diff --git a/mindspore/nn/__init__.py b/mindspore/nn/__init__.py
index 8d5e7d3b0a..e5c133a9a6 100644
--- a/mindspore/nn/__init__.py
+++ b/mindspore/nn/__init__.py
@@ -17,13 +17,15 @@ Neural Networks Cells.
 
 Pre-defined building blocks or computing units to construct Neural Networks.
 """
-from . import layer, loss, optim, metrics, wrap
+from . import layer, loss, optim, metrics, wrap, distribution
 from .cell import Cell, GraphKernel
 from .layer import *
 from .loss import *
 from .optim import *
 from .metrics import *
 from .wrap import *
+from .distribution import *
+
 
 __all__ = ["Cell", "GraphKernel"]
 __all__.extend(layer.__all__)
@@ -31,5 +33,7 @@ __all__.extend(loss.__all__)
 __all__.extend(optim.__all__)
 __all__.extend(metrics.__all__)
 __all__.extend(wrap.__all__)
+__all__.extend(distribution.__all__)
+
 
 __all__.sort()
diff --git a/mindspore/nn/distribution/__init__.py b/mindspore/nn/distribution/__init__.py
new file mode 100644
index 0000000000..55b4b03ef7
--- /dev/null
+++ b/mindspore/nn/distribution/__init__.py
@@ -0,0 +1,27 @@
+# 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.
+# ============================================================================
+"""
+Distribution.
+
+The high-level components(Distributions) used to construct the probabilistic network.
+"""
+
+from .distribution import Distribution
+from .normal import Normal
+from .bernoulli import Bernoulli
+
+__all__ = ['Distribution',
+           'Normal',
+           'Bernoulli',]
diff --git a/mindspore/nn/distribution/_utils/__init__.py b/mindspore/nn/distribution/_utils/__init__.py
new file mode 100644
index 0000000000..816485643a
--- /dev/null
+++ b/mindspore/nn/distribution/_utils/__init__.py
@@ -0,0 +1,24 @@
+# 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.
+# ============================================================================
+"""
+Distribution operation utility functions.
+"""
+from .utils import *
+
+__all__ = ['check_scalar', 'convert_to_batch', 'cast_to_tensor',
+           'calc_batch_size', 'check_greater',
+           'check_greater_equal_zero',
+           'calc_broadcast_shape_from_param',
+           'check_scalar_from_param', 'check_prob']
diff --git a/mindspore/nn/distribution/_utils/utils.py b/mindspore/nn/distribution/_utils/utils.py
new file mode 100644
index 0000000000..108cff6614
--- /dev/null
+++ b/mindspore/nn/distribution/_utils/utils.py
@@ -0,0 +1,199 @@
+
+# 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.
+# ============================================================================
+"""Utitly functions to help distribution class."""
+import numpy as np
+from mindspore.ops import _utils as utils
+from ....common.tensor import Tensor, MetaTensor
+from ....common.parameter import Parameter
+from ....common import dtype as mstype
+
+
+def check_scalar(value):
+    """
+    Check if input value is a scalar.
+    """
+    return np.isscalar(value)
+
+
+def cast_to_tensor(t, dtype=mstype.float32):
+    """
+    Cast an user input value into a Tensor of dtype.
+
+    Args:
+        t (int, float, list, numpy.ndarray, Tensor, Parameter): object to be cast to Tensor.
+        dtype (mindspore.dtype): dtype of the Tensor. Default: mstype.float32.
+
+    Raises:
+        RuntimeError: if t cannot be cast to Tensor.
+
+    Returns:
+        Tensor.
+    """
+    if isinstance(t, Parameter):
+        return t
+    if isinstance(t, Tensor):
+        #check if the Tensor in shape of Tensor(4)
+        if t.dim() == 0:
+            value = t.asnumpy()
+            return Tensor([t], dtype=dtype)
+        #convert the type of tensor to dtype
+        t.set_dtype(dtype)
+        return t
+    if isinstance(t, (list, np.ndarray)):
+        return Tensor(t, dtype=dtype)
+    if check_scalar(t):
+        return Tensor([t], dtype=dtype)
+    raise RuntimeError("Input type is not supported.")
+
+def calc_batch_size(batch_shape):
+    """
+    Calculate the size of a given batch_shape.
+
+    Args:
+        batch_shape (tuple): batch shape to be calculated.
+
+    Returns:
+        int.
+    """
+    return int(np.prod(batch_shape))
+
+def convert_to_batch(t, batch_shape, dtype):
+    """
+    Convert a Tensor to a given batch shape.
+
+    Args:
+        t (Tensor, Parameter): Tensor to be converted.
+        batch_shape (tuple): desired batch shape.
+        dtype (mindspore.dtype): desired dtype.
+
+    Raises:
+        RuntimeError: if the converison cannot be done.
+
+    Returns:
+        Tensor, with shape of batch_shape.
+    """
+    if isinstance(t, Parameter):
+        return t
+    t = cast_to_tensor(t, dtype)
+    if t.shape != batch_shape:
+        mul = calc_batch_size(batch_shape) // t.size()
+        if (calc_batch_size(batch_shape) % t.size()) != 0:
+            raise RuntimeError("Cannot cast the tensor to the given batch shape.")
+        temp = list(t.asnumpy()) * mul
+        temp = np.reshape(temp, batch_shape)
+        return Tensor(temp, dtype)
+    return t
+
+def check_scalar_from_param(params):
+    """
+    Check if params are all scalars.
+
+    Args:
+        params (dict): parameters used to initialize distribution.
+
+    Notes: String parameters are excluded.
+    """
+    for value in params.values():
+        if isinstance(value, (str, type(params['dtype']))):
+            continue
+        elif check_scalar(value):
+            continue
+        else:
+            return False
+    return True
+
+
+def calc_broadcast_shape_from_param(params):
+    """
+    Calculate the broadcast shape from params.
+
+    Args:
+        params (dict): parameters used to initialize distribution.
+
+    Returns:
+        tuple.
+    """
+    broadcast_shape = []
+    for value in params.values():
+        if isinstance(value, (str, type(params['dtype']))):
+            continue
+        if value is None:
+            return None
+        if isinstance(value, Parameter):
+            value_t = value.default_input
+        else:
+            value_t = cast_to_tensor(value, params['dtype'])
+        broadcast_shape = utils.get_broadcast_shape(broadcast_shape, list(value_t.shape), params['name'])
+    return tuple(broadcast_shape)
+
+def check_greater_equal_zero(value, name):
+    """
+    Check if the given Tensor is greater zero.
+
+    Args:
+        value (Tensor, Parameter): value to be checked.
+        name (str) : name of the value.
+
+    Raises:
+        ValueError: if the input value is less than zero.
+
+    """
+    if isinstance(value, Parameter):
+        if isinstance(value.default_input, MetaTensor):
+            return
+        value = value.default_input
+    comp = np.less(value.asnumpy(), np.zeros(value.shape))
+    if comp.any():
+        raise ValueError(f'{name} should be greater than zero.')
+
+def check_greater(a, b, name_a, name_b):
+    """
+    Check if Tensor b is strictly greater than Tensor a.
+
+    Args:
+        a (Tensor): input tensor a.
+        b (Tensor): input tensor b.
+        name_a (str): name of Tensor_a.
+        name_b (str): name of Tensor_b.
+
+    Raises:
+        ValueError: if b is less than or equal to a
+    """
+    comp = np.less(a.asnumpy(), b.asnumpy())
+    if not comp.all():
+        raise ValueError(f'{name_a} should be less than {name_b}')
+
+
+def check_prob(p):
+    """
+    Check if p is a proper probability, i.e. 0 <= p <=1.
+
+    Args:
+        p (Tensor, Parameter): value to be checked.
+
+    Raises:
+        ValueError: if p is not a proper probability.
+    """
+    if isinstance(p, Parameter):
+        if isinstance(p.default_input, MetaTensor):
+            return
+        p = p.default_input
+    comp = np.less(p.asnumpy(), np.zeros(p.shape))
+    if comp.any():
+        raise ValueError('Probabilities should be greater than or equal to zero')
+    comp = np.greater(p.asnumpy(), np.ones(p.shape))
+    if comp.any():
+        raise ValueError('Probabilities should be less than or equal to one')
diff --git a/mindspore/nn/distribution/bernoulli.py b/mindspore/nn/distribution/bernoulli.py
new file mode 100644
index 0000000000..d0d8a5b08a
--- /dev/null
+++ b/mindspore/nn/distribution/bernoulli.py
@@ -0,0 +1,167 @@
+# 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.
+# ============================================================================
+"""Bernoulli Distribution"""
+from mindspore.ops import operations as P
+from .distribution import Distribution
+from ._utils.utils import cast_to_tensor, check_prob
+from ...common import dtype as mstype
+
+class Bernoulli(Distribution):
+    """
+    Example class: Bernoulli Distribution.
+
+    Args:
+        probs (int, float, list, numpy.ndarray, Tensor, Parameter): probability of 1 as outcome.
+        seed (int): seed to use in sampling. Default: 0.
+        dtype (mindspore.dtype): type of the distribution. Default: mstype.int32.
+        name (str): name of the distribution. Default: Bernoulli.
+
+    Note:
+        probs should be proper probabilities (0 <= p <= 1).
+
+    Examples:
+        >>>    # To initialize a Bernoulli distribution which has equal probability of getting 1 and 0
+        >>>    b = nn.Bernoulli(0.5, dtype = mstype.int32)
+        >>>    # The following create two independent Bernoulli distributions
+        >>>    b = nn.Bernoulli([0.7, 0.2], dtype = mstype.int32)
+    """
+
+    def __init__(self,
+                 probs=None,
+                 seed=0,
+                 dtype=mstype.int32,
+                 name="Bernoulli"):
+        """
+        Constructor of Bernoulli distribution.
+        """
+        param = dict(locals())
+        super(Bernoulli, self).__init__(dtype, name, param)
+        if probs is not None:
+            self._probs = cast_to_tensor(probs)
+            check_prob(self._probs)
+        else:
+            self._probs = probs
+
+        # ops needed for the class
+        self.log = P.Log()
+        self.add = P.TensorAdd()
+        self.mul = P.Mul()
+        self.sqrt = P.Sqrt()
+        self.realdiv = P.RealDiv()
+        self.shape = P.Shape()
+        self.const = P.ScalarToArray()
+        self.less = P.Less()
+        self.cast = P.Cast()
+        self.normal = P.Normal(seed=seed)
+        self.erf = P.Erf()
+        self.sqrt = P.Sqrt()
+
+    def extend_repr(self):
+        str_info = f'probs = {self._probs}'
+        return str_info
+
+    def probs(self):
+        """
+        Returns the probability for the outcome is 1.
+        """
+        return self._probs
+
+    def _mean(self, name='mean', probs1=None):
+        r"""
+        .. math::
+            MEAN(B) = probs1
+        """
+        if name == 'mean':
+            return self._probs if probs1 is None else probs1
+        return None
+
+    def _var(self, name='var', probs1=None):
+        r"""
+        .. math::
+            VAR(B) = probs1 * probs0
+        """
+        if name in ('sd', 'var'):
+            probs1 = self._probs if probs1 is None else probs1
+            probs0 = self.add(1, -1 * probs1)
+            return self.mul(probs0, probs1)
+        return None
+
+    def _prob(self, name, value, probs=None):
+        r"""
+        pmf of Bernoulli distribution.
+
+        Args:
+            name (str): name of the function. Should be "prob" when passed in from construct.
+            value (Tensor): a Tensor composed of only zeros and ones.
+            probs (Tensor): probability of outcome is 1. Default: self._probs.
+
+        .. math::
+            pmf(k) = probs1 if k = 1;
+            pmf(k) = probs0 if k = 0;
+        """
+        if name in ('prob', 'log_prob'):
+            probs1 = self._probs if probs is None else probs
+            probs0 = self.add(1, -1 * probs1)
+            return self.add(self.mul(probs1, value),
+                            self.mul(probs0, self.add(1, -1 * value)))
+        return None
+
+    def _kl_loss(self, name, dist, probs1_b, probs1_a=None):
+        r"""
+        Evaluate bernoulli-bernoulli kl divergence, i.e. KL(a||b).
+
+        Args:
+            name (str): name of the funtion. Should always be "kl_loss" when passed in from construct.
+            dist (str): type of the distributions. Should be "Bernoulli" in this case.
+            probs1_b (Tensor): probs1 of distribution b.
+            probs1_a (Tensor): probs1 of distribution a. Default: self._probs.
+
+        .. math::
+            KL(a||b) = probs1_a * \log(\fract{probs1_a}{probs1_b}) +
+                       probs0_a * \log(\fract{probs0_a}{probs0_b})
+        """
+        if name == 'kl_loss' and dist == 'Bernoulli':
+            probs1_a = self._probs if probs1_a is None else probs1_a
+            probs0_a = self.add(1, -1 * probs1_a)
+            probs0_b = self.add(1, -1 * probs1_b)
+            return self.add(probs1_a * self.log(self.realdiv(probs1_a, probs1_b)),
+                            probs0_a * self.log(self.realdiv(probs0_a, probs0_b)))
+        return None
+
+    def _sample(self, name, shape=(), probs=None):
+        """
+        Sampling.
+
+        Args:
+            name (str): name of the function. Should always be 'sample' when passed in from construct.
+            shape (tuple): shape of the sample. Default: ().
+            probs (Tensor): probs1 of the samples. Default: self._probs.
+
+        Returns:
+            Tensor, shape is shape + batch_shape.
+        """
+        if name == 'sample':
+            probs1 = self._probs if probs is None else probs
+            batch_shape = self.shape(probs1)
+            sample_shape = shape + batch_shape
+            mean_zero = self.const(0.0)
+            sd_one = self.const(1.0)
+            sqrt_two = self.sqrt(self.const(2.0))
+            sample_norm = self.normal(sample_shape, mean_zero, sd_one)
+            sample_uniform = 0.5 * (1 + self.erf(self.realdiv(sample_norm, sqrt_two)))
+            sample = self.less(sample_uniform, probs1)
+            sample = self.cast(sample, self._dtype)
+            return sample
+        return None
diff --git a/mindspore/nn/distribution/distribution.py b/mindspore/nn/distribution/distribution.py
new file mode 100644
index 0000000000..1ed7906a9e
--- /dev/null
+++ b/mindspore/nn/distribution/distribution.py
@@ -0,0 +1,200 @@
+# 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.
+# ============================================================================
+"""basic"""
+from ..cell import Cell
+from ._utils.utils import calc_broadcast_shape_from_param
+
+
+class Distribution(Cell):
+    """
+    Base class for all mathematical distributions.
+
+    Args:
+        dtype (mindspore.dtype): type of the distribution.
+        name (str): name of the distribution.
+        param (dict): parameters used to initialize the distribution.
+
+    Note:
+        Derived class should override operations such as ,_mean, _prob,
+        and _log_prob. Functions should be called through construct when
+        used inside a network in the form  of function name followed by
+        arguments.
+
+    Examples:
+        >>> class MyNormalDistribution(Distribution):
+        >>>    def __init__(self):
+        >>>        super(MyDistribution, self).__init__()
+        >>>        self._mean_value = Tensor([2.0,3.0])
+        >>>        self._sd_value = Tensor([2.0,3.0])
+        >>>
+        >>>    def _mean(self):
+        >>>        return self._mean_value
+
+    """
+    def __init__(self,
+                 dtype,
+                 name,
+                 param):
+
+        """
+        Constructor of distribution class.
+        """
+        super(Distribution, self).__init__()
+        self._name = name
+        self._dtype = dtype
+        self._parameters = {}
+        # parsing parameters
+        for k in param.keys():
+            if not(k == 'self' or k.startswith('_')):
+                self._parameters[k] = param[k]
+        # some attributes
+        self._broadcast_shape = calc_broadcast_shape_from_param(
+            self._parameters)
+
+        # set the function to call according to the derived class's attributes
+        self._set_prob()
+        self._set_log_prob()
+        self._set_sd()
+
+    def _set_prob(self):
+        """
+        Set probability funtion based on the availability of _prob and _log_likehood.
+        """
+        if hasattr(self, '_prob'):
+            self._call_prob = self._prob
+        elif hasattr(self, '_log_likelihood'):
+            self._call_prob = self._calc_prob_from_log_likelihood
+
+    def _set_sd(self):
+        """
+        Set standard deviation based on the availability of _sd and _var.
+        """
+        if hasattr(self, '_sd'):
+            self._call_sd = self._sd
+        elif hasattr(self, '_var'):
+            self._call_sd = self._calc_sd_from_var
+
+    def _set_log_prob(self):
+        """
+        Set log probability based on the availability of _prob and _log_likelihood.
+        """
+        if hasattr(self, '_log_likelihood'):
+            self._call_log_prob = self._log_likelihood
+        if hasattr(self, '_prob'):
+            self._call_log_prob = self._calc_log_prob_from_prob
+
+    def log_likelihood(self, *args):
+        """
+        Evaluate the log probability at the given value.
+
+        Note:
+            value is casted to Tensor for further calculation.
+
+        Returns:
+            Tensor, shape is the broadcast_shape of the distribution.
+        """
+        return self._call_log_prob(*args)
+
+    def _calc_prob_from_log_likelihood(self, *args):
+        r"""
+        Evaluate prob from log probability.
+
+        .. math::
+            probability(x) = \exp(log_likehood(x))
+        """
+        return self.exp(self._log_likelihood(*args))
+
+    def prob(self, *args):
+        """
+        Evaluate the prob (pdf or pmf) at given value.
+
+        Note:
+            value is casted to Tensor for further calculation.
+
+        Returns:
+            Tensor, shape is the broadcast_shape of the distribution.
+        """
+        return self._call_prob(*args)
+
+    def _calc_log_prob_from_prob(self, *args):
+        r"""
+        Evaluate log probability from probability.
+
+        .. math::
+            log_prob(x) = \log(prob(x))
+        """
+        return self.log(self._prob(*args))
+
+    def kl_loss(self, **kwargs):
+        """
+        Evaluate the KL divergence. Parameters of the second distribution should be
+        passed in through **kwargs.
+
+        Returns:
+            Tensor, shape is the broadcast_shape of the distribution and input distribution.
+        """
+        return self._kl_loss(**kwargs)
+
+    def mean(self, **kwargs):
+        """
+        Evaluate the mean.
+
+        Returns:
+            Tensor, shape is the broadcast_shape of the distribution.
+        """
+        return self._mean(**kwargs)
+
+    def sd(self, **kwargs):
+        """
+        Evaluate the standard deviation.
+
+        Returns:
+            Tensor, shape is the broadcast_shape of the distribution.
+        """
+        return self._call_sd(**kwargs)
+
+    def _calc_sd_from_var(self, *args):
+        r"""
+        Evaluate log probability from probability.
+
+        .. math::
+            STD(x) = \sqrt(VAR(x))
+        """
+        return self.sqrt(self._var(*args))
+
+    def construct(self, *inputs):
+        """
+        Override construct in Cell.
+
+        Args:
+            *inputs: inputs[0] is always the name of the function.
+
+        Notes:
+            Always raise RuntimeError as Distribution should not be called directly.
+        """
+
+        if inputs[0] == 'log_prob':
+            return self._call_log_prob(*inputs)
+        if inputs[0] == 'prob':
+            return self._call_prob(*inputs)
+        if inputs[0] == 'kl_loss':
+            return self._kl_loss(*inputs)
+        if inputs[0] == 'mean':
+            return self._mean(*inputs)
+        if inputs[0] == 'sd':
+            return self._call_sd(*inputs)
+        if inputs[0] == 'sample':
+            return self._sample(*inputs)
+        return None
diff --git a/mindspore/nn/distribution/normal.py b/mindspore/nn/distribution/normal.py
new file mode 100644
index 0000000000..344dbd2eeb
--- /dev/null
+++ b/mindspore/nn/distribution/normal.py
@@ -0,0 +1,169 @@
+# 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.
+# ============================================================================
+"""Normal Distribution"""
+import numpy as np
+from mindspore.ops import operations as P
+from .distribution import Distribution
+from ._utils.utils import convert_to_batch, check_greater_equal_zero
+from ...common import dtype as mstype
+from ...context import get_context
+
+class Normal(Distribution):
+    """
+    Example class: Normal distribution.
+
+    Args:
+        mean (int, float, list, numpy.ndarray, Tensor, Parameter): mean of the Gaussian distribution.
+        sd (int, float, list, numpy.ndarray, Tensor, Parameter): stddev of the Gaussian distribution.
+        seed (int): seed to use in sampling. Default: 0.
+        dtype (mindspore.dtype): type of the distribution. Default: mstype.float32.
+        name (str): name of the distribution. Default: Normal.
+
+
+    Note:
+        Standard deviation should be greater than zero.
+
+    Examples:
+        >>>    # To initialize a normal distribution of mean 3.0 and standard deviation 4.0
+        >>>    n = nn.Normal(3.0, 4.0, dtype=mstype.float32)
+        >>>    # The following create two independent normal distributions
+        >>>    n = nn.Normal([3.0, 3.0], [4.0, 4.0], dtype=mstype.float32)
+    """
+
+    def __init__(self,
+                 mean=None,
+                 sd=None,
+                 seed=0,
+                 dtype=mstype.float32,
+                 name="Normal"):
+        """
+        Constructor of normal distribution.
+        """
+        param = dict(locals())
+        super(Normal, self).__init__(dtype, name, param)
+        if  mean is not None and sd is not None:
+            self._mean_value = convert_to_batch(mean, self._broadcast_shape, dtype)
+            self._sd_value = convert_to_batch(sd, self._broadcast_shape, dtype)
+            check_greater_equal_zero(self._sd_value, "Standard deviation")
+        else:
+            self._mean_value = mean
+            self._sd_value = sd
+
+        #ops needed for the class
+        self.exp = P.Exp()
+        self.add = P.TensorAdd()
+        self.mul = P.Mul()
+        self.sq = P.Square()
+        self.log = P.Log()
+        self.sqrt = P.Sqrt()
+        self.realdiv = P.RealDiv()
+        self.expm1 = P.Expm1() if get_context('device_target') == 'Ascend' else self._expm1_by_step
+        self.normal = P.Normal(seed=seed)
+        self.shape = P.Shape()
+        self.zeroslike = P.ZerosLike()
+        self.const = P.ScalarToArray()
+
+    def extend_repr(self):
+        str_info = f'mean = {self._mean_value}, standard deviation = {self._sd_value}'
+        return str_info
+
+    def _expm1_by_step(self, x):
+        """
+        Expm1 ops under GPU context.
+        """
+        return self.add(self.exp(x), -1)
+
+    def _mean(self, name='mean', mean=None, sd=None):
+        """
+        Mean of the distribution.
+        """
+        if name == 'mean':
+            mean = self._mean_value if mean is None or sd is None else mean
+            return mean
+        return None
+
+    def _sd(self, name='sd', mean=None, sd=None):
+        """
+        Standard deviation of the distribution.
+        """
+        if name in ('sd', 'var'):
+            sd = self._sd_value if mean is None or sd is None else sd
+            return sd
+        return None
+
+    def _log_likelihood(self, name, value, mean=None, sd=None):
+        r"""
+        Evaluate log probability.
+
+        .. math::
+            L(x) = -1* \fract{(x - \mu)^2}{2. * \sigma^2} - \log(\sqrt(2* \pi * \sigma^2))
+        """
+        if name in ('prob', 'log_prob'):
+            mean = self._mean_value if mean is None else mean
+            sd = self._sd_value if sd is None else sd
+            unnormalized_log_prob = -1. * self.realdiv(self.sq(self.add(value, -1. * mean)),
+                                                       2. * self.sq(sd))
+            neg_normalization = -1. * self.log(self.sqrt(2. * np.pi * self.sq(sd)))
+            return self.add(unnormalized_log_prob, neg_normalization)
+        return None
+
+    def _kl_loss(self, name, dist, mean_b, sd_b, mean_a=None, sd_a=None):
+        r"""
+        Evaluate Normal-Normal kl divergence, i.e. KL(a||b).
+
+        Args:
+            name (str): name of the funtion passed in from construct. Should always be "kl_loss".
+            dist (str): type of the distributions. Should be "Normal" in this case.
+            mean_b (Tensor): mean of distribution b.
+            sd_b (Tensor): standard deviation distribution b.
+            mean_a (Tensor): mean of distribution a. Default: self._mean_value.
+            sd_a (Tensor): standard deviation distribution a. Default: self._sd_value.
+
+        .. math::
+            KL(a||b) = 0.5 * (\fract{MEAN(a)}{STD(b)} - \fract{MEAN(b)}{STD(b)}) ^ 2 +
+                       0.5 * EXPM1(2 * (\log(STD(a)) - \log(STD(b))) - (\log(STD(a)) - \log(STD(b)))
+        """
+        if name == 'kl_loss' and dist == 'Normal':
+            mean_a = self._mean_value if mean_a is None else mean_a
+            sd_a = self._sd_value if sd_a is None else sd_a
+            diff_log_scale = self.add(self.log(sd_a), - self.log(sd_b))
+            squared_diff = self.sq(self.add(self.realdiv(mean_a, sd_b), - self.realdiv(mean_b, sd_b)))
+            return self.add(self.add(0.5 * squared_diff, 0.5 * self.expm1(2 * diff_log_scale)), - diff_log_scale)
+        return None
+
+    def _sample(self, name, shape=(), mean=None, sd=None):
+        """
+        Sampling.
+
+        Args:
+            name (str): name of the function. Should always be 'sample' when passed in from construct.
+            shape (tuple): shape of the sample. Default: ().
+            mean (Tensor): mean of the samples. Default: self._mean_value.
+            sd (Tensor): standard deviation of the samples. Default: self._sd_value.
+
+        Returns:
+            Tensor, shape is shape + batch_shape.
+        """
+        if name == 'sample':
+            mean = self._mean_value if mean is None else mean
+            sd = self._sd_value if sd is None else sd
+            batch_shape = self.shape(self.add(self.zeroslike(mean), self.zeroslike(sd)))
+            sample_shape = shape + batch_shape
+            mean_zero = self.const(0.0)
+            sd_one = self.const(1.0)
+            sample_norm = self.normal(sample_shape, mean_zero, sd_one)
+            sample = self.add(mean, self.mul(sample_norm, sd))
+            return sample
+        return None
diff --git a/tests/st/ops/ascend/test_distribution/test_bernoulli.py b/tests/st/ops/ascend/test_distribution/test_bernoulli.py
new file mode 100644
index 0000000000..5652d536c7
--- /dev/null
+++ b/tests/st/ops/ascend/test_distribution/test_bernoulli.py
@@ -0,0 +1,147 @@
+# 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 bernoulli distribution"""
+import numpy as np
+from scipy import stats
+import mindspore.context as context
+import mindspore.nn as nn
+from mindspore import Tensor
+from mindspore.common.api import ms_function
+from mindspore import dtype
+
+context.set_context(mode=context.GRAPH_MODE, device_target="Ascend")
+
+class Net(nn.Cell):
+    """
+    Test class: probability of bernoulli distribution.
+    """
+    def __init__(self):
+        super(Net, self).__init__()
+        self.b = nn.Bernoulli(0.7, dtype=dtype.int32)
+
+    @ms_function
+    def construct(self, x_):
+        return self.b('prob', x_)
+
+class Net1(nn.Cell):
+    """
+    Test class: log probability of bernoulli distribution.
+    """
+    def __init__(self):
+        super(Net1, self).__init__()
+        self.b = nn.Bernoulli(0.7, dtype=dtype.int32)
+
+    @ms_function
+    def construct(self, x_):
+        return self.b('log_prob', x_)
+
+class Net2(nn.Cell):
+    """
+    Test class: kl_loss between bernoulli distributions.
+    """
+    def __init__(self):
+        super(Net2, self).__init__()
+        self.b = nn.Bernoulli(0.7, dtype=dtype.int32)
+
+    @ms_function
+    def construct(self, x_):
+        return self.b('kl_loss', 'Bernoulli', x_)
+
+class Net3(nn.Cell):
+    """
+    Test class: mean/sd of bernoulli distribution.
+    """
+    def __init__(self):
+        super(Net3, self).__init__()
+        self.b = nn.Bernoulli([0.5, 0.5], dtype=dtype.int32)
+
+    @ms_function
+    def construct(self):
+        return self.b('mean'), self.b('sd')
+
+class Net4(nn.Cell):
+    """
+    Test class: log probability of bernoulli distribution.
+    """
+    def __init__(self, shape, seed=0):
+        super(Net4, self).__init__()
+        self.b = nn.Bernoulli([0.7, 0.5], seed=seed, dtype=dtype.int32)
+        self.shape = shape
+
+    @ms_function
+    def construct(self, probs=None):
+        return self.b('sample', self.shape, probs)
+
+def test_pmf():
+    """
+    Test pmf.
+    """
+    bernoulli_benchmark = stats.bernoulli(0.7)
+    expect_pmf = bernoulli_benchmark.pmf([0, 1, 0, 1, 1]).astype(np.float32)
+    pdf = Net()
+    x_ = Tensor(np.array([0, 1, 0, 1, 1]).astype(np.int32), dtype=dtype.float32)
+    output = pdf(x_)
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_pmf) < tol).all()
+
+def test_log_likelihood():
+    """
+    Test log_pmf.
+    """
+    bernoulli_benchmark = stats.bernoulli(0.7)
+    expect_logpmf = bernoulli_benchmark.logpmf([0, 1, 0, 1, 1]).astype(np.float32)
+    logprob = Net1()
+    x_ = Tensor(np.array([0, 1, 0, 1, 1]).astype(np.int32), dtype=dtype.float32)
+    output = logprob(x_)
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_logpmf) < tol).all()
+
+def test_kl_loss():
+    """
+    Test kl_loss.
+    """
+    probs1_a = 0.7
+    probs1_b = 0.5
+    probs0_a = 1 - probs1_a
+    probs0_b = 1 - probs1_b
+    expect_kl_loss = probs1_a * np.log(probs1_a / probs1_b) + probs0_a * np.log(probs0_a / probs0_b)
+    kl_loss = Net2()
+    output = kl_loss(Tensor([probs1_b], dtype=dtype.float32))
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_kl_loss) < tol).all()
+
+def test_basics():
+    """
+    Test mean/standard deviation and probs.
+    """
+    basics = Net3()
+    mean, sd = basics()
+    expect_mean = [0.5, 0.5]
+    assert (mean.asnumpy() == expect_mean).all()
+    assert (sd.asnumpy() == expect_mean).all()
+    b = nn.Bernoulli([0.7, 0.5], dtype=dtype.int32)
+    probs = b.probs()
+    expect_probs = [0.7, 0.5]
+    tol = 1e-6
+    assert (np.abs(probs.asnumpy() - expect_probs) < tol).all()
+
+def test_sample():
+    """
+    Test sample.
+    """
+    shape = (2, 3)
+    sample = Net4(shape)
+    output = sample()
+    assert output.shape == (2, 3, 2)
diff --git a/tests/st/ops/ascend/test_distribution/test_normal.py b/tests/st/ops/ascend/test_distribution/test_normal.py
new file mode 100644
index 0000000000..52bb1173ee
--- /dev/null
+++ b/tests/st/ops/ascend/test_distribution/test_normal.py
@@ -0,0 +1,152 @@
+# 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 normal distribution"""
+import numpy as np
+from scipy import stats
+import mindspore.context as context
+import mindspore.nn as nn
+from mindspore import Tensor
+from mindspore.common.api import ms_function
+from mindspore import dtype
+
+context.set_context(mode=context.GRAPH_MODE, device_target="Ascend")
+
+class Net(nn.Cell):
+    """
+    Test class: probability of normal distribution.
+    """
+    def __init__(self):
+        super(Net, self).__init__()
+        self.n = nn.Normal(np.array([3.0]), np.array([[2.0], [4.0]]), dtype=dtype.float32)
+
+    @ms_function
+    def construct(self, x_):
+        return self.n('prob', x_)
+
+class Net1(nn.Cell):
+    """
+    Test class: log probability of normal distribution.
+    """
+    def __init__(self):
+        super(Net1, self).__init__()
+        self.n = nn.Normal(np.array([3.0]), np.array([[2.0], [4.0]]), dtype=dtype.float32)
+
+    @ms_function
+    def construct(self, x_):
+        return self.n('log_prob', x_)
+
+class Net2(nn.Cell):
+    """
+    Test class: kl_loss of normal distribution.
+    """
+    def __init__(self):
+        super(Net2, self).__init__()
+        self.n = nn.Normal(np.array([3.0]), np.array([4.0]), dtype=dtype.float32)
+
+    @ms_function
+    def construct(self, x_, y_):
+        return self.n('kl_loss', 'Normal', x_, y_)
+
+class Net3(nn.Cell):
+    """
+    Test class: mean/sd of normal distribution.
+    """
+    def __init__(self):
+        super(Net3, self).__init__()
+        self.n = nn.Normal(np.array([3.0]), np.array([2.0, 4.0]), dtype=dtype.float32)
+
+    @ms_function
+    def construct(self):
+        return self.n('mean'), self.n('sd')
+
+class Net4(nn.Cell):
+    """
+    Test class: mean/sd of normal distribution.
+    """
+    def __init__(self, shape, seed=0):
+        super(Net4, self).__init__()
+        self.n = nn.Normal(np.array([3.0]), np.array([[2.0], [4.0]]), seed=seed, dtype=dtype.float32)
+        self.shape = shape
+
+    @ms_function
+    def construct(self, mean=None, sd=None):
+        return self.n('sample', self.shape, mean, sd)
+
+def test_pdf():
+    """
+    Test pdf.
+    """
+    norm_benchmark = stats.norm(np.array([3.0]), np.array([[2.0], [4.0]]))
+    expect_pdf = norm_benchmark.pdf([1.0, 2.0]).astype(np.float32)
+    pdf = Net()
+    output = pdf(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_pdf) < tol).all()
+
+def test_log_likelihood():
+    """
+    Test log_pdf.
+    """
+    norm_benchmark = stats.norm(np.array([3.0]), np.array([[2.0], [4.0]]))
+    expect_logpdf = norm_benchmark.logpdf([1.0, 2.0]).astype(np.float32)
+    logprob = Net1()
+    output = logprob(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_logpdf) < tol).all()
+
+def test_kl_loss():
+    """
+    Test kl_loss.
+    """
+    mean_a = np.array([3.0]).astype(np.float32)
+    sd_a = np.array([4.0]).astype(np.float32)
+
+    mean_b = np.array([1.0]).astype(np.float32)
+    sd_b = np.array([1.0]).astype(np.float32)
+
+    diff_log_scale = np.log(sd_a) - np.log(sd_b)
+    squared_diff = np.square(mean_a / sd_b - mean_b / sd_b)
+    expect_kl_loss = 0.5 * squared_diff + 0.5 * np.expm1(2 * diff_log_scale) - diff_log_scale
+
+    kl_loss = Net2()
+    mean = Tensor(mean_b, dtype=dtype.float32)
+    sd = Tensor(sd_b, dtype=dtype.float32)
+    output = kl_loss(mean, sd)
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_kl_loss) < tol).all()
+
+def test_basics():
+    """
+    Test mean/standard deviation.
+    """
+    basics = Net3()
+    mean, sd = basics()
+    expect_mean = [3.0, 3.0]
+    expect_sd = [2.0, 4.0]
+    tol = 1e-6
+    assert (np.abs(mean.asnumpy() - expect_mean) < tol).all()
+    assert (np.abs(sd.asnumpy() - expect_sd) < tol).all()
+
+def test_sample():
+    """
+    Test sample.
+    """
+    shape = (2, 3)
+    seed = 10
+    mean = Tensor([2.0], dtype=dtype.float32)
+    sd = Tensor([2.0, 2.0, 2.0], dtype=dtype.float32)
+    sample = Net4(shape, seed=seed)
+    output = sample(mean, sd)
+    assert output.shape == (2, 3, 3)
diff --git a/tests/ut/python/nn/test_distribution.py b/tests/ut/python/nn/test_distribution.py
new file mode 100644
index 0000000000..845c64a110
--- /dev/null
+++ b/tests/ut/python/nn/test_distribution.py
@@ -0,0 +1,369 @@
+# 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.
+# ============================================================================
+"""
+Test nn.Distribution.
+
+Including Normal Distribution and Bernoulli Distribution.
+"""
+import pytest
+import numpy as np
+
+import mindspore.nn as nn
+from mindspore import dtype
+from mindspore import Tensor
+
+def test_normal_shape_errpr():
+    """
+    Invalid shapes.
+    """
+    with pytest.raises(ValueError):
+        nn.Normal([[2.], [1.]], [[2.], [3.], [4.]], dtype=dtype.float32)
+
+def test_no_arguments():
+    """
+    No args passed in during initialization.
+    """
+    n = nn.Normal()
+    assert isinstance(n, nn.Distribution)
+    b = nn.Bernoulli()
+    assert isinstance(b, nn.Distribution)
+
+def test_with_arguments():
+    """
+    Args passed in during initialization.
+    """
+    n = nn.Normal([3.0], [4.0], dtype=dtype.float32)
+    assert isinstance(n, nn.Distribution)
+    b = nn.Bernoulli([0.3, 0.5], dtype=dtype.int32)
+    assert isinstance(b, nn.Distribution)
+
+class NormalProb(nn.Cell):
+    """
+    Normal distribution: initialize with mean/sd.
+    """
+    def __init__(self):
+        super(NormalProb, self).__init__()
+        self.normal = nn.Normal(3.0, 4.0, dtype=dtype.float32)
+
+    def construct(self, value):
+        x = self.normal('prob', value)
+        y = self.normal('log_prob', value)
+        return x, y
+
+def test_normal_prob():
+    """
+    Test pdf/log_pdf: passing value through construct.
+    """
+    net = NormalProb()
+    value = Tensor([0.5, 1.0], dtype=dtype.float32)
+    pdf, log_pdf = net(value)
+    assert isinstance(pdf, Tensor)
+    assert isinstance(log_pdf, Tensor)
+
+class NormalProb1(nn.Cell):
+    """
+    Normal distribution: initialize without mean/sd.
+    """
+    def __init__(self):
+        super(NormalProb1, self).__init__()
+        self.normal = nn.Normal()
+
+    def construct(self, value, mean, sd):
+        x = self.normal('prob', value, mean, sd)
+        y = self.normal('log_prob', value, mean, sd)
+        return x, y
+
+def test_normal_prob1():
+    """
+    Test pdf/logpdf: passing mean/sd, value through construct.
+    """
+    net = NormalProb1()
+    value = Tensor([0.5, 1.0], dtype=dtype.float32)
+    mean = Tensor([0.0], dtype=dtype.float32)
+    sd = Tensor([1.0], dtype=dtype.float32)
+    pdf, log_pdf = net(value, mean, sd)
+    assert isinstance(pdf, Tensor)
+    assert isinstance(log_pdf, Tensor)
+
+class NormalProb2(nn.Cell):
+    """
+    Normal distribution: initialize with mean/sd.
+    """
+    def __init__(self):
+        super(NormalProb2, self).__init__()
+        self.normal = nn.Normal(3.0, 4.0, dtype=dtype.float32)
+
+    def construct(self, value, mean, sd):
+        x = self.normal('prob', value, mean, sd)
+        y = self.normal('log_prob', value, mean, sd)
+        return x, y
+
+def test_normal_prob2():
+    """
+    Test pdf/log_pdf: passing mean/sd through construct.
+    Overwrite original mean/sd.
+    """
+    net = NormalProb2()
+    value = Tensor([0.5, 1.0], dtype=dtype.float32)
+    mean = Tensor([0.0], dtype=dtype.float32)
+    sd = Tensor([1.0], dtype=dtype.float32)
+    pdf, log_pdf = net(value, mean, sd)
+    assert isinstance(pdf, Tensor)
+    assert isinstance(log_pdf, Tensor)
+
+class BernoulliProb(nn.Cell):
+    """
+    Bernoulli distribution: initialize with probs.
+    """
+    def __init__(self):
+        super(BernoulliProb, self).__init__()
+        self.bernoulli = nn.Bernoulli(0.5, dtype=dtype.int32)
+
+    def construct(self, value):
+        return self.bernoulli('prob', value)
+
+class BernoulliLogProb(nn.Cell):
+    """
+    Bernoulli distribution: initialize with probs.
+    """
+    def __init__(self):
+        super(BernoulliLogProb, self).__init__()
+        self.bernoulli = nn.Bernoulli(0.5, dtype=dtype.int32)
+
+    def construct(self, value):
+        return self.bernoulli('log_prob', value)
+
+
+def test_bernoulli_prob():
+    """
+    Test pmf/log_pmf: passing value through construct.
+    """
+    net = BernoulliProb()
+    value = Tensor([1, 0, 1, 0, 1], dtype=dtype.float32)
+    pmf = net(value)
+    assert isinstance(pmf, Tensor)
+
+def test_bernoulli_log_prob():
+    """
+    Test pmf/log_pmf: passing value through construct.
+    """
+    net = BernoulliLogProb()
+    value = Tensor([1, 0, 1, 0, 1], dtype=dtype.float32)
+    log_pmf = net(value)
+    assert isinstance(log_pmf, Tensor)
+
+class BernoulliProb1(nn.Cell):
+    """
+    Bernoulli distribution: initialize without probs.
+    """
+    def __init__(self):
+        super(BernoulliProb1, self).__init__()
+        self.bernoulli = nn.Bernoulli()
+
+    def construct(self, value, probs):
+        return self.bernoulli('prob', value, probs)
+
+class BernoulliLogProb1(nn.Cell):
+    """
+    Bernoulli distribution: initialize without probs.
+    """
+    def __init__(self):
+        super(BernoulliLogProb1, self).__init__()
+        self.bernoulli = nn.Bernoulli()
+
+    def construct(self, value, probs):
+        return self.bernoulli('log_prob', value, probs)
+
+
+def test_bernoulli_prob1():
+    """
+    Test pmf/log_pmf: passing probs through construct.
+    """
+    net = BernoulliProb1()
+    value = Tensor([1, 0, 1, 0, 1], dtype=dtype.float32)
+    probs = Tensor([0.3], dtype=dtype.float32)
+    pmf = net(value, probs)
+    assert isinstance(pmf, Tensor)
+
+def test_bernoulli_log_prob1():
+    """
+    Test pmf/log_pmf: passing probs through construct.
+    """
+    net = BernoulliLogProb1()
+    value = Tensor([1, 0, 1, 0, 1], dtype=dtype.float32)
+    probs = Tensor([0.3], dtype=dtype.float32)
+    log_pmf = net(value, probs)
+    assert isinstance(log_pmf, Tensor)
+
+class BernoulliProb2(nn.Cell):
+    """
+    Bernoulli distribution: initialize with probs.
+    """
+    def __init__(self):
+        super(BernoulliProb2, self).__init__()
+        self.bernoulli = nn.Bernoulli(0.5)
+
+    def construct(self, value, probs):
+        return self.bernoulli('prob', value, probs)
+
+class BernoulliLogProb2(nn.Cell):
+    """
+    Bernoulli distribution: initialize with probs.
+    """
+    def __init__(self):
+        super(BernoulliLogProb2, self).__init__()
+        self.bernoulli = nn.Bernoulli(0.5)
+
+    def construct(self, value, probs):
+        return self.bernoulli('log_prob', value, probs)
+
+
+def test_bernoulli_prob2():
+    """
+    Test pmf/log_pmf: passing probs/value through construct.
+    Overwrite original probs.
+    """
+    net = BernoulliProb2()
+    value = Tensor([1, 0, 1, 0, 1], dtype=dtype.float32)
+    probs = Tensor([0.3], dtype=dtype.float32)
+    pmf = net(value, probs)
+    assert isinstance(pmf, Tensor)
+
+def test_bernoulli_log_prob2():
+    """
+    Test pmf/log_pmf: passing probs/value through construct.
+    Overwrite original probs.
+    """
+    net = BernoulliLogProb2()
+    value = Tensor([1, 0, 1, 0, 1], dtype=dtype.float32)
+    probs = Tensor([0.3], dtype=dtype.float32)
+    log_pmf = net(value, probs)
+    assert isinstance(log_pmf, Tensor)
+
+
+class NormalKl(nn.Cell):
+    """
+    Test class: kl_loss of Normal distribution.
+    """
+    def __init__(self):
+        super(NormalKl, self).__init__()
+        self.n = nn.Normal(np.array([3.0]), np.array([4.0]), dtype=dtype.float32)
+
+    def construct(self, x_, y_):
+        return self.n('kl_loss', 'Normal', x_, y_)
+
+class BernoulliKl(nn.Cell):
+    """
+    Test class: kl_loss between Bernoulli distributions.
+    """
+    def __init__(self):
+        super(BernoulliKl, self).__init__()
+        self.b = nn.Bernoulli(0.7, dtype=dtype.int32)
+
+    def construct(self, x_):
+        return self.b('kl_loss', 'Bernoulli', x_)
+
+def test_kl():
+    """
+    Test kl_loss function.
+    """
+    nor_net = NormalKl()
+    mean_b = np.array([1.0]).astype(np.float32)
+    sd_b = np.array([1.0]).astype(np.float32)
+    mean = Tensor(mean_b, dtype=dtype.float32)
+    sd = Tensor(sd_b, dtype=dtype.float32)
+    loss = nor_net(mean, sd)
+    assert isinstance(loss, Tensor)
+
+    ber_net = BernoulliKl()
+    probs_b = Tensor([0.3], dtype=dtype.float32)
+    loss = ber_net(probs_b)
+    assert isinstance(loss, Tensor)
+
+
+class NormalKlNoArgs(nn.Cell):
+    """
+    Test class: kl_loss of Normal distribution.
+    No args during initialization.
+    """
+    def __init__(self):
+        super(NormalKlNoArgs, self).__init__()
+        self.n = nn.Normal(dtype=dtype.float32)
+
+    def construct(self, x_, y_, w_, v_):
+        return self.n('kl_loss', 'Normal', x_, y_, w_, v_)
+
+class BernoulliKlNoArgs(nn.Cell):
+    """
+    Test class: kl_loss between Bernoulli distributions.
+    No args during initialization.
+    """
+    def __init__(self):
+        super(BernoulliKlNoArgs, self).__init__()
+        self.b = nn.Bernoulli(dtype=dtype.int32)
+
+    def construct(self, x_, y_):
+        return self.b('kl_loss', 'Bernoulli', x_, y_)
+
+def test_kl_no_args():
+    """
+    Test kl_loss function.
+    """
+    nor_net = NormalKlNoArgs()
+    mean_b = np.array([1.0]).astype(np.float32)
+    sd_b = np.array([1.0]).astype(np.float32)
+    mean_a = np.array([2.0]).astype(np.float32)
+    sd_a = np.array([3.0]).astype(np.float32)
+    mean_b = Tensor(mean_b, dtype=dtype.float32)
+    sd_b = Tensor(sd_b, dtype=dtype.float32)
+    mean_a = Tensor(mean_a, dtype=dtype.float32)
+    sd_a = Tensor(sd_a, dtype=dtype.float32)
+    loss = nor_net(mean_b, sd_b, mean_a, sd_a)
+    assert isinstance(loss, Tensor)
+
+    ber_net = BernoulliKlNoArgs()
+    probs_b = Tensor([0.3], dtype=dtype.float32)
+    probs_a = Tensor([0.7], dtype=dtype.float32)
+    loss = ber_net(probs_b, probs_a)
+    assert isinstance(loss, Tensor)
+
+
+
+class NormalBernoulli(nn.Cell):
+    """
+    Test class: basic mean/sd function.
+    """
+    def __init__(self):
+        super(NormalBernoulli, self).__init__()
+        self.n = nn.Normal(3.0, 4.0, dtype=dtype.float32)
+        self.b = nn.Bernoulli(0.5, dtype=dtype.int32)
+
+    def construct(self):
+        normal_mean = self.n('mean')
+        normal_sd = self.n('sd')
+        bernoulli_mean = self.b('mean')
+        bernoulli_sd = self.b('sd')
+        return normal_mean, normal_sd, bernoulli_mean, bernoulli_sd
+
+def test_bascis():
+    """
+    Test mean/sd functionality of Normal and Bernoulli.
+    """
+    net = NormalBernoulli()
+    normal_mean, normal_sd, bernoulli_mean, bernoulli_sd = net()
+    assert isinstance(normal_mean, Tensor)
+    assert isinstance(normal_sd, Tensor)
+    assert isinstance(bernoulli_mean, Tensor)
+    assert isinstance(bernoulli_sd, Tensor)