diff --git a/mindspore/nn/probability/bijector/bijector.py b/mindspore/nn/probability/bijector/bijector.py
index 35abd2d5210..bc395f573c3 100644
--- a/mindspore/nn/probability/bijector/bijector.py
+++ b/mindspore/nn/probability/bijector/bijector.py
@@ -16,8 +16,10 @@
 from mindspore import context
 from mindspore.nn.cell import Cell
 from mindspore.ops import operations as P
+from mindspore.common import dtype as mstype
+from mindspore.common.tensor import Tensor
 from mindspore._checkparam import Validator as validator
-from ..distribution._utils.utils import CheckTensor, cast_to_tensor
+from ..distribution._utils.utils import CheckTensor, cast_to_tensor, raise_type_error
 from ..distribution import Distribution
 from ..distribution import TransformedDistribution
 
@@ -32,6 +34,17 @@ class Bijector(Cell):
         name (str): The name of the Bijector. Default: None.
         dtype (mindspore.dtype): The type of the distributions that the Bijector can operate on. Default: None.
         param (dict): The parameters used to initialize the Bijector. Default: None.
+
+    Note:
+        `dtype` of bijector represents the type of the distributions that the bijector could operate on.
+        When `dtype` is None, there is no enforcement on the type of input value except that the input value
+        has to be float type. During initilization, when `dtype` is None, there is no enforcement on the dtype
+        of the parameters. All parameters should have the same float type, otherwise a TypeError will be raised.
+        Specifically, the parameter type will follow the dtype of the input value, i.e. parameters of the bijector
+        will be casted into the same type as input value when `dtype`is None.
+        When `dtype` is specified, it is forcing the parameters and input value to be the same dtype as `dtype`.
+        When the type of parameters or the type of the input value is not the same as `dtype`, a TypeError will be
+        raised. Only subtype of mindspore.float_type can be used to specify bijector's `dtype`.
     """
 
     def __init__(self,
@@ -48,6 +61,8 @@ class Bijector(Cell):
         validator.check_value_type(
             'is_constant_jacobian', is_constant_jacobian, [bool], name)
         validator.check_value_type('is_injective', is_injective, [bool], name)
+        if dtype is not None:
+            validator.check_type_name("dtype", dtype, mstype.float_type, type(self).__name__)
         self._name = name
         self._dtype = dtype
         self._parameters = {}
@@ -57,6 +72,12 @@ class Bijector(Cell):
                 continue
             if not(k == 'self' or k.startswith('_')):
                 self._parameters[k] = param[k]
+
+        # if no bijector is used as an argument during initilization
+        if 'bijector' not in param.keys():
+            self._batch_shape = self._calc_batch_shape()
+            self._is_scalar_batch = self._check_is_scalar_batch()
+
         self._is_constant_jacobian = is_constant_jacobian
         self._is_injective = is_injective
 
@@ -68,6 +89,8 @@ class Bijector(Cell):
         self.dtype_base = P.DType()
         self.shape_base = P.Shape()
         self.fill_base = P.Fill()
+        self.sametypeshape_base = P.SameTypeShape()
+        self.issubclass_base = P.IsSubClass()
 
     @property
     def name(self):
@@ -89,6 +112,38 @@ class Bijector(Cell):
     def is_injective(self):
         return self._is_injective
 
+    @property
+    def batch_shape(self):
+        return self._batch_shape
+
+    @property
+    def is_scalar_batch(self):
+        return self._is_scalar_batch
+
+    def _check_value_dtype(self, value):
+        """
+        Firstly check if the input value is Tensor. Then, if `self.dtype` is None, check
+        if the input tensor is or can be directly cast into a float tensor.
+        If `self.dtype` is not None, check if the input tensor's dtype is `self.dtype`.
+        """
+        self.checktensor(value, 'input value of bijector')
+        value_type = self.dtype_base(value)
+        if self.dtype is None:
+            if self.issubclass_base(value_type, mstype.float_):
+                return value
+            return raise_type_error('input value of bijector', value_type, mstype.float_)
+        dtype_tensor = self.fill_base(self.dtype, self.shape_base(value), 0.0)
+        self.sametypeshape_base(value, dtype_tensor)
+        return value
+
+    def _shape_mapping(self, shape):
+        shape_tensor = self.fill_base(self.parameter_type, shape, 0.0)
+        dist_shape_tensor = self.fill_base(self.parameter_type, self.batch_shape, 0.0)
+        return (shape_tensor + dist_shape_tensor).shape
+
+    def shape_mapping(self, shape):
+        return self._shape_mapping(shape)
+
     def _add_parameter(self, value, name):
         """
         Cast `value` to a tensor and add it to `self.default_parameters`.
@@ -98,26 +153,51 @@ class Bijector(Cell):
         if not hasattr(self, 'default_parameters'):
             self.default_parameters = []
             self.parameter_names = []
+            self.common_dtype = None
         # cast value to a tensor if it is not None
-        value_t = None if value is None else cast_to_tensor(value, self.parameter_type)
-        self.default_parameters += [value_t,]
+        if isinstance(value, bool) or value is None:
+            raise TypeError(f"{name} cannot be type {type(value)}")
+        value_t = Tensor(value)
+        # if the bijector's dtype is not specified
+        if self.dtype is None:
+            if self.common_dtype is None:
+                self.common_dtype = value_t.dtype
+            elif value_t.dtype != self.common_dtype:
+                raise TypeError(f"{name} should have the same dtype as other arguments.")
+        # check if the dtype of the input_parameter agrees with the bijector's dtype
+        elif value_t.dtype != self.dtype:
+            raise TypeError(f"{name} should have the same dtype as the bijector's dtype.")
+        self.default_parameters += [value,]
         self.parameter_names += [name,]
         return value_t
 
-    def _calc_event_shape(self):
+    def _calc_batch_shape(self):
         """
-        Calculate event_shape based on parameters.
+        Calculate batch_shape based on parameters.
         """
-        broadcast_shape = None
-        for param in self.default_parameters:
-            if broadcast_shape is None:
-                broadcast_shape = self.shape_base(param)
-                broadcast_shape_tensor = self.fill_base(self.parameter_type, broadcast_shape, 0.0)
+        param_dict = self.parameters['param_dict']
+        broadcast_shape_tensor = None
+        for value in param_dict.values():
+            if value is None:
+                return None
+            if broadcast_shape_tensor is None:
+                broadcast_shape_tensor = cast_to_tensor(value)
             else:
-                broadcast_shape = self.shape_base(param + broadcast_shape_tensor)
-                broadcast_shape_tensor = self.fill_base(self.parameter_type, broadcast_shape, 0.0)
-        return broadcast_shape
+                value = cast_to_tensor(value)
+                broadcast_shape_tensor = (value + broadcast_shape_tensor)
+        return broadcast_shape_tensor.shape
 
+    def _check_is_scalar_batch(self):
+        """
+        Check if the parameters used during initialization are scalars.
+        """
+        param_dict = self.parameters['param_dict']
+        for value in param_dict.values():
+            if value is None:
+                continue
+            if not isinstance(value, (int, float)):
+                return False
+        return True
 
     def _check_value(self, value, name):
         """
@@ -127,32 +207,35 @@ class Bijector(Cell):
         return value
 
     def cast_param_by_value(self, value, para):
+        """
+        Cast the parameter(s) of the bijector to be the same type of input_value.
+        """
         local = self.cast_base(para, self.dtype_base(value))
         return local
 
-    def forward(self, *args, **kwargs):
+    def forward(self, value, *args, **kwargs):
         """
         Forward transformation: transform the input value to another distribution.
         """
-        return self._forward(*args, **kwargs)
+        return self._forward(value, *args, **kwargs)
 
-    def inverse(self, *args, **kwargs):
+    def inverse(self, value, *args, **kwargs):
         """
         Inverse transformation: transform the input value back to the original distribution.
         """
-        return self._inverse(*args, **kwargs)
+        return self._inverse(value, *args, **kwargs)
 
-    def forward_log_jacobian(self, *args, **kwargs):
+    def forward_log_jacobian(self, value, *args, **kwargs):
         """
         Logarithm of the derivative of the forward transformation.
         """
-        return self._forward_log_jacobian(*args, **kwargs)
+        return self._forward_log_jacobian(value, *args, **kwargs)
 
-    def inverse_log_jacobian(self, *args, **kwargs):
+    def inverse_log_jacobian(self, value, *args, **kwargs):
         """
         Logarithm of the derivative of the inverse transformation.
         """
-        return self._inverse_log_jacobian(*args, **kwargs)
+        return self._inverse_log_jacobian(value, *args, **kwargs)
 
     def __call__(self, *args, **kwargs):
         """
@@ -167,7 +250,7 @@ class Bijector(Cell):
             *args: args[0] shall be either a distribution or the name of a Bijector function.
         """
         if isinstance(args[0], Distribution):
-            return TransformedDistribution(self, args[0], self.distribution.dtype)
+            return TransformedDistribution(self, args[0])
         return super(Bijector, self).__call__(*args, **kwargs)
 
     def construct(self, name, *args, **kwargs):
diff --git a/mindspore/nn/probability/bijector/gumbel_cdf.py b/mindspore/nn/probability/bijector/gumbel_cdf.py
index eef7affc6a0..a2f53048747 100644
--- a/mindspore/nn/probability/bijector/gumbel_cdf.py
+++ b/mindspore/nn/probability/bijector/gumbel_cdf.py
@@ -13,10 +13,8 @@
 # limitations under the License.
 # ============================================================================
 """GumbelCDF Bijector"""
-from mindspore.common import dtype as mstype
-from mindspore._checkparam import Validator
 from mindspore.ops import operations as P
-from ..distribution._utils.utils import check_greater_zero, set_param_type
+from ..distribution._utils.utils import check_greater_zero
 from ..distribution._utils.custom_ops import exp_generic, log_generic
 from .bijector import Bijector
 
@@ -30,12 +28,11 @@ class GumbelCDF(Bijector):
         Y = \exp(-\exp(\frac{-(X - loc)}{scale}))
 
     Note:
-        For `reverse` and `reverse_log_jacobian`, input should be in range of (0, 1).
+        For `inverse` and `inverse_log_jacobian`, input should be in range of (0, 1).
 
     Args:
-        loc (int, float, list, numpy.ndarray, Tensor): The location. Default: 0..
-        scale (int, float, list, numpy.ndarray, Tensor): The scale. Default: 1.0.
-        dtype (mindspore.dtype): Type of the distribution which the bijector operates on. Default: float32.
+        loc (float, list, numpy.ndarray, Tensor): The location. Default: 0..
+        scale (float, list, numpy.ndarray, Tensor): The scale. Default: 1.0.
         name (str): The name of the Bijector. Default: 'Gumbel_CDF'.
 
     Examples:
@@ -61,22 +58,18 @@ class GumbelCDF(Bijector):
     def __init__(self,
                  loc=0.0,
                  scale=1.0,
-                 dtype=mstype.float32,
                  name='GumbelCDF'):
         """
         Constructor of GumbelCDF Bijector.
         """
         param = dict(locals())
-        valid_dtype = mstype.float_type + mstype.int_type + mstype.uint_type
-        Validator.check_type_name("dtype", dtype, valid_dtype, type(self).__name__)
-        parameter_type = set_param_type({'loc': loc, "scale": scale}, dtype)
-        super(GumbelCDF, self).__init__(name=name, dtype=dtype, param=param)
+        param['param_dict'] = {'loc': loc, 'scale': scale}
+        super(GumbelCDF, self).__init__(name=name, param=param)
 
-        self._parameter_type = parameter_type
         self._loc = self._add_parameter(loc, 'loc')
         self._scale = self._add_parameter(scale, 'scale')
         check_greater_zero(self._scale, "scale")
-        self._event_shape = self._calc_event_shape()
+
 
         self.cast = P.Cast()
         self.exp = exp_generic
@@ -91,38 +84,34 @@ class GumbelCDF(Bijector):
     def scale(self):
         return self._scale
 
-    @property
-    def event_shape(self):
-        return self._event_shape
-
-    @property
-    def parameter_type(self):
-        return self._parameter_type
-
     def extend_repr(self):
-        return f'loc = {self.loc}, scale = {self.scale}'
-
-    def shape_mapping(self, shape):
-        return shape
+        if self.is_scalar_batch:
+            str_info = f'loc = {self.loc}, scale = {self.scale}'
+        else:
+            str_info = f'batch_shape = {self.batch_shape}'
+        return str_info
 
     def _forward(self, x):
-        x = self._check_value(x, 'value')
-        x = self.cast(x, self.parameter_type)
-        z = (x - self.loc) / self.scale
+        x = self._check_value_dtype(x)
+        loc_local = self.cast_param_by_value(x, self.loc)
+        scale_local = self.cast_param_by_value(x, self.scale)
+        z = (x - loc_local) / scale_local
         return self.exp(-self.exp(-z))
 
     def _inverse(self, y):
-        y = self._check_value(y, 'value')
-        y = self.cast(y, self.parameter_type)
-        return self.loc - self.scale * self.log(-self.log(y))
+        y = self._check_value_dtype(y)
+        loc_local = self.cast_param_by_value(y, self.loc)
+        scale_local = self.cast_param_by_value(y, self.scale)
+        return loc_local - scale_local * self.log(-self.log(y))
 
     def _forward_log_jacobian(self, x):
-        x = self._check_value(x, 'value')
-        x = self.cast(x, self.parameter_type)
-        z = (x - self.loc) / self.scale
-        return -z - self.exp(-z) - self.log(self.scale)
+        x = self._check_value_dtype(x)
+        loc_local = self.cast_param_by_value(x, self.loc)
+        scale_local = self.cast_param_by_value(x, self.scale)
+        z = (x - loc_local) / scale_local
+        return -z - self.exp(-z) - self.log(scale_local)
 
     def _inverse_log_jacobian(self, y):
-        y = self._check_value(y, 'value')
-        y = self.cast(y, self.parameter_type)
-        return self.log(self.scale / (-1. * y * self.log(y)))
+        y = self._check_value_dtype(y)
+        scale_local = self.cast_param_by_value(y, self.scale)
+        return self.log(scale_local / (-1. * y * self.log(y)))
diff --git a/mindspore/nn/probability/bijector/invert.py b/mindspore/nn/probability/bijector/invert.py
index 17f8dbc27a0..3cb63a9b5e9 100644
--- a/mindspore/nn/probability/bijector/invert.py
+++ b/mindspore/nn/probability/bijector/invert.py
@@ -53,23 +53,17 @@ class Invert(Bijector):
         name = (name + bijector.name) if name == 'Invert' else name
         super(Invert, self).__init__(is_constant_jacobian=bijector.is_constant_jacobian,
                                      is_injective=bijector.is_injective,
-                                     dtype=bijector.dtype,
                                      name=name,
+                                     dtype=bijector.dtype,
                                      param=param)
         self._bijector = bijector
-        if hasattr(self._bijector, 'event_shape'):
-            self._event_shape = self.bijector.event_shape
-        else:
-            self._event_shape = ()
+        self._batch_shape = self.bijector.batch_shape
+        self._is_scalar_batch = self.bijector.is_scalar_batch
 
     @property
     def bijector(self):
         return self._bijector
 
-    @property
-    def event_shape(self):
-        return self._event_shape
-
     def inverse(self, y):
         return self.bijector("forward", y)
 
diff --git a/mindspore/nn/probability/bijector/power_transform.py b/mindspore/nn/probability/bijector/power_transform.py
index 58c2b5bc54f..9a2ba0e2643 100644
--- a/mindspore/nn/probability/bijector/power_transform.py
+++ b/mindspore/nn/probability/bijector/power_transform.py
@@ -14,8 +14,7 @@
 # ============================================================================
 """Power Bijector"""
 from mindspore.ops import operations as P
-from mindspore._checkparam import Validator as validator
-from mindspore._checkparam import Rel
+from ..distribution._utils.utils import check_greater_equal_zero
 from ..distribution._utils.custom_ops import exp_generic, expm1_generic, log_generic, log1p_generic
 from .bijector import Bijector
 
@@ -37,7 +36,7 @@ class PowerTransform(Bijector):
         ValueError: When the power is less than 0 or is not known statically.
 
     Args:
-        power (int or float): The scale factor. Default: 0.
+        power (float, list, numpy.ndarray, Tensor): The scale factor. Default: 0.
         name (str): The name of the bijector. Default: 'PowerTransform'.
 
     Examples:
@@ -64,10 +63,11 @@ class PowerTransform(Bijector):
                  power=0,
                  name='PowerTransform'):
         param = dict(locals())
+        param['param_dict'] = {'power': power}
         super(PowerTransform, self).__init__(name=name, param=param)
-        validator.check_value_type('power', power, [int, float], self.name)
-        validator.check_number("power", power, 0, Rel.GE, self.name)
-        self._power = power
+        self._power = self._add_parameter(power, 'power')
+        check_greater_equal_zero(self._power, 'Power')
+
         self.pow = P.Pow()
         self.dtypeop = P.DType()
         self.cast = P.Cast()
@@ -81,13 +81,15 @@ class PowerTransform(Bijector):
         return self._power
 
     def extend_repr(self):
-        return f'power = {self.power}'
+        if self.is_scalar_batch:
+            str_info = f'power = {self.power}'
+        else:
+            str_info = f'batch_shape = {self.batch_shape}'
+        return str_info
 
-    def shape_mapping(self, shape):
-        return shape
 
     def _forward(self, x):
-        x = self._check_value(x, 'value')
+        x = self._check_value_dtype(x)
         power_local = self.cast_param_by_value(x, self.power)
         if power_local == 0:
             forward_v = self.exp(x)
@@ -96,7 +98,7 @@ class PowerTransform(Bijector):
         return forward_v
 
     def _inverse(self, y):
-        y = self._check_value(y, 'value')
+        y = self._check_value_dtype(y)
         power_local = self.cast_param_by_value(y, self.power)
         if power_local == 0:
             inverse_v = self.log(y)
@@ -116,7 +118,7 @@ class PowerTransform(Bijector):
                 f'(x) = e^\frac{\log(xc + 1)}{c} * \frac{1}{xc + 1}
                 \log(f'(x)) =  (\frac{1}{c} - 1) * \log(xc + 1)
         """
-        x = self._check_value(x, 'value')
+        x = self._check_value_dtype(x)
         power_local = self.cast_param_by_value(x, self.power)
         if power_local == 0:
             forward_log_j = x
@@ -136,7 +138,7 @@ class PowerTransform(Bijector):
                 f'(x) = \frac{e^c\log(y)}{y}
                 \log(f'(x)) =  \log(\frac{e^c\log(y)}{y}) = (c-1) * \log(y)
         """
-        y = self._check_value(y, 'value')
+        y = self._check_value_dtype(y)
         power_local = self.cast_param_by_value(y, self.power)
         inverse_log_j = (power_local - 1) * self.log(y)
         return inverse_log_j
diff --git a/mindspore/nn/probability/bijector/scalar_affine.py b/mindspore/nn/probability/bijector/scalar_affine.py
index f6ab8b8a806..94f7865daa3 100644
--- a/mindspore/nn/probability/bijector/scalar_affine.py
+++ b/mindspore/nn/probability/bijector/scalar_affine.py
@@ -14,8 +14,6 @@
 # ============================================================================
 """Scalar Affine Bijector"""
 from mindspore.ops import operations as P
-from mindspore._checkparam import Validator as validator
-from ..distribution._utils.utils import cast_to_tensor
 from ..distribution._utils.custom_ops import log_generic
 from .bijector import Bijector
 
@@ -30,10 +28,14 @@ class ScalarAffine(Bijector):
     where a is the scale factor and b is the shift factor.
 
     Args:
-        scale (float): The scale factor. Default: 1.0.
-        shift (float): The shift factor. Default: 0.0.
+        scale (float, list, numpy.ndarray, Tensor): The scale factor. Default: 1.0.
+        shift (float, list, numpy.ndarray, Tensor): The shift factor. Default: 0.0.
         name (str): The name of the bijector. Default: 'ScalarAffine'.
 
+    Note:
+        If `shift`, `scale` are passed in as numpy.ndarray or tensor, they have to have
+        the same dtype otherwise an error will be raised.
+
     Examples:
         >>> # To initialize a ScalarAffine bijector of scale 1 and shift 2.
         >>> scalaraffine = nn.probability.bijector.ScalarAffine(1, 2)
@@ -61,10 +63,7 @@ class ScalarAffine(Bijector):
         Constructor of ScalarAffine Bijector.
         """
         param = dict(locals())
-        validator.check_value_type(
-            'scale', scale, [int, float], type(self).__name__)
-        validator.check_value_type(
-            'shift', shift, [int, float], type(self).__name__)
+        param['param_dict'] = {'scale': scale, 'shift': shift}
         super(ScalarAffine, self).__init__(
             is_constant_jacobian=True,
             is_injective=True,
@@ -72,8 +71,8 @@ class ScalarAffine(Bijector):
             dtype=None,
             param=param)
 
-        self._scale = cast_to_tensor(scale)
-        self._shift = cast_to_tensor(shift)
+        self._scale = self._add_parameter(scale, 'scale')
+        self._shift = self._add_parameter(shift, 'shift')
 
         self.abs = P.Abs()
         self.oneslike = P.OnesLike()
@@ -90,17 +89,18 @@ class ScalarAffine(Bijector):
         return self._shift
 
     def extend_repr(self):
-        return f'scale = {self.scale}, shift = {self.shift}'
-
-    def shape_mapping(self, shape):
-        return shape
+        if self.is_scalar_batch:
+            str_info = f'scale = {self.scale}, shift = {self.shift}'
+        else:
+            str_info = f'batch_shape = {self.batch_shape}'
+        return str_info
 
     def _forward(self, x):
         r"""
         .. math::
             f(x) = a * x + b
         """
-        x = self._check_value(x, 'value')
+        x = self._check_value_dtype(x)
         scale_local = self.cast_param_by_value(x, self.scale)
         shift_local = self.cast_param_by_value(x, self.shift)
         forward_v = scale_local * x + shift_local * self.oneslike(x)
@@ -111,7 +111,7 @@ class ScalarAffine(Bijector):
         .. math::
             f(y) = \frac{y - b}{a}
         """
-        y = self._check_value(y, 'value')
+        y = self._check_value_dtype(y)
         scale_local = self.cast_param_by_value(y, self.scale)
         shift_local = self.cast_param_by_value(y, self.shift)
         inverse_v = (y - shift_local) / scale_local
@@ -124,7 +124,7 @@ class ScalarAffine(Bijector):
             f'(x) = a
             \log(f'(x)) = \log(a)
         """
-        x = self._check_value(x, 'value')
+        x = self._check_value_dtype(x)
         scale_local = self.cast_param_by_value(x, self.scale)
         forward_log_j = self.log(self.abs(scale_local))
         return forward_log_j
@@ -136,7 +136,7 @@ class ScalarAffine(Bijector):
             f'(x) = \frac{1.0}{a}
             \log(f'(x)) = - \log(a)
         """
-        y = self._check_value(y, 'value')
+        y = self._check_value_dtype(y)
         scale_local = self.cast_param_by_value(y, self.scale)
         inverse_log_j = -1. * self.log(self.abs(scale_local))
         return inverse_log_j
diff --git a/mindspore/nn/probability/bijector/softplus.py b/mindspore/nn/probability/bijector/softplus.py
index 93184ddde36..17aa498acae 100644
--- a/mindspore/nn/probability/bijector/softplus.py
+++ b/mindspore/nn/probability/bijector/softplus.py
@@ -16,8 +16,6 @@
 import numpy as np
 from mindspore.ops import operations as P
 from mindspore.nn.layer.activation import LogSigmoid
-from mindspore._checkparam import Validator as validator
-from ..distribution._utils.utils import cast_to_tensor
 from ..distribution._utils.custom_ops import exp_generic, expm1_generic, log_generic
 from .bijector import Bijector
 
@@ -32,7 +30,7 @@ class Softplus(Bijector):
     where k is the sharpness factor.
 
     Args:
-        sharpness (float): The scale factor. Default: 1.0.
+        sharpness (float, list, numpy.ndarray, Tensor): The scale factor. Default: 1.0.
         name (str): The name of the Bijector. Default: 'Softplus'.
 
     Examples:
@@ -61,10 +59,9 @@ class Softplus(Bijector):
         Constructor of Softplus Bijector.
         """
         param = dict(locals())
-        validator.check_value_type('sharpness', sharpness,
-                                   [int, float], type(self).__name__)
-        super(Softplus, self).__init__(name=name, param=param)
-        self._sharpness = cast_to_tensor(sharpness)
+        param['param_dict'] = {'sharpness': sharpness}
+        super(Softplus, self).__init__(name=name, dtype=None, param=param)
+        self._sharpness = self._add_parameter(sharpness, 'sharpness')
 
         self.exp = exp_generic
         self.log = log_generic
@@ -118,13 +115,14 @@ class Softplus(Bijector):
         return self._sharpness
 
     def extend_repr(self):
-        return f'sharpness = {self.sharpness}'
-
-    def shape_mapping(self, shape):
-        return shape
+        if self.is_scalar_batch:
+            str_info = f'sharpness = {self.sharpness}'
+        else:
+            str_info = f'batch_shape = {self.batch_shape}'
+        return str_info
 
     def _forward(self, x):
-        x = self._check_value(x, 'value')
+        x = self._check_value_dtype(x)
         sharpness_local = self.cast_param_by_value(x, self.sharpness)
         scaled_value = sharpness_local * x
         forward_v = self.softplus(scaled_value) / sharpness_local
@@ -136,7 +134,7 @@ class Softplus(Bijector):
             f(x) = \frac{\log(1 + e^{kx}))}{k}
             f^{-1}(y) = \frac{\log(e^{ky} - 1)}{k}
         """
-        y = self._check_value(y, 'value')
+        y = self._check_value_dtype(y)
         sharpness_local = self.cast_param_by_value(y, self.sharpness)
         scaled_value = sharpness_local * y
         inverse_v = self.inverse_softplus(scaled_value) / sharpness_local
@@ -149,7 +147,7 @@ class Softplus(Bijector):
             f'(x) = \frac{e^{kx}}{ 1 + e^{kx}}
             \log(f'(x)) =  kx - \log(1 + e^{kx}) = kx - f(kx)
         """
-        x = self._check_value(x, 'value')
+        x = self._check_value_dtype(x)
         sharpness_local = self.cast_param_by_value(x, self.sharpness)
         scaled_value = sharpness_local * x
         forward_log_j = self.log_sigmoid(scaled_value)
@@ -162,7 +160,7 @@ class Softplus(Bijector):
             f'(y) = \frac{e^{ky}}{e^{ky} - 1}
             \log(f'(y)) = ky - \log(e^{ky} - 1) = ky - f(ky)
         """
-        y = self._check_value(y, 'value')
+        y = self._check_value_dtype(y)
         sharpness_local = self.cast_param_by_value(y, self.sharpness)
         scaled_value = sharpness_local * y
         inverse_log_j = scaled_value - self.inverse_softplus(scaled_value)
diff --git a/mindspore/nn/probability/distribution/_utils/utils.py b/mindspore/nn/probability/distribution/_utils/utils.py
index c344e9c06f4..8e269fbd56e 100644
--- a/mindspore/nn/probability/distribution/_utils/utils.py
+++ b/mindspore/nn/probability/distribution/_utils/utils.py
@@ -229,6 +229,11 @@ def raise_not_implemented_util(func_name, obj, *args, **kwargs):
     raise NotImplementedError(
         f"{func_name} is not implemented for {obj} distribution.")
 
+@constexpr
+def raise_type_error(name, cur_type, required_type):
+    raise TypeError(
+        f"For {name} , the type should be or be subclass of {required_type}, but got {cur_type}")
+
 
 @constexpr
 def check_distribution_name(name, expected_name):
@@ -304,7 +309,7 @@ def set_param_type(args, hint_type):
         TypeError: if tensors in args are not the same dtype.
     """
     int_type = mstype.int_type + mstype.uint_type
-    if hint_type in int_type:
+    if hint_type in int_type or hint_type is None:
         hint_type = mstype.float32
     common_dtype = None
     for name, arg in args.items():
diff --git a/mindspore/nn/probability/distribution/distribution.py b/mindspore/nn/probability/distribution/distribution.py
index d218d885374..8dfda69af8f 100644
--- a/mindspore/nn/probability/distribution/distribution.py
+++ b/mindspore/nn/probability/distribution/distribution.py
@@ -72,13 +72,12 @@ class Distribution(Cell):
             if not(k == 'self' or k.startswith('_')):
                 self._parameters[k] = param[k]
 
-        # some attributes
-        if 'distribution' in self.parameters.keys():
-            self.parameter_type = self.parameters['distribution'].parameter_type
-        else:
+        # if not a transformed distribution, set the following attribute
+        if 'distribution' not in self.parameters.keys():
             self.parameter_type = set_param_type(self.parameters['param_dict'], dtype)
-        self._broadcast_shape = self._calc_broadcast_shape()
-        self._is_scalar_batch = self._check_is_scalar_batch()
+            self._batch_shape = self._calc_batch_shape()
+            self._is_scalar_batch = self._check_is_scalar_batch()
+            self._broadcast_shape = self._batch_shape
 
         # set the function to call according to the derived class's attributes
         self._set_prob()
@@ -128,6 +127,10 @@ class Distribution(Cell):
     def is_scalar_batch(self):
         return self._is_scalar_batch
 
+    @property
+    def batch_shape(self):
+        return self._batch_shape
+
     @property
     def broadcast_shape(self):
         return self._broadcast_shape
@@ -208,8 +211,6 @@ class Distribution(Cell):
         """
         Check if the parameters used during initialization are scalars.
         """
-        if 'distribution' in self.parameters.keys():
-            return self.parameters['distribution'].is_scalar_batch
         param_dict = self.parameters['param_dict']
         for value in param_dict.values():
             if value is None:
@@ -218,12 +219,10 @@ class Distribution(Cell):
                 return False
         return True
 
-    def _calc_broadcast_shape(self):
+    def _calc_batch_shape(self):
         """
         Calculate the broadcast shape of the parameters used during initialization.
         """
-        if 'distribution' in self.parameters.keys():
-            return self.parameters['distribution'].broadcast_shape
         param_dict = self.parameters['param_dict']
         broadcast_shape_tensor = None
         for value in param_dict.values():
@@ -362,14 +361,14 @@ class Distribution(Cell):
         """
         return self._get_dist_args(*args, **kwargs)
 
-    def _get_dist_type(self, *args, **kwargs):
-        return raise_not_implemented_util('get_dist_type', self.name, *args, **kwargs)
+    def _get_dist_type(self):
+        return raise_not_implemented_util('get_dist_type', self.name)
 
-    def get_dist_type(self, *args, **kwargs):
+    def get_dist_type(self):
         """
         Return the type of the distribution.
         """
-        return self._get_dist_type(*args, **kwargs)
+        return self._get_dist_type()
 
     def _raise_not_implemented_error(self, func_name):
         name = self.name
@@ -751,5 +750,5 @@ class Distribution(Cell):
         if name == 'get_dist_args':
             return self._get_dist_args(*args, **kwargs)
         if name == 'get_dist_type':
-            return self._get_dist_type(*args, **kwargs)
+            return self._get_dist_type()
         return raise_not_implemented_util(name, self.name, *args, **kwargs)
diff --git a/mindspore/nn/probability/distribution/gumbel.py b/mindspore/nn/probability/distribution/gumbel.py
index f598e29d55e..50d891ee82d 100644
--- a/mindspore/nn/probability/distribution/gumbel.py
+++ b/mindspore/nn/probability/distribution/gumbel.py
@@ -103,17 +103,12 @@ class Gumbel(TransformedDistribution):
         """
         valid_dtype = mstype.float_type
         Validator.check_type_name("dtype", dtype, valid_dtype, type(self).__name__)
-        gumbel_cdf = msb.GumbelCDF(loc, scale, dtype)
+        gumbel_cdf = msb.GumbelCDF(loc, scale)
         super(Gumbel, self).__init__(
             distribution=msd.Uniform(0.0, 1.0, dtype=dtype),
             bijector=msb.Invert(gumbel_cdf),
             seed=seed, name=name)
 
-        self.parameter_type = gumbel_cdf.parameter_type
-        self._broadcast_shape = gumbel_cdf.event_shape
-        if self._broadcast_shape != ():
-            self._is_scalar_batch = False
-
         # overwrite default_parameters and parameter_names
         self._reset_parameters()
         self._loc = self._add_parameter(loc, 'loc')
@@ -202,6 +197,7 @@ class Gumbel(TransformedDistribution):
                 where z = \frac{x - loc}{scale}
         """
         value = self._check_value(value, 'value')
+        value = self.cast(value, self.dtype)
         z = (value - self.loc) / self.scale
         return -(z + self.exp(-z)) - self.log(self.scale)
 
@@ -210,6 +206,8 @@ class Gumbel(TransformedDistribution):
         .. math::
             cdf_pdf(X) = \exp(-\exp(-\frac{x - loc}{scale})
         """
+        value = self._check_value(value, 'value')
+        value = self.cast(value, self.dtype)
         return self._gumbel_bijector("forward", value)
 
     def _cross_entropy(self, dist, loc_b, scale_b):
@@ -251,12 +249,14 @@ class Gumbel(TransformedDistribution):
                self.expm1((loc_b - self.loc) / scale_b + self.lgamma(self.scale / scale_b + 1.))
 
     def _sample(self, shape=()):
+        shape = self.checktuple(shape, 'shape')
         origin_shape = shape + self._broadcast_shape
         if origin_shape == ():
             sample_shape = (1,)
         else:
             sample_shape = origin_shape
         org_sample = self.distribution("sample", sample_shape)
+        org_sample = self.cast(org_sample, self.dtype)
         value = self.bijector("forward", org_sample)
         if origin_shape == ():
             value = self.squeeze(value)
diff --git a/mindspore/nn/probability/distribution/log_normal.py b/mindspore/nn/probability/distribution/log_normal.py
index 64bc160ff2e..c82e79f75c9 100644
--- a/mindspore/nn/probability/distribution/log_normal.py
+++ b/mindspore/nn/probability/distribution/log_normal.py
@@ -137,6 +137,11 @@ class LogNormal(msd.TransformedDistribution):
                                         bijector=msb.Exp(),
                                         seed=seed, name=name)
 
+        # overwrite default_parameters and parameter_names
+        self._reset_parameters()
+        self._loc = self._add_parameter(loc, 'loc')
+        self._scale = self._add_parameter(scale, 'scale')
+
         self.log_2pi = np.log(2 * np.pi)
 
         #ops needed for the class
@@ -154,12 +159,12 @@ class LogNormal(msd.TransformedDistribution):
     @property
     def loc(self):
         """Distribution parameter for the pre-transformed mean."""
-        return self.distribution("mean")
+        return self._loc
 
     @property
     def scale(self):
         """Distribution parameter for the pre-transformed standard deviation."""
-        return self.distribution("sd")
+        return self._scale
 
     def _get_dist_type(self):
         return "LogNormal"
@@ -168,18 +173,18 @@ class LogNormal(msd.TransformedDistribution):
         if loc is not None:
             self.checktensor(loc, 'loc')
         else:
-            loc = self.distribution("mean")
+            loc = self.loc
         if scale is not None:
             self.checktensor(scale, 'scale')
         else:
-            scale = self.distribution("sd")
+            scale = self.scale
         return loc, scale
 
     def extend_repr(self):
         if self.is_scalar_batch:
-            s = f'loc = {self._mean_value}, scale = {self._sd_value}'
+            s = f'loc = {self.loc}, scale = {self.scale}'
         else:
-            s = f'batch_shape = {self._broadcast_shape}'
+            s = f'batch_shape = {self.broadcast_shape}'
         return s
 
     def _mean(self, loc=None, scale=None):
diff --git a/mindspore/nn/probability/distribution/transformed_distribution.py b/mindspore/nn/probability/distribution/transformed_distribution.py
index 1bcc77781df..927420291c9 100644
--- a/mindspore/nn/probability/distribution/transformed_distribution.py
+++ b/mindspore/nn/probability/distribution/transformed_distribution.py
@@ -16,6 +16,7 @@
 import numpy as np
 from mindspore._checkparam import Validator as validator
 from mindspore.ops import operations as P
+from mindspore.common import dtype as mstype
 import mindspore.nn as nn
 from .distribution import Distribution
 from ._utils.utils import raise_not_impl_error
@@ -30,7 +31,7 @@ class TransformedDistribution(Distribution):
 
     Args:
         bijector (Bijector): The transformation to perform.
-        distribution (Distribution): The original distribution.
+        distribution (Distribution): The original distribution. Must has dtype of mindspore.float_type.
         seed (int): The seed is used in sampling. The global seed is used if it is None. Default:None.
           If this seed is given when a TransformedDistribution object is initialised, the object's sampling function
           will use this seed; elsewise, the underlying distribution's seed will be used.
@@ -40,6 +41,12 @@ class TransformedDistribution(Distribution):
         The arguments used to initialize the original distribution cannot be None.
         For example, mynormal = nn.Normal(dtype=dtyple.float32) cannot be used to initialized a
         TransformedDistribution since `mean` and `sd` are not specified.
+        `batch_shape` is the batch_shape of the original distribution.
+        `broadcast_shape` is the broadcast shape between the original distribution and bijector.
+        `is_scalar_batch` is only true if both the original distribution and the bijector are scalar batches.
+        `default_parameters`, `parameter_names` and `parameter_type` are set to be consistent with the original
+        distribution. Derived class can overwrite `default_parameters` and `parameter_names` by calling
+        `reset_parameters` followed by `add_parameter`.
 
     Examples:
         >>> # To initialize a transformed distribution, e.g. a lognormal distribution,
@@ -75,28 +82,34 @@ class TransformedDistribution(Distribution):
                                    [nn.probability.bijector.Bijector], type(self).__name__)
         validator.check_value_type('distribution', distribution,
                                    [Distribution], type(self).__name__)
+        validator.check_type_name("dtype", distribution.dtype, mstype.float_type, type(self).__name__)
         super(TransformedDistribution, self).__init__(seed, distribution.dtype, name, param)
 
         self._bijector = bijector
         self._distribution = distribution
-        self._is_linear_transformation = bijector.is_constant_jacobian
-        self.default_parameters = distribution.default_parameters
-        self.parameter_names = distribution.parameter_names
+
+        # set attributes
+        self._is_linear_transformation = self.bijector.is_constant_jacobian
+        self._dtype = self.distribution.dtype
+        self._is_scalar_batch = self.distribution.is_scalar_batch and self.bijector.is_scalar_batch
+        self._batch_shape = self.distribution.batch_shape
+
+        self.default_parameters = self.distribution.default_parameters
+        self.parameter_names = self.distribution.parameter_names
+        # by default, set the parameter_type to be the distribution's parameter_type
+        self.parameter_type = self.distribution.parameter_type
 
         self.exp = exp_generic
         self.log = log_generic
         self.isnan = P.IsNan()
+        self.cast_base = P.Cast()
         self.equal_base = P.Equal()
         self.select_base = P.Select()
-        self.fill = P.Fill()
+        self.fill_base = P.Fill()
+
+        # broadcast bijector batch_shape and distribution batch_shape
+        self._broadcast_shape = self._broadcast_bijector_dist()
 
-        # check if batch shape of the distribution and event shape is broadcastable
-        if hasattr(self.bijector, 'event_shape'):
-            event_shape_tensor = self.fill(self.dtype, self.bijector.event_shape, 0.0)
-            broadcast_shape_tensor = self.fill(self.dtype, self.broadcast_shape, 0.0)
-            self._batch_event = (event_shape_tensor + broadcast_shape_tensor).shape
-        else:
-            self._batch_event = self.broadcast_shape
 
     @property
     def bijector(self):
@@ -108,12 +121,22 @@ class TransformedDistribution(Distribution):
 
     @property
     def dtype(self):
-        return self.distribution.dtype
+        return self._dtype
 
     @property
     def is_linear_transformation(self):
         return self._is_linear_transformation
 
+    def _broadcast_bijector_dist(self):
+        """
+        check if the batch shape of base distribution and the bijector is broadcastable.
+        """
+        if self.batch_shape is None or self.bijector.batch_shape is None:
+            return None
+        bijector_shape_tensor = self.fill_base(self.dtype, self.bijector.batch_shape, 0.0)
+        dist_shape_tensor = self.fill_base(self.dtype, self.batch_shape, 0.0)
+        return (bijector_shape_tensor + dist_shape_tensor).shape
+
     def _cdf(self, value, *args, **kwargs):
         r"""
         .. math::
diff --git a/tests/ut/python/nn/probability/bijector/test_bijector.py b/tests/ut/python/nn/probability/bijector/test_bijector.py
new file mode 100644
index 00000000000..f3ae926c5bf
--- /dev/null
+++ b/tests/ut/python/nn/probability/bijector/test_bijector.py
@@ -0,0 +1,191 @@
+# 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 exp"""
+import numpy as np
+import pytest
+
+import mindspore.nn as nn
+import mindspore.nn.probability.bijector as msb
+from mindspore import Tensor
+from mindspore import dtype
+
+class MyBijector(msb.Bijector):
+    """
+    Customized bijector class with dtype not specified.
+    """
+    def __init__(self, param1, param2):
+        param = dict(locals())
+        param['param_dict'] = {'param1': param1, 'param2': param2}
+        super(MyBijector, self).__init__(name='MyBijector', dtype=None, param=param)
+
+        self._param1 = self._add_parameter(param1, 'param1')
+        self._param2 = self._add_parameter(param2, 'param2')
+
+    @property
+    def param1(self):
+        return self._param1
+
+    @property
+    def param2(self):
+        return self._param2
+
+    def _forward(self, value):
+        value = self._check_value_dtype(value)
+        param1_local = self.cast_param_by_value(value, self.param1)
+        param2_local = self.cast_param_by_value(value, self.param2)
+        return value * param1_local + param2_local
+
+class MySecondBijector(msb.Bijector):
+    """
+    Customized bijector class with dtype specified.
+    """
+    def __init__(self, param1, param2):
+        param = dict(locals())
+        param['param_dict'] = {'param1': param1, 'param2': param2}
+        super(MySecondBijector, self).__init__(name='MySecondBijector', dtype=dtype.float32, param=param)
+
+        self._param1 = self._add_parameter(param1, 'param1')
+        self._param2 = self._add_parameter(param2, 'param2')
+
+    @property
+    def param1(self):
+        return self._param1
+
+    @property
+    def param2(self):
+        return self._param2
+
+    def _forward(self, value):
+        value = self._check_value_dtype(value)
+        param1_local = self.cast_param_by_value(value, self.param1)
+        param2_local = self.cast_param_by_value(value, self.param2)
+        return value * param1_local + param2_local
+
+def test_arguments_same_type():
+    """
+    Test bijector initializations.
+    """
+    param1_1 = np.array(1.0).astype(np.float16)
+    param2_1 = np.array(2.0).astype(np.float32)
+    with pytest.raises(TypeError):
+        MyBijector(param1_1, param2_1)
+    param1_2 = Tensor(1.0, dtype=dtype.float16)
+    param2_2 = Tensor(2.0, dtype=dtype.float32)
+    with pytest.raises(TypeError):
+        MyBijector(param1_2, param2_2)
+    with pytest.raises(TypeError):
+        MyBijector(True, param2_2)
+    with pytest.raises(TypeError):
+        MyBijector(None, param2_2)
+    param1_3 = Tensor(1.0, dtype=dtype.float32)
+    param2_3 = Tensor(2.0, dtype=dtype.float32)
+    bijector = MyBijector(param1_3, param2_3)
+    assert isinstance(bijector, msb.Bijector)
+    param1_4 = np.array([1.0, 2.0]).astype(np.float16)
+    param2_4 = np.array([1.0, 2.0]).astype(np.float16)
+    bijector = MyBijector(param1_4, param2_4)
+    assert isinstance(bijector, msb.Bijector)
+    bijector = MyBijector(1.0, 2.0)
+    assert isinstance(bijector, msb.Bijector)
+
+def test_arguments_with_dtype_specified():
+    """
+    Customized bijector class with dtype not specified.
+    """
+    param1_1 = np.array(1.0).astype(np.float16)
+    param2_1 = np.array(2.0).astype(np.float16)
+    with pytest.raises(TypeError):
+        MySecondBijector(param1_1, param2_1)
+    param1_2 = Tensor(1.0, dtype=dtype.float16)
+    param2_2 = Tensor(2.0, dtype=dtype.float32)
+    with pytest.raises(TypeError):
+        MySecondBijector(param1_2, param2_2)
+    with pytest.raises(TypeError):
+        MySecondBijector(True, param2_2)
+    with pytest.raises(TypeError):
+        MySecondBijector(None, param2_2)
+    param1_3 = Tensor(1.0, dtype=dtype.float32)
+    param2_3 = Tensor(2.0, dtype=dtype.float32)
+    bijector = MyBijector(param1_3, param2_3)
+    assert isinstance(bijector, msb.Bijector)
+    param1_4 = np.array(2.0).astype(np.float32)
+    param2_4 = np.array(1.0).astype(np.float32)
+    bijector = MyBijector(param1_4, param2_4)
+    assert isinstance(bijector, msb.Bijector)
+
+class Net1(nn.Cell):
+    """
+    Test input value when bijector's dtype is not specified.
+    """
+    def __init__(self):
+        super(Net1, self).__init__()
+        self.bijector = MyBijector(np.array(1.0).astype(np.float32), np.array(2.0).astype(np.float32))
+
+    def construct(self, value):
+        return self.bijector.forward(value)
+
+class Net2(nn.Cell):
+    """
+    Test input value when bijector's dtype is specified.
+    """
+    def __init__(self):
+        super(Net2, self).__init__()
+        self.bijector = MySecondBijector(np.array(1.0).astype(np.float32), np.array(2.0).astype(np.float32))
+
+    def construct(self, value):
+        return self.bijector.forward(value)
+
+def test_input_value():
+    """
+    Test validity of input value.
+    """
+    net = Net1()
+    value = None
+    with pytest.raises(TypeError):
+        ans = net(value)
+    value = 1.0
+    with pytest.raises(TypeError):
+        ans = net(value)
+    value = Tensor(1.0, dtype=dtype.int32)
+    with pytest.raises(TypeError):
+        ans = net(value)
+    value = Tensor(1.0, dtype=dtype.float32)
+    ans = net(value)
+    assert ans.dtype == dtype.float32
+    value = Tensor(1.0, dtype=dtype.float16)
+    ans = net(value)
+    assert ans.dtype == dtype.float16
+
+def test_input_value2():
+    """
+    Test validity of input value.
+    """
+    net = Net2()
+    value = None
+    with pytest.raises(TypeError):
+        ans = net(value)
+    value = 1.0
+    with pytest.raises(TypeError):
+        ans = net(value)
+    value = Tensor(1.0, dtype=dtype.int32)
+    with pytest.raises(TypeError):
+        ans = net(value)
+    value = Tensor(1.0, dtype=dtype.float16)
+    with pytest.raises(TypeError):
+        ans = net(value)
+    value = Tensor(1.0, dtype=dtype.float32)
+    ans = net(value)
+    assert ans.dtype == dtype.float32
+ 
\ No newline at end of file
diff --git a/tests/ut/python/nn/probability/distribution/test_distribution.py b/tests/ut/python/nn/probability/distribution/test_distribution.py
index bea14a4d65e..8542343c1a5 100644
--- a/tests/ut/python/nn/probability/distribution/test_distribution.py
+++ b/tests/ut/python/nn/probability/distribution/test_distribution.py
@@ -1,3 +1,7 @@
+# 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