variable]:
+                if isinstance(arg, cls):
+                    valid_arg = True
+                    break
+            assert valid_arg, "type of input args must be float, list, numpy.ndarray or Tensor."
+            if isinstance(arg, float):
+                arg = np.zeros(1) + arg
+            arg_np = np.array(arg)
+            arg_dtype = arg_np.dtype
+            if str(arg_dtype) not in ['float32']:
+                warnings.warn(
+                    "data type of argument only support float32, your argument will be convert to float32."
+                )
+                arg_np = arg_np.astype('float32')
+            tmp = tmp + arg_np
+            numpy_args.append(arg_np)
+
+        dtype = tmp.dtype
+        for arg in numpy_args:
+            arg_broadcasted, _ = np.broadcast_arrays(arg, tmp)
+            arg_variable = tensor.create_tensor(dtype=dtype)
+            tensor.assign(arg_broadcasted, arg_variable)
+            variable_args.append(arg_variable)
+
+        return tuple(variable_args)
+
+
+class Uniform(Distribution):
+    """Uniform distribution with `low` and `high` parameters.
+
+    Mathematical Details
+
+    The probability density function (pdf) is,
+
+    .. math::
+
+        pdf(x; a, b) = \\frac{1}{Z}, \ a <=x <b
+
+    .. math::
+
+        Z = b - a
+
+    In the above equation:
+
+    * :math:`low = a`,
+    * :math:`high = b`,
+    * :math:`Z`: is the normalizing constant.
+
+    The parameters `low` and `high` must be shaped in a way that supports
+    [broadcasting](https://www.paddlepaddle.org.cn/documentation/docs/en/develop/beginners_guide/basic_concept/broadcasting_en.html) (e.g., `high - low` is a valid operation).
+
+    Args:
+        low(int|float|list|numpy.ndarray|Tensor): The lower boundary of uniform distribution.The data type is float32 or int
+        high(int|float|list|numpy.ndarray|Tensor): The higher boundary of uniform distribution.The data type is float32 or int
+        name(str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
+
+    Examples:
+        .. code-block:: python
+
+          import numpy as np
+          import paddle
+          from paddle.distribution import Uniform
+
+          paddle.disable_static()
+          # Without broadcasting, a single uniform distribution [3, 4]:
+          u1 = Uniform(low=3.0, high=4.0)
+          # 2 distributions [1, 3], [2, 4]
+          u2 = Uniform(low=[1.0, 2.0], high=[3.0, 4.0])
+          # 4 distributions
+          u3 = Uniform(low=[[1.0, 2.0], [3.0, 4.0]],
+                    high=[[1.5, 2.5], [3.5, 4.5]])
+
+          # With broadcasting:
+          u4 = Uniform(low=3.0, high=[5.0, 6.0, 7.0])
+
+          # Complete example
+          value_npdata = np.array([0.8], dtype="float32")
+          value_tensor = paddle.to_tensor(value_npdata)
+
+          uniform = Uniform([0.], [2.])
+
+          sample = uniform.sample([2])
+          # a random tensor created by uniform distribution with shape: [2, 1]
+          entropy = uniform.entropy()
+          # [0.6931472] with shape: [1]
+          lp = uniform.log_prob(value_tensor)
+          # [-0.6931472] with shape: [1]
+          p = uniform.probs(value_tensor)
+          # [0.5] with shape: [1]
+    """
+
+    def __init__(self, low, high, name=None):
+        if not in_dygraph_mode():
+            check_type(low, 'low',
+                       (int, float, np.ndarray, tensor.Variable, list),
+                       'Uniform')
+            check_type(high, 'high',
+                       (int, float, np.ndarray, tensor.Variable, list),
+                       'Uniform')
+
+        self.all_arg_is_float = False
+        self.batch_size_unknown = False
+        self.name = name if name is not None else 'Uniform'
+
+        if isinstance(low, int):
+            low = float(low)
+        if isinstance(high, int):
+            high = float(high)
+
+        if self._validate_args(low, high):
+            self.batch_size_unknown = True
+            self.low = low
+            self.high = high
+        else:
+            if isinstance(low, float) and isinstance(high, float):
+                self.all_arg_is_float = True
+            self.low, self.high = self._to_variable(low, high)
+
+    def sample(self, shape, seed=0):
+        """Generate samples of the specified shape.
+
+        Args:
+          shape (list): 1D `int32`. Shape of the generated samples.
+          seed (int): Python integer number.
+
+        Returns:
+          Tensor: A tensor with prepended dimensions shape.The data type is float32.
+
+        """
+        if not in_dygraph_mode():
+            check_type(shape, 'shape', (list), 'sample')
+            check_type(seed, 'seed', (int), 'sample')
+
+        name = self.name + '_sample'
+        batch_shape = list((self.low + self.high).shape)
+        if self.batch_size_unknown:
+            output_shape = shape + batch_shape
+            zero_tmp = tensor.fill_constant_batch_size_like(
+                self.low + self.high, batch_shape + shape, self.low.dtype, 0.)
+            uniform_random_tmp = nn.uniform_random_batch_size_like(
+                zero_tmp, zero_tmp.shape, min=0., max=1., seed=seed)
+            output = uniform_random_tmp * (zero_tmp + self.high - self.low
+                                           ) + self.low
+            return nn.reshape(output, output_shape, name=name)
+        else:
+            output_shape = shape + batch_shape
+            output = nn.uniform_random(
+                output_shape, seed=seed) * (tensor.zeros(
+                    output_shape, dtype=self.low.dtype) +
+                                            (self.high - self.low))
+            output = elementwise_add(output, self.low, name=name)
+            if self.all_arg_is_float:
+                return nn.reshape(output, shape, name=name)
+            else:
+                return output
+
+    def log_prob(self, value):
+        """Log probability density/mass function.
+
+        Args:
+          value (Tensor): The input tensor.
+
+        Returns:
+          Tensor: log probability.The data type is same with value.
+
+        """
+        name = self.name + '_log_prob'
+        if in_dygraph_mode():
+            lb_bool = self.low < value
+            ub_bool = value < self.high
+            lb = tensor.cast(lb_bool, dtype=value.dtype)
+            ub = tensor.cast(ub_bool, dtype=value.dtype)
+            return elementwise_sub(
+                nn.log(lb * ub), nn.log(self.high - self.low), name=name)
+
+        check_variable_and_dtype(value, 'value', ['float32', 'float64'],
+                                 'log_prob')
+
+        lb_bool = control_flow.less_than(self.low, value)
+        ub_bool = control_flow.less_than(value, self.high)
+        lb = tensor.cast(lb_bool, dtype=value.dtype)
+        ub = tensor.cast(ub_bool, dtype=value.dtype)
+        return elementwise_sub(
+            nn.log(lb * ub), nn.log(self.high - self.low), name=name)
+
+    def probs(self, value):
+        """Probability density/mass function.
+
+        Args:
+          value (Tensor): The input tensor.
+
+        Returns:
+          Tensor: probability.The data type is same with value.
+
+        """
+        name = self.name + '_probs'
+        if in_dygraph_mode():
+            lb_bool = self.low < value
+            ub_bool = value < self.high
+            lb = tensor.cast(lb_bool, dtype=value.dtype)
+            ub = tensor.cast(ub_bool, dtype=value.dtype)
+            return elementwise_div((lb * ub), (self.high - self.low), name=name)
+
+        check_variable_and_dtype(value, 'value', ['float32', 'float64'],
+                                 'log_prob')
+
+        lb_bool = control_flow.less_than(self.low, value)
+        ub_bool = control_flow.less_than(value, self.high)
+        lb = tensor.cast(lb_bool, dtype=value.dtype)
+        ub = tensor.cast(ub_bool, dtype=value.dtype)
+        return elementwise_div((lb * ub), (self.high - self.low), name=name)
+
+    def entropy(self):
+        """Shannon entropy in nats.
+
+        Returns:
+          Tensor: Shannon entropy of uniform distribution.The data type is float32.
+
+        """
+        name = self.name + '_entropy'
+        return nn.log(self.high - self.low, name=name)
+
+
+class Normal(Distribution):
+    """The Normal distribution with location `loc` and `scale` parameters.
+
+    Mathematical details
+
+    The probability density function (pdf) is,
+
+    .. math::
+
+        pdf(x; \mu, \sigma) = \\frac{1}{Z}e^{\\frac {-0.5 (x - \mu)^2}  {\sigma^2} }
+
+    .. math::
+
+        Z = (2 \pi \sigma^2)^{0.5}
+
+    In the above equation:
+
+    * :math:`loc = \mu`: is the mean.
+    * :math:`scale = \sigma`: is the std.
+    * :math:`Z`: is the normalization constant.
+
+    Args:
+        loc(int|float|list|numpy.ndarray|Tensor): The mean of normal distribution.The data type is float32 or int.
+        scale(int|float|list|numpy.ndarray|Tensor): The std of normal distribution.The data type is float32 or int.
+        name(str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
+
+    Examples:
+        .. code-block:: python
+          
+          import numpy as np
+          import paddle
+          from paddle.distribution import Normal
+
+          paddle.disable_static()
+          # Define a single scalar Normal distribution.
+          dist = Normal(loc=0., scale=3.)
+          # Define a batch of two scalar valued Normals.
+          # The first has mean 1 and standard deviation 11, the second 2 and 22.
+          dist = Normal(loc=[1., 2.], scale=[11., 22.])
+          # Get 3 samples, returning a 3 x 2 tensor.
+          dist.sample([3])
+
+          # Define a batch of two scalar valued Normals.
+          # Both have mean 1, but different standard deviations.
+          dist = Normal(loc=1., scale=[11., 22.])
+
+          # Complete example
+          value_npdata = np.array([0.8], dtype="float32")
+          value_tensor = paddle.to_tensor(value_npdata)
+
+          normal_a = Normal([0.], [1.])
+          normal_b = Normal([0.5], [2.])
+          sample = normal_a.sample([2])
+          # a random tensor created by normal distribution with shape: [2, 1]
+          entropy = normal_a.entropy()
+          # [1.4189385] with shape: [1]
+          lp = normal_a.log_prob(value_tensor)
+          # [-1.2389386] with shape: [1]
+          p = normal_a.probs(value_tensor)
+          # [0.28969154] with shape: [1]
+          kl = normal_a.kl_divergence(normal_b)
+          # [0.34939718] with shape: [1]
+    """
+
+    def __init__(self, loc, scale, name=None):
+        if not in_dygraph_mode():
+            check_type(loc, 'loc',
+                       (int, float, np.ndarray, tensor.Variable, list),
+                       'Normal')
+            check_type(scale, 'scale',
+                       (int, float, np.ndarray, tensor.Variable, list),
+                       'Normal')
+
+        self.batch_size_unknown = False
+        self.all_arg_is_float = False
+        self.name = name if name is not None else 'Normal'
+
+        if isinstance(loc, int):
+            loc = float(loc)
+        if isinstance(scale, int):
+            scale = float(scale)
+
+        if self._validate_args(loc, scale):
+            self.batch_size_unknown = True
+            self.loc = loc
+            self.scale = scale
+        else:
+            if isinstance(loc, float) and isinstance(scale, float):
+                self.all_arg_is_float = True
+            self.loc, self.scale = self._to_variable(loc, scale)
+
+    def sample(self, shape, seed=0):
+        """Generate samples of the specified shape.
+
+        Args:
+          shape (list): 1D `int32`. Shape of the generated samples.
+          seed (int): Python integer number.
+
+        Returns:
+          Tensor: A tensor with prepended dimensions shape.The data type is float32.
+
+        """
+        if not in_dygraph_mode():
+            check_type(shape, 'shape', (list), 'sample')
+            check_type(seed, 'seed', (int), 'sample')
+
+        batch_shape = list((self.loc + self.scale).shape)
+        name = self.name + '_sample'
+
+        if self.batch_size_unknown:
+            output_shape = shape + batch_shape
+            zero_tmp = tensor.fill_constant_batch_size_like(
+                self.loc + self.scale, batch_shape + shape, self.loc.dtype, 0.)
+            zero_tmp_shape = nn.shape(zero_tmp)
+            normal_random_tmp = nn.gaussian_random(
+                zero_tmp_shape, mean=0., std=1., seed=seed)
+            output = normal_random_tmp * (zero_tmp + self.scale) + self.loc
+            return nn.reshape(output, output_shape, name=name)
+        else:
+            output_shape = shape + batch_shape
+            output = nn.gaussian_random(output_shape, mean=0., std=1., seed=seed) * \
+                     (tensor.zeros(output_shape, dtype=self.loc.dtype) + self.scale)
+            output = elementwise_add(output, self.loc, name=name)
+            if self.all_arg_is_float:
+                return nn.reshape(output, shape, name=name)
+            else:
+                return output
+
+    def entropy(self):
+        """Shannon entropy in nats.
+
+        Returns:
+          Tensor: Shannon entropy of normal distribution.The data type is float32.
+
+        """
+        name = self.name + '_entropy'
+        batch_shape = list((self.loc + self.scale).shape)
+        zero_tmp = tensor.fill_constant_batch_size_like(
+            self.loc + self.scale, batch_shape, self.loc.dtype, 0.)
+        return elementwise_add(
+            0.5 + zero_tmp,
+            0.5 * math.log(2 * math.pi) + nn.log((self.scale + zero_tmp)),
+            name=name)
+
+    def log_prob(self, value):
+        """Log probability density/mass function.
+
+        Args:
+          value (Tensor): The input tensor.
+
+        Returns:
+          Tensor: log probability.The data type is same with value.
+
+        """
+        if not in_dygraph_mode():
+            check_variable_and_dtype(value, 'value', ['float32', 'float64'],
+                                     'log_prob')
+
+        name = self.name + '_log_prob'
+        var = self.scale * self.scale
+        log_scale = nn.log(self.scale)
+        return elementwise_sub(
+            -1. * ((value - self.loc) * (value - self.loc)) / (2. * var),
+            log_scale + math.log(math.sqrt(2. * math.pi)),
+            name=name)
+
+    def probs(self, value):
+        """Probability density/mass function.
+
+        Args:
+          value (Tensor): The input tensor.
+
+        Returns:
+          Tensor: probability.The data type is same with value.
+
+        """
+        if not in_dygraph_mode():
+            check_variable_and_dtype(value, 'value', ['float32', 'float64'],
+                                     'log_prob')
+
+        name = self.name + '_probs'
+        var = self.scale * self.scale
+        return elementwise_div(
+            ops.exp(-1. * ((value - self.loc) * (value - self.loc)) /
+                    (2. * var)), (math.sqrt(2 * math.pi) * self.scale),
+            name=name)
+
+    def kl_divergence(self, other):
+        """The KL-divergence between two normal distributions.
+
+        Args:
+            other (Normal): instance of Normal.
+
+        Returns:
+            Tensor: kl-divergence between two normal distributions.The data type is float32.
+
+        """
+        if not in_dygraph_mode():
+            check_type(other, 'other', Normal, 'kl_divergence')
+
+        name = self.name + '_kl_divergence'
+        var_ratio = self.scale / other.scale
+        var_ratio = (var_ratio * var_ratio)
+        t1 = (self.loc - other.loc) / other.scale
+        t1 = (t1 * t1)
+        return elementwise_add(
+            0.5 * var_ratio, 0.5 * (t1 - 1. - nn.log(var_ratio)), name=name)
diff --git a/python/paddle/fluid/tests/unittests/test_distribution.py b/python/paddle/fluid/tests/unittests/test_distribution.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ccaa3266e087a38ac38667c62487e69c6bb6bf6
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/test_distribution.py
@@ -0,0 +1,725 @@
+#   Copyright (c) 2020 PaddlePaddle 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.
+
+import numpy as np
+import unittest
+import paddle
+from paddle import fluid
+from paddle.fluid import layers
+from paddle.distribution import *
+import math
+
+
+class DistributionNumpy():
+    def sample(self):
+        raise NotImplementedError
+
+    def entropy(self):
+        raise NotImplementedError
+
+    def kl_divergence(self, other):
+        raise NotImplementedError
+
+    def log_prob(self, value):
+        raise NotImplementedError
+
+    def probs(self, value):
+        raise NotImplementedError
+
+
+class UniformNumpy(DistributionNumpy):
+    def __init__(self, low, high):
+        self.low = np.array(low).astype('float32')
+        self.high = np.array(high).astype('float32')
+
+    def sample(self, shape):
+        shape = tuple(shape) + (self.low + self.high).shape
+        return self.low + (np.random.uniform(size=shape) *
+                           (self.high - self.low))
+
+    def log_prob(self, value):
+        lb = np.less(self.low, value).astype('float32')
+        ub = np.less(value, self.high).astype('float32')
+        return np.log(lb * ub) - np.log(self.high - self.low)
+
+    def probs(self, value):
+        lb = np.less(self.low, value).astype('float32')
+        ub = np.less(value, self.high).astype('float32')
+        return (lb * ub) / (self.high - self.low)
+
+    def entropy(self):
+        return np.log(self.high - self.low)
+
+
+class NormalNumpy(DistributionNumpy):
+    def __init__(self, loc, scale):
+        self.loc = np.array(loc).astype('float32')
+        self.scale = np.array(scale).astype('float32')
+
+    def sample(self, shape):
+        shape = tuple(shape) + (self.loc + self.scale).shape
+        return self.loc + (np.random.randn(*shape) * self.scale)
+
+    def log_prob(self, value):
+        var = self.scale * self.scale
+        log_scale = np.log(self.scale)
+        return -((value - self.loc) * (value - self.loc)) / (
+            2. * var) - log_scale - math.log(math.sqrt(2. * math.pi))
+
+    def probs(self, value):
+        var = self.scale * self.scale
+        return np.exp(-1. * ((value - self.loc) * (value - self.loc)) /
+                      (2. * var)) / (math.sqrt(2 * math.pi) * self.scale)
+
+    def entropy(self):
+        return 0.5 + 0.5 * np.log(np.array(2. * math.pi).astype(
+            'float32')) + np.log(self.scale)
+
+    def kl_divergence(self, other):
+        var_ratio = (self.scale / other.scale)
+        var_ratio = var_ratio * var_ratio
+        t1 = ((self.loc - other.loc) / other.scale)
+        t1 = (t1 * t1)
+        return 0.5 * (var_ratio + t1 - 1 - np.log(var_ratio))
+
+
+class DistributionTest(unittest.TestCase):
+    def setUp(self, use_gpu=False):
+        self.use_gpu = use_gpu
+        if not use_gpu:
+            place = fluid.CPUPlace()
+            self.gpu_id = -1
+        else:
+            place = fluid.CUDAPlace(0)
+            self.gpu_id = 0
+        self.executor = fluid.Executor(place)
+
+    def build_normal_common_net(self, batch_size, dims, loc_float, scale_float,
+                                other_loc_float, other_scale_float, scale_np,
+                                other_scale_np, loc_np, other_loc_np, loc,
+                                scale, other_loc, other_scale, values):
+        normal_int = Normal(int(loc_float), int(scale_float))
+        normal_float = Normal(loc_float, scale_float)
+        other_normal_float = Normal(other_loc_float, other_scale_float)
+
+        normal_float_np_broadcast = Normal(loc_float, scale_np)
+        other_normal_float_np_broadcast = Normal(other_loc_float,
+                                                 other_scale_np)
+
+        normal_np = Normal(loc_np, scale_np)
+        other_normal_np = Normal(other_loc_np, other_scale_np)
+
+        normal_variable = Normal(loc, scale)
+        other_normal_variable = Normal(other_loc, other_scale)
+
+        sample_int = normal_int.sample([batch_size, dims])
+        sample_float = normal_float.sample([batch_size, dims])
+        sample_float_np_broadcast = normal_float_np_broadcast.sample(
+            [batch_size, dims])
+        sample_np = normal_np.sample([batch_size, dims])
+        sample_variable = normal_variable.sample([batch_size, dims])
+
+        entropy_int = normal_int.entropy()
+        entropy_float = normal_float.entropy()
+        entropy_float_np_broadcast = normal_float_np_broadcast.entropy()
+        entropy_np = normal_np.entropy()
+        entropy_variable = normal_variable.entropy()
+
+        lp_float_np_broadcast = normal_float_np_broadcast.log_prob(values)
+        lp_np = normal_np.log_prob(values)
+        lp_variable = normal_variable.log_prob(values)
+
+        p_float_np_broadcast = normal_float_np_broadcast.probs(values)
+        p_np = normal_np.probs(values)
+        p_variable = normal_variable.probs(values)
+
+        kl_float = normal_float.kl_divergence(other_normal_float)
+        kl_float_np_broadcast = normal_float_np_broadcast.kl_divergence(
+            other_normal_float_np_broadcast)
+        kl_np = normal_np.kl_divergence(other_normal_np)
+        kl_variable = normal_variable.kl_divergence(other_normal_variable)
+
+        fetch_list = [
+            sample_int, sample_float, sample_float_np_broadcast, sample_np,
+            sample_variable, entropy_int, entropy_float,
+            entropy_float_np_broadcast, entropy_np, entropy_variable,
+            lp_float_np_broadcast, lp_np, lp_variable, p_float_np_broadcast,
+            p_np, p_variable, kl_float, kl_float_np_broadcast, kl_np,
+            kl_variable
+        ]
+        return fetch_list
+
+    def build_normal_static(self, test_program, batch_size, dims, loc_float,
+                            scale_float, other_loc_float, other_scale_float,
+                            scale_np, other_scale_np, loc_np, other_loc_np,
+                            values_np):
+        with fluid.program_guard(test_program):
+            loc = layers.data(name='loc', shape=[dims], dtype='float32')
+            scale = layers.data(name='scale', shape=[dims], dtype='float32')
+
+            other_loc = layers.data(
+                name='other_loc', shape=[dims], dtype='float32')
+            other_scale = layers.data(
+                name='other_scale', shape=[dims], dtype='float32')
+
+            values = layers.data(name='values', shape=[dims], dtype='float32')
+
+            fetch_list = self.build_normal_common_net(
+                batch_size, dims, loc_float, scale_float, other_loc_float,
+                other_scale_float, scale_np, other_scale_np, loc_np,
+                other_loc_np, loc, scale, other_loc, other_scale, values)
+
+        feed_vars = {
+            'loc': loc_np,
+            'scale': scale_np,
+            'other_loc': other_loc_np,
+            'other_scale': other_scale_np,
+            'values': values_np
+        }
+        return feed_vars, fetch_list
+
+    def build_normal_dygraph(self, batch_size, dims, loc_float, scale_float,
+                             other_loc_float, other_scale_float, scale_np,
+                             other_scale_np, loc_np, other_loc_np, values_np):
+        loc = paddle.to_tensor(loc_np)
+        scale = paddle.to_tensor(scale_np)
+        other_loc = paddle.to_tensor(other_loc_np)
+        other_scale = paddle.to_tensor(other_scale_np)
+        values = paddle.to_tensor(values_np)
+
+        fetch_list = self.build_normal_common_net(
+            batch_size, dims, loc_float, scale_float, other_loc_float,
+            other_scale_float, scale_np, other_scale_np, loc_np, other_loc_np,
+            loc, scale, other_loc, other_scale, values)
+        fetch_list_numpy = [t.numpy() for t in fetch_list]
+        return fetch_list_numpy
+
+    def get_normal_random_input(self, batch_size, dims):
+        loc_np = np.random.randn(batch_size, dims).astype('float32')
+        other_loc_np = np.random.randn(batch_size, dims).astype('float32')
+
+        loc_float = (np.random.ranf() - 0.5) * 4
+        scale_float = (np.random.ranf() - 0.5) * 4
+        while scale_float < 0:
+            scale_float = (np.random.ranf() - 0.5) * 4
+
+        other_loc_float = (np.random.ranf() - 0.5) * 4
+        other_scale_float = (np.random.ranf() - 0.5) * 4
+        while other_scale_float < 0:
+            other_scale_float = (np.random.ranf() - 0.5) * 4
+
+        scale_np = np.random.randn(batch_size, dims).astype('float32')
+        other_scale_np = np.random.randn(batch_size, dims).astype('float32')
+        values_np = np.random.randn(batch_size, dims).astype('float32')
+
+        while not np.all(scale_np > 0):
+            scale_np = np.random.randn(batch_size, dims).astype('float32')
+        while not np.all(other_scale_np > 0):
+            other_scale_np = np.random.randn(batch_size, dims).astype('float32')
+        return [
+            loc_np, other_loc_np, loc_float, scale_float, other_loc_float,
+            other_scale_float, scale_np, other_scale_np, values_np
+        ]
+
+    def compare_normal_with_numpy(self,
+                                  data_list,
+                                  output_list,
+                                  batch_size=2,
+                                  dims=3,
+                                  tolerance=1e-6):
+        loc_np, other_loc_np, loc_float, scale_float, other_loc_float, other_scale_float, scale_np, other_scale_np, values_np = data_list
+
+        np_normal_int = NormalNumpy(int(loc_float), int(scale_float))
+        np_normal_float = NormalNumpy(loc_float, scale_float)
+        np_other_normal_float = NormalNumpy(other_loc_float, other_scale_float)
+        np_normal_float_np_broadcast = NormalNumpy(loc_float, scale_np)
+        np_other_normal_float_np_broadcast = NormalNumpy(other_loc_float,
+                                                         other_scale_np)
+        np_normal = NormalNumpy(loc_np, scale_np)
+        np_other_normal = NormalNumpy(other_loc_np, other_scale_np)
+
+        gt_sample_int = np_normal_int.sample([batch_size, dims])
+        gt_sample_float = np_normal_float.sample([batch_size, dims])
+        gt_sample_float_np_broadcast = np_normal_float_np_broadcast.sample(
+            [batch_size, dims])
+        gt_sample_np = np_normal.sample([batch_size, dims])
+        gt_entropy_int = np_normal_int.entropy()
+        gt_entropy_float = np_normal_float.entropy()
+        gt_entropy_float_np_broadcast = np_normal_float_np_broadcast.entropy()
+        gt_entropy = np_normal.entropy()
+        gt_lp_float_np_broadcast = np_normal_float_np_broadcast.log_prob(
+            values_np)
+        gt_lp = np_normal.log_prob(values_np)
+        gt_p_float_np_broadcast = np_normal_float_np_broadcast.probs(values_np)
+        gt_p = np_normal.probs(values_np)
+        gt_kl_float = np_normal_float.kl_divergence(np_other_normal_float)
+        gt_kl_float_np_broadcast = np_normal_float_np_broadcast.kl_divergence(
+            np_other_normal_float_np_broadcast)
+        gt_kl = np_normal.kl_divergence(np_other_normal)
+
+        [
+            output_sample_int, output_sample_float,
+            output_sample_float_np_broadcast, output_sample_np,
+            output_sample_variable, output_entropy_int, output_entropy_float,
+            output_entropy_float_np_broadcast, output_entropy_np,
+            output_entropy_variable, output_lp_float_np_broadcast, output_lp_np,
+            output_lp_variable, output_p_float_np_broadcast, output_p_np,
+            output_p_variable, output_kl_float, output_kl_float_np_broadcast,
+            output_kl_np, output_kl_variable
+        ] = output_list
+
+        np.testing.assert_allclose(
+            output_sample_int.shape,
+            gt_sample_int.shape,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_sample_float.shape,
+            gt_sample_float.shape,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_sample_float_np_broadcast.shape,
+            gt_sample_float_np_broadcast.shape,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_sample_np.shape,
+            gt_sample_np.shape,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_sample_variable.shape,
+            gt_sample_np.shape,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_entropy_int, gt_entropy_int, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_entropy_float,
+            gt_entropy_float,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_entropy_float_np_broadcast,
+            gt_entropy_float_np_broadcast,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_entropy_np, gt_entropy, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_entropy_variable, gt_entropy, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_lp_float_np_broadcast,
+            gt_lp_float_np_broadcast,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_lp_np, gt_lp, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_lp_variable, gt_lp, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_p_float_np_broadcast,
+            gt_p_float_np_broadcast,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_p_np, gt_p, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_p_variable, gt_p, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_kl_float, gt_kl_float, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_kl_float_np_broadcast,
+            gt_kl_float_np_broadcast,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_kl_np, gt_kl, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_kl_variable, gt_kl, rtol=tolerance, atol=tolerance)
+
+    def test_normal_distribution_static(self,
+                                        batch_size=2,
+                                        dims=3,
+                                        tolerance=1e-6):
+        test_program = fluid.Program()
+        data_list = self.get_normal_random_input(batch_size, dims)
+        loc_np, other_loc_np, loc_float, scale_float, other_loc_float, other_scale_float, scale_np, other_scale_np, values_np = data_list
+
+        feed_vars, fetch_list = self.build_normal_static(
+            test_program, batch_size, dims, loc_float, scale_float,
+            other_loc_float, other_scale_float, scale_np, other_scale_np,
+            loc_np, other_loc_np, values_np)
+        self.executor.run(fluid.default_startup_program())
+
+        output_list = self.executor.run(program=test_program,
+                                        feed=feed_vars,
+                                        fetch_list=fetch_list)
+
+        self.compare_normal_with_numpy(data_list, output_list, batch_size, dims,
+                                       tolerance)
+
+    def test_normal_distribution_dygraph(self,
+                                         batch_size=2,
+                                         dims=3,
+                                         tolerance=1e-6):
+        paddle.disable_static()
+        data_list = self.get_normal_random_input(batch_size, dims)
+        loc_np, other_loc_np, loc_float, scale_float, other_loc_float, other_scale_float, scale_np, other_scale_np, values_np = data_list
+
+        output_list = self.build_normal_dygraph(
+            batch_size, dims, loc_float, scale_float, other_loc_float,
+            other_scale_float, scale_np, other_scale_np, loc_np, other_loc_np,
+            values_np)
+
+        self.compare_normal_with_numpy(data_list, output_list, batch_size, dims,
+                                       tolerance)
+        paddle.enable_static()
+
+    def build_uniform_common_net(self, batch_size, dims, low_float, high_float,
+                                 high_np, low_np, values_np, low, high, values):
+        uniform_int = Uniform(int(low_float), int(high_float))
+        uniform_float = Uniform(low_float, high_float)
+        uniform_float_np_broadcast = Uniform(low_float, high_np)
+        uniform_np = Uniform(low_np, high_np)
+        uniform_variable = Uniform(low, high)
+
+        sample_int = uniform_int.sample([batch_size, dims])
+        sample_float = uniform_float.sample([batch_size, dims])
+        sample_float_np_broadcast = uniform_float_np_broadcast.sample(
+            [batch_size, dims])
+        sample_np = uniform_np.sample([batch_size, dims])
+        sample_variable = uniform_variable.sample([batch_size, dims])
+
+        entropy_int = uniform_int.entropy()
+        entropy_float = uniform_float.entropy()
+        entropy_float_np_broadcast = uniform_float_np_broadcast.entropy()
+        entropy_np = uniform_np.entropy()
+        entropy_variable = uniform_variable.entropy()
+
+        lp_float_np_broadcast = uniform_float_np_broadcast.log_prob(values)
+        lp_np = uniform_np.log_prob(values)
+        lp_variable = uniform_variable.log_prob(values)
+
+        p_float_np_broadcast = uniform_float_np_broadcast.probs(values)
+        p_np = uniform_np.probs(values)
+        p_variable = uniform_variable.probs(values)
+
+        fetch_list = [
+            sample_int, sample_float, sample_float_np_broadcast, sample_np,
+            sample_variable, entropy_int, entropy_float,
+            entropy_float_np_broadcast, entropy_np, entropy_variable,
+            lp_float_np_broadcast, lp_np, lp_variable, p_float_np_broadcast,
+            p_np, p_variable
+        ]
+        return fetch_list
+
+    def build_uniform_static(self, test_program, batch_size, dims, low_float,
+                             high_float, high_np, low_np, values_np):
+        with fluid.program_guard(test_program):
+            low = layers.data(name='low', shape=[dims], dtype='float32')
+            high = layers.data(name='high', shape=[dims], dtype='float32')
+
+            values = layers.data(name='values', shape=[dims], dtype='float32')
+
+            fetch_list = self.build_uniform_common_net(
+                batch_size, dims, low_float, high_float, high_np, low_np,
+                values_np, low, high, values)
+
+        feed_vars = {'low': low_np, 'high': high_np, 'values': values_np}
+        return feed_vars, fetch_list
+
+    def build_uniform_dygraph(self, batch_size, dims, low_float, high_float,
+                              high_np, low_np, values_np):
+        low = paddle.to_tensor(low_np)
+        high = paddle.to_tensor(high_np)
+        values = paddle.to_tensor(values_np)
+
+        fetch_list = self.build_uniform_common_net(batch_size, dims, low_float,
+                                                   high_float, high_np, low_np,
+                                                   values_np, low, high, values)
+        fetch_list_numpy = [t.numpy() for t in fetch_list]
+        return fetch_list_numpy
+
+    def compare_uniform_with_numpy(self,
+                                   data_list,
+                                   output_list,
+                                   batch_size=2,
+                                   dims=3,
+                                   tolerance=1e-6):
+        [low_np, low_float, high_float, high_np, values_np] = data_list
+
+        np_uniform_int = UniformNumpy(int(low_float), int(high_float))
+        np_uniform_float = UniformNumpy(low_float, high_float)
+        np_uniform_float_np_broadcast = UniformNumpy(low_float, high_np)
+        np_uniform = UniformNumpy(low_np, high_np)
+
+        gt_sample_int = np_uniform_int.sample([batch_size, dims])
+        gt_sample_float = np_uniform_float.sample([batch_size, dims])
+        gt_sample_float_np_broadcast = np_uniform_float_np_broadcast.sample(
+            [batch_size, dims])
+        gt_sample_np = np_uniform.sample([batch_size, dims])
+        gt_entropy_int = np_uniform_int.entropy()
+        gt_entropy_float = np_uniform_float.entropy()
+        gt_entropy_float_np_broadcast = np_uniform_float_np_broadcast.entropy()
+        gt_entropy = np_uniform.entropy()
+        gt_lp_float_np_broadcast = np_uniform_float_np_broadcast.log_prob(
+            values_np)
+        gt_lp = np_uniform.log_prob(values_np)
+        gt_p_float_np_broadcast = np_uniform_float_np_broadcast.probs(values_np)
+        gt_p = np_uniform.probs(values_np)
+
+        [
+            output_sample_int, output_sample_float,
+            output_sample_float_np_broadcast, output_sample_np,
+            output_sample_variable, output_entropy_int, output_entropy_float,
+            output_entropy_float_np_broadcast, output_entropy_np,
+            output_entropy_variable, output_lp_float_np_broadcast, output_lp_np,
+            output_lp_variable, output_p_float_np_broadcast, output_p_np,
+            output_p_variable
+        ] = output_list
+
+        np.testing.assert_allclose(
+            output_sample_int.shape,
+            gt_sample_int.shape,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_sample_float.shape,
+            gt_sample_float.shape,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_sample_float_np_broadcast.shape,
+            gt_sample_float_np_broadcast.shape,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_sample_np.shape,
+            gt_sample_np.shape,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_sample_variable.shape,
+            gt_sample_np.shape,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_entropy_int, gt_entropy_int, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_entropy_float,
+            gt_entropy_float,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_entropy_float_np_broadcast,
+            gt_entropy_float_np_broadcast,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_entropy_np, gt_entropy, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_entropy_variable, gt_entropy, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_lp_float_np_broadcast,
+            gt_lp_float_np_broadcast,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_lp_np, gt_lp, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_lp_variable, gt_lp, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_p_float_np_broadcast,
+            gt_p_float_np_broadcast,
+            rtol=tolerance,
+            atol=tolerance)
+        np.testing.assert_allclose(
+            output_p_np, gt_p, rtol=tolerance, atol=tolerance)
+        np.testing.assert_allclose(
+            output_p_variable, gt_p, rtol=tolerance, atol=tolerance)
+
+    def test_uniform_distribution_static(self,
+                                         batch_size=2,
+                                         dims=3,
+                                         tolerance=1e-6):
+        test_program = fluid.Program()
+
+        low_np = np.random.randn(batch_size, dims).astype('float32')
+        low_float = np.random.uniform(-2, 1)
+        high_float = np.random.uniform(1, 3)
+        high_np = np.random.uniform(-5.0, 5.0,
+                                    (batch_size, dims)).astype('float32')
+        values_np = np.random.randn(batch_size, dims).astype('float32')
+
+        data_list = [low_np, low_float, high_float, high_np, values_np]
+
+        feed_vars, fetch_list = self.build_uniform_static(
+            test_program, batch_size, dims, low_float, high_float, high_np,
+            low_np, values_np)
+
+        self.executor.run(fluid.default_startup_program())
+
+        # result calculated by paddle
+        output_list = self.executor.run(program=test_program,
+                                        feed=feed_vars,
+                                        fetch_list=fetch_list)
+        self.compare_uniform_with_numpy(data_list, output_list, batch_size,
+                                        dims, tolerance)
+
+    def test_uniform_distribution_dygraph(self,
+                                          batch_size=2,
+                                          dims=3,
+                                          tolerance=1e-6):
+        paddle.disable_static()
+
+        low_np = np.random.randn(batch_size, dims).astype('float32')
+        low_float = np.random.uniform(-2, 1)
+        high_float = np.random.uniform(1, 3)
+        high_np = np.random.uniform(-5.0, 5.0,
+                                    (batch_size, dims)).astype('float32')
+        values_np = np.random.randn(batch_size, dims).astype('float32')
+
+        data_list = [low_np, low_float, high_float, high_np, values_np]
+        output_list = self.build_uniform_dygraph(
+            batch_size, dims, low_float, high_float, high_np, low_np, values_np)
+
+        self.compare_uniform_with_numpy(data_list, output_list, batch_size,
+                                        dims, tolerance)
+        paddle.enable_static()
+
+
+class DistributionTestError(unittest.TestCase):
+    def test_distribution_error(self):
+        distribution = Distribution()
+
+        self.assertRaises(NotImplementedError, distribution.sample)
+        self.assertRaises(NotImplementedError, distribution.entropy)
+
+        normal = Normal(0.0, 1.0)
+        self.assertRaises(NotImplementedError, distribution.kl_divergence,
+                          normal)
+
+        value_npdata = np.array([0.8], dtype="float32")
+        value_tensor = layers.create_tensor(dtype="float32")
+        self.assertRaises(NotImplementedError, distribution.log_prob,
+                          value_tensor)
+        self.assertRaises(NotImplementedError, distribution.probs, value_tensor)
+
+    def test_normal_error(self):
+        normal = Normal(0.0, 1.0)
+
+        value = [1.0, 2.0]
+        # type of value must be variable
+        self.assertRaises(TypeError, normal.log_prob, value)
+
+        value = [1.0, 2.0]
+        # type of value must be variable
+        self.assertRaises(TypeError, normal.probs, value)
+
+        shape = 1.0
+        # type of shape must be list
+        self.assertRaises(TypeError, normal.sample, shape)
+
+        seed = 1.0
+        # type of seed must be int
+        self.assertRaises(TypeError, normal.sample, [2, 3], seed)
+
+        normal_other = Uniform(1.0, 2.0)
+        # type of other must be an instance of Normal
+        self.assertRaises(TypeError, normal.kl_divergence, normal_other)
+
+    def test_uniform_error(self):
+        uniform = Uniform(0.0, 1.0)
+
+        value = [1.0, 2.0]
+        # type of value must be variable
+        self.assertRaises(TypeError, uniform.log_prob, value)
+
+        value = [1.0, 2.0]
+        # type of value must be variable
+        self.assertRaises(TypeError, uniform.probs, value)
+
+        shape = 1.0
+        # type of shape must be list
+        self.assertRaises(TypeError, uniform.sample, shape)
+
+        seed = 1.0
+        # type of seed must be int
+        self.assertRaises(TypeError, uniform.sample, [2, 3], seed)
+
+
+class DistributionTestName(unittest.TestCase):
+    def get_prefix(self, string):
+        return (string.split('.')[0])
+
+    def test_normal_name(self):
+        name = 'test_normal'
+        normal1 = Normal(0.0, 1.0, name=name)
+        self.assertEqual(normal1.name, name)
+
+        normal2 = Normal(0.0, 1.0)
+        self.assertEqual(normal2.name, 'Normal')
+
+        paddle.enable_static()
+
+        sample = normal1.sample([2])
+        self.assertEqual(self.get_prefix(sample.name), name + '_sample')
+
+        entropy = normal1.entropy()
+        self.assertEqual(self.get_prefix(entropy.name), name + '_entropy')
+
+        value_npdata = np.array([0.8], dtype="float32")
+        value_tensor = layers.create_tensor(dtype="float32")
+        layers.assign(value_npdata, value_tensor)
+
+        lp = normal1.log_prob(value_tensor)
+        self.assertEqual(self.get_prefix(lp.name), name + '_log_prob')
+
+        p = normal1.probs(value_tensor)
+        self.assertEqual(self.get_prefix(p.name), name + '_probs')
+
+        kl = normal1.kl_divergence(normal2)
+        self.assertEqual(self.get_prefix(kl.name), name + '_kl_divergence')
+
+    def test_uniform_name(self):
+        name = 'test_uniform'
+        uniform1 = Uniform(0.0, 1.0, name=name)
+        self.assertEqual(uniform1.name, name)
+
+        uniform2 = Uniform(0.0, 1.0)
+        self.assertEqual(uniform2.name, 'Uniform')
+
+        paddle.enable_static()
+
+        sample = uniform1.sample([2])
+        self.assertEqual(self.get_prefix(sample.name), name + '_sample')
+
+        entropy = uniform1.entropy()
+        self.assertEqual(self.get_prefix(entropy.name), name + '_entropy')
+
+        value_npdata = np.array([0.8], dtype="float32")
+        value_tensor = layers.create_tensor(dtype="float32")
+        layers.assign(value_npdata, value_tensor)
+
+        lp = uniform1.log_prob(value_tensor)
+        self.assertEqual(self.get_prefix(lp.name), name + '_log_prob')
+
+        p = uniform1.probs(value_tensor)
+        self.assertEqual(self.get_prefix(p.name), name + '_probs')
+
+
+if __name__ == '__main__':
+    unittest.main()