diff --git a/mindspore/nn/probability/bijector/bijector.py b/mindspore/nn/probability/bijector/bijector.py
index ac011fda33..1e36ae0906 100644
--- a/mindspore/nn/probability/bijector/bijector.py
+++ b/mindspore/nn/probability/bijector/bijector.py
@@ -26,7 +26,7 @@ class Bijector(Cell):
         is_constant_jacobian (bool): if the bijector has constant derivative. Default: False.
         is_injective (bool): if the bijector is an one-to-one mapping. Default: True.
         name (str): name of the bijector. Default: None.
-        dtype (mstype): type of the distribution the bijector can operate on. Default: None.
+        dtype (mindspore.dtype): type of the distribution the bijector can operate on. Default: None.
         param (dict): parameters used to initialize the bijector. Default: None.
     """
     def __init__(self,
@@ -110,7 +110,7 @@ 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])
+            return TransformedDistribution(self, args[0], self.distribution.dtype)
         return super(Bijector, self).__call__(*args, **kwargs)
 
     def construct(self, name, *args, **kwargs):
diff --git a/mindspore/nn/probability/bijector/softplus.py b/mindspore/nn/probability/bijector/softplus.py
index 26f70c8fc7..105beb061b 100644
--- a/mindspore/nn/probability/bijector/softplus.py
+++ b/mindspore/nn/probability/bijector/softplus.py
@@ -22,7 +22,10 @@ from .bijector import Bijector
 class Softplus(Bijector):
     r"""
     Softplus Bijector.
-    This Bijector performs the operation: Y = \frac{\log(1 + e ^ {kX})}{k}, where k is the sharpness factor.
+    This Bijector performs the operation, where k is the sharpness factor.
+
+    .. math::
+    Y = \frac{\log(1 + e ^ {kX})}{k}
 
     Args:
         sharpness (float): scale factor. Default: 1.0.
diff --git a/mindspore/nn/probability/distribution/_utils/utils.py b/mindspore/nn/probability/distribution/_utils/utils.py
index 2c11106be5..2a5cf5e7bf 100644
--- a/mindspore/nn/probability/distribution/_utils/utils.py
+++ b/mindspore/nn/probability/distribution/_utils/utils.py
@@ -184,7 +184,7 @@ def check_greater(a, b, name_a, name_b):
 
 def check_prob(p):
     """
-    Check if p is a proper probability, i.e. 0 <= p <=1.
+    Check if p is a proper probability, i.e. 0 < p <1.
 
     Args:
         p (Tensor, Parameter): value to be checked.
@@ -196,12 +196,12 @@ def check_prob(p):
         if not isinstance(p.default_input, Tensor):
             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')
+    comp = np.less(np.zeros(p.shape), p.asnumpy())
+    if not comp.all():
+        raise ValueError('Probabilities should be greater than zero')
+    comp = np.greater(np.ones(p.shape), p.asnumpy())
+    if not comp.all():
+        raise ValueError('Probabilities should be less than one')
 
 
 def logits_to_probs(logits, is_binary=False):
diff --git a/mindspore/nn/probability/distribution/bernoulli.py b/mindspore/nn/probability/distribution/bernoulli.py
index 028ee175f1..9b48dd7a5e 100644
--- a/mindspore/nn/probability/distribution/bernoulli.py
+++ b/mindspore/nn/probability/distribution/bernoulli.py
@@ -110,6 +110,7 @@ class Bernoulli(Distribution):
         self.const = P.ScalarToArray()
         self.dtypeop = P.DType()
         self.erf = P.Erf()
+        self.exp = P.Exp()
         self.fill = P.Fill()
         self.log = P.Log()
         self.less = P.Less()
@@ -159,7 +160,7 @@ class Bernoulli(Distribution):
         """
         probs1 = self.probs if probs1 is None else probs1
         probs0 = 1.0 - probs1
-        return probs0 * probs1
+        return self.exp(self.log(probs0) + self.log(probs1))
 
     def _entropy(self, probs=None):
         r"""
@@ -183,7 +184,7 @@ class Bernoulli(Distribution):
             return self._entropy(probs=probs1_a) + self._kl_loss(dist, probs1_b, probs1_a)
         return None
 
-    def _prob(self, value, probs=None):
+    def _log_prob(self, value, probs=None):
         r"""
         pmf of Bernoulli distribution.
 
@@ -197,7 +198,7 @@ class Bernoulli(Distribution):
         """
         probs1 = self.probs if probs is None else probs
         probs0 = 1.0 - probs1
-        return (probs1 * value) + (probs0 * (1.0 - value))
+        return self.log(probs1) * value + self.log(probs0) * (1.0 - value)
 
     def _cdf(self, value, probs=None):
         r"""
diff --git a/mindspore/nn/probability/distribution/distribution.py b/mindspore/nn/probability/distribution/distribution.py
index d3e7d3ccd9..fffc7ed69e 100644
--- a/mindspore/nn/probability/distribution/distribution.py
+++ b/mindspore/nn/probability/distribution/distribution.py
@@ -15,6 +15,7 @@
 """basic"""
 from mindspore.nn.cell import Cell
 from mindspore._checkparam import Validator as validator
+from mindspore._checkparam import Rel
 from ._utils.utils import calc_broadcast_shape_from_param, check_scalar_from_param
 
 class Distribution(Cell):
@@ -28,12 +29,15 @@ class Distribution(Cell):
 
     Note:
         Derived class should override operations such as ,_mean, _prob,
-        and _log_prob. Arguments should be passed in through *args or **kwargs.
+        and _log_prob. Required arguments, such as value for _prob,
+        should be passed in through args or kwargs. dist_spec_args which specify
+        a new distribution are optional.
 
-        Dist_spec_args are unique for each type of distribution. For example, mean and sd
-        are the dist_spec_args for a Normal distribution.
+        dist_spec_args are unique for each type of distribution. For example, mean and sd
+        are the dist_spec_args for a Normal distribution, while rate is the dist_spec_args
+        for exponential distribution.
 
-        For all functions, passing in dist_spec_args, are optional.
+        For all functions, passing in dist_spec_args, is optional.
         Passing in the additional dist_spec_args will make the result to be evaluated with
         new distribution specified by the dist_spec_args. But it won't change the
         original distribuion.
@@ -49,7 +53,7 @@ class Distribution(Cell):
         """
         super(Distribution, self).__init__()
         validator.check_value_type('name', name, [str], 'distribution_name')
-        validator.check_value_type('seed', seed, [int], name)
+        validator.check_integer('seed', seed, 0, Rel.GE, name)
 
         self._name = name
         self._seed = seed
@@ -191,7 +195,7 @@ class Distribution(Cell):
 
         Note:
             Args must include value.
-            Dist_spec_args are optional.
+            dist_spec_args are optional.
         """
         return self._call_log_prob(*args, **kwargs)
 
@@ -210,7 +214,7 @@ class Distribution(Cell):
 
         Note:
             Args must include value.
-            Dist_spec_args are optional.
+            dist_spec_args are optional.
         """
         return self._call_prob(*args, **kwargs)
 
@@ -229,7 +233,7 @@ class Distribution(Cell):
 
         Note:
             Args must include value.
-            Dist_spec_args are optional.
+            dist_spec_args are optional.
         """
         return self._call_cdf(*args, **kwargs)
 
@@ -266,7 +270,7 @@ class Distribution(Cell):
 
         Note:
             Args must include value.
-            Dist_spec_args are optional.
+            dist_spec_args are optional.
         """
         return self._call_log_cdf(*args, **kwargs)
 
@@ -285,7 +289,7 @@ class Distribution(Cell):
 
         Note:
             Args must include value.
-            Dist_spec_args are optional.
+            dist_spec_args are optional.
         """
         return self._call_survival(*args, **kwargs)
 
@@ -313,7 +317,7 @@ class Distribution(Cell):
 
         Note:
             Args must include value.
-            Dist_spec_args are optional.
+            dist_spec_args are optional.
         """
         return self._call_log_survival(*args, **kwargs)
 
@@ -341,7 +345,7 @@ class Distribution(Cell):
         Evaluate the mean.
 
         Note:
-            Dist_spec_args are optional.
+            dist_spec_args are optional.
         """
         return self._mean(*args, **kwargs)
 
@@ -350,7 +354,7 @@ class Distribution(Cell):
         Evaluate the mode.
 
         Note:
-            Dist_spec_args are optional.
+            dist_spec_args are optional.
         """
         return self._mode(*args, **kwargs)
 
@@ -359,7 +363,7 @@ class Distribution(Cell):
         Evaluate the standard deviation.
 
         Note:
-            Dist_spec_args are optional.
+            dist_spec_args are optional.
         """
         return self._call_sd(*args, **kwargs)
 
@@ -368,7 +372,7 @@ class Distribution(Cell):
         Evaluate the variance.
 
         Note:
-            Dist_spec_args are optional.
+            dist_spec_args are optional.
         """
         return self._call_var(*args, **kwargs)
 
@@ -395,7 +399,7 @@ class Distribution(Cell):
         Evaluate the entropy.
 
         Note:
-            Dist_spec_args are optional.
+            dist_spec_args are optional.
         """
         return self._entropy(*args, **kwargs)
 
@@ -424,7 +428,7 @@ class Distribution(Cell):
 
         Note:
             Shape of the sample is default to ().
-            Dist_spec_args are optional.
+            dist_spec_args are optional.
         """
         return self._sample(*args, **kwargs)
 
diff --git a/mindspore/nn/probability/distribution/exponential.py b/mindspore/nn/probability/distribution/exponential.py
index 8564935e09..410f829f5d 100644
--- a/mindspore/nn/probability/distribution/exponential.py
+++ b/mindspore/nn/probability/distribution/exponential.py
@@ -199,7 +199,7 @@ class Exponential(Distribution):
             pdf(x) = rate * \exp(-1 * \lambda * x) if x >= 0 else 0
         """
         rate = self.rate if rate is None else rate
-        prob = rate * self.exp(-1. * rate * value)
+        prob = self.exp(self.log(rate) - rate * value)
         zeros = self.fill(self.dtypeop(prob), self.shape(prob), 0.0)
         comp = self.less(value, zeros)
         return self.select(comp, zeros, prob)
diff --git a/mindspore/nn/probability/distribution/geometric.py b/mindspore/nn/probability/distribution/geometric.py
index 2c67bb5588..fbdfc8263b 100644
--- a/mindspore/nn/probability/distribution/geometric.py
+++ b/mindspore/nn/probability/distribution/geometric.py
@@ -113,6 +113,7 @@ class Geometric(Distribution):
         self.cast = P.Cast()
         self.const = P.ScalarToArray()
         self.dtypeop = P.DType()
+        self.exp = P.Exp()
         self.fill = P.Fill()
         self.floor = P.Floor()
         self.issubclass = P.IsSubClass()
@@ -205,7 +206,7 @@ class Geometric(Distribution):
             value = self.floor(value)
         else:
             return None
-        pmf = self.pow((1.0 - probs1), value) * probs1
+        pmf = self.exp(self.log(1.0 - probs1) * value + self.log(probs1))
         zeros = self.fill(self.dtypeop(probs1), self.shape(pmf), 0.0)
         comp = self.less(value, zeros)
         return self.select(comp, zeros, pmf)
diff --git a/mindspore/nn/probability/distribution/normal.py b/mindspore/nn/probability/distribution/normal.py
index e1dfbee89d..1db22d9f73 100644
--- a/mindspore/nn/probability/distribution/normal.py
+++ b/mindspore/nn/probability/distribution/normal.py
@@ -18,7 +18,7 @@ from mindspore.ops import operations as P
 from mindspore.ops import composite as C
 from mindspore.common import dtype as mstype
 from .distribution import Distribution
-from ._utils.utils import convert_to_batch, check_greater_equal_zero, check_type
+from ._utils.utils import convert_to_batch, check_greater_zero, check_type
 
 
 class Normal(Distribution):
@@ -106,7 +106,7 @@ class Normal(Distribution):
         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")
+            check_greater_zero(self._sd_value, "Standard deviation")
         else:
             self._mean_value = mean
             self._sd_value = sd
@@ -166,7 +166,7 @@ class Normal(Distribution):
             H(X) = \log(\sqrt(numpy.e * 2. * numpy.pi * \sq(\sigma)))
         """
         sd = self._sd_value if sd is None else sd
-        return self.log(self.sqrt(np.e * 2. * np.pi * self.sq(sd)))
+        return self.log(self.sqrt(self.const(np.e * 2. * np.pi))) + self.log(sd)
 
     def _cross_entropy(self, dist, mean_b, sd_b, mean_a=None, sd_a=None):
         r"""
@@ -198,7 +198,7 @@ class Normal(Distribution):
         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.sq(value - mean)) / (2. * self.sq(sd))
-        neg_normalization = -1. * self.log(self.sqrt(2. * np.pi * self.sq(sd)))
+        neg_normalization = -1. * self.log(self.sqrt(self.const(2. * np.pi))) - self.log(sd)
         return unnormalized_log_prob + neg_normalization
 
     def _cdf(self, value, mean=None, sd=None):
diff --git a/mindspore/nn/probability/distribution/uniform.py b/mindspore/nn/probability/distribution/uniform.py
index 6aff1ef775..db248c24d7 100644
--- a/mindspore/nn/probability/distribution/uniform.py
+++ b/mindspore/nn/probability/distribution/uniform.py
@@ -216,8 +216,8 @@ class Uniform(Distribution):
         """
         low = self.low if low is None else low
         high = self.high if high is None else high
-        ones = self.fill(self.dtype, self.shape(value), 1.0)
-        prob = ones / (high - low)
+        neg_ones = self.fill(self.dtype, self.shape(value), -1.0)
+        prob = self.exp(neg_ones * self.log(high - low))
         broadcast_shape = self.shape(prob)
         zeros = self.fill(self.dtypeop(prob), broadcast_shape, 0.0)
         comp_lo = self.less(value, low)
diff --git a/tests/ut/python/nn/distribution/test_bernoulli.py b/tests/ut/python/nn/distribution/test_bernoulli.py
index cecf563219..e04438f0a9 100644
--- a/tests/ut/python/nn/distribution/test_bernoulli.py
+++ b/tests/ut/python/nn/distribution/test_bernoulli.py
@@ -28,7 +28,7 @@ def test_arguments():
     """
     b = msd.Bernoulli()
     assert isinstance(b, msd.Distribution)
-    b = msd.Bernoulli([0.0, 0.3, 0.5, 1.0], dtype=dtype.int32)
+    b = msd.Bernoulli([0.1, 0.3, 0.5, 0.9], dtype=dtype.int32)
     assert isinstance(b, msd.Distribution)
 
 def test_type():
@@ -51,6 +51,10 @@ def test_prob():
         msd.Bernoulli([-0.1], dtype=dtype.int32)
     with pytest.raises(ValueError):
         msd.Bernoulli([1.1], dtype=dtype.int32)
+    with pytest.raises(ValueError):
+        msd.Bernoulli([0.0], dtype=dtype.int32)
+    with pytest.raises(ValueError):
+        msd.Bernoulli([1.0], dtype=dtype.int32)
 
 class BernoulliProb(nn.Cell):
     """
diff --git a/tests/ut/python/nn/distribution/test_geometric.py b/tests/ut/python/nn/distribution/test_geometric.py
index 11c12f62dc..4685adaa42 100644
--- a/tests/ut/python/nn/distribution/test_geometric.py
+++ b/tests/ut/python/nn/distribution/test_geometric.py
@@ -29,7 +29,7 @@ def test_arguments():
     """
     g = msd.Geometric()
     assert isinstance(g, msd.Distribution)
-    g = msd.Geometric([0.0, 0.3, 0.5, 1.0], dtype=dtype.int32)
+    g = msd.Geometric([0.1, 0.3, 0.5, 0.9], dtype=dtype.int32)
     assert isinstance(g, msd.Distribution)
 
 def test_type():
@@ -52,6 +52,10 @@ def test_prob():
         msd.Geometric([-0.1], dtype=dtype.int32)
     with pytest.raises(ValueError):
         msd.Geometric([1.1], dtype=dtype.int32)
+    with pytest.raises(ValueError):
+        msd.Geometric([0.0], dtype=dtype.int32)
+    with pytest.raises(ValueError):
+        msd.Geometric([1.0], dtype=dtype.int32)
 
 class GeometricProb(nn.Cell):
     """
diff --git a/tests/ut/python/nn/distribution/test_normal.py b/tests/ut/python/nn/distribution/test_normal.py
index 76602bde80..d7ca2f4954 100644
--- a/tests/ut/python/nn/distribution/test_normal.py
+++ b/tests/ut/python/nn/distribution/test_normal.py
@@ -42,6 +42,12 @@ def test_seed():
     with pytest.raises(TypeError):
         msd.Normal(0., 1., seed='seed')
 
+def test_sd():
+    with pytest.raises(ValueError):
+        msd.Normal(0., 0.)
+    with pytest.raises(ValueError):
+        msd.Normal(0., -1.)
+
 def test_arguments():
     """
     args passing during initialization.