diff --git a/HISTORY.md b/HISTORY.md
index fcb7568255..ef5bf1d95f 100644
--- a/HISTORY.md
+++ b/HISTORY.md
@@ -33,6 +33,8 @@
 
 ### mlpack 3.3.0
 ###### 2020-04-07
+  * Added `Normal Distribution` to `ann/dists` (#2382).
+
   * Templated return type of `Forward function` of loss functions (#2339).
 
   * Added `R2 Score` regression metric (#2323).
diff --git a/src/mlpack/methods/ann/dists/CMakeLists.txt b/src/mlpack/methods/ann/dists/CMakeLists.txt
index eea77c413c..fadec3c3c1 100644
--- a/src/mlpack/methods/ann/dists/CMakeLists.txt
+++ b/src/mlpack/methods/ann/dists/CMakeLists.txt
@@ -3,6 +3,8 @@
 set(SOURCES
   bernoulli_distribution.hpp
   bernoulli_distribution_impl.hpp
+  normal_distribution.hpp
+  normal_distribution_impl.hpp
 )
 
 # Add directory name to sources.
diff --git a/src/mlpack/methods/ann/dists/normal_distribution.hpp b/src/mlpack/methods/ann/dists/normal_distribution.hpp
new file mode 100644
index 0000000000..8f9844fd49
--- /dev/null
+++ b/src/mlpack/methods/ann/dists/normal_distribution.hpp
@@ -0,0 +1,145 @@
+/**
+ * @file normal_distribution.hpp
+ * @author xiaohong ji
+ * @author Nishant Kumar
+ *
+ * Definition of the Normal distribution class.
+ *
+ * mlpack is free software; you may redistribute it and/or modify it under the
+ * terms of the 3-clause BSD license.  You should have received a copy of the
+ * 3-clause BSD license along with mlpack.  If not, see
+ * http://www.opensource.org/licenses/BSD-3-Clause for more information.
+ */
+#ifndef MLPACK_METHODS_ANN_DISTRIBUTIONS_NORMAL_DISTRIBUTION_HPP
+#define MLPACK_METHODS_ANN_DISTRIBUTIONS_NORMAL_DISTRIBUTION_HPP
+
+#include <mlpack/prereqs.hpp>
+#include "../activation_functions/logistic_function.hpp"
+
+namespace mlpack {
+namespace ann /** Artificial Neural Network. */ {
+
+/**
+ * Implementation of the Normal Distribution function.
+ *
+ * Normal distribution is a function which accepts a mean and a standard deviation
+ * term and creates a probablity distribution out of it.
+ * 
+ * @tparam DataType Type of the input data. (arma::colvec, arma::mat,
+ *         arma::sp_mat or arma::cube).
+ */
+template <typename DataType = arma::mat>
+class NormalDistribution
+{
+ public:
+  /**
+   * Default constructor, which creates a Normal distribution with zero
+   * dimension.
+   */
+  NormalDistribution();
+
+  /**
+   * Create a Normal distribution with the given mean and sigma.
+   *
+   * @param mean The mean of the normal distribution.
+   * @param sigma The standard deviation of the normal distribution.
+   */
+  NormalDistribution(const DataType& mean, const DataType& sigma);
+
+  /**
+   * Return the probabilities of the given matrix of observations.
+   *
+   * @param observation The observation matrix.
+   */
+  DataType Probability(const DataType& observation) const
+  {
+    return arma::exp(LogProbability(observation));
+  }
+
+  /**
+   * Return the log probabilities of the given matrix of observations.
+   *
+   * @param observation The observation matrix.
+   */
+  DataType LogProbability(const DataType& observation) const;
+
+  /**
+   * Stores the gradient of the probabilities of the observations
+   * with respect to mean and standard deviation.
+   *
+   * @param observation The observation matrix.
+   * @param dmu The gradient with respect to mean.
+   * @param dsigma The gradient with respect to the standard deviation.
+   */
+  void ProbBackward(const DataType& observation,
+                    DataType& dmu,
+                    DataType& dsigma) const;
+
+  /**
+   * Calculates the normal probability density function for each
+   * data point (column) in the given matrix.
+   *
+   * @param x The observation matrix.
+   * @param probabilities Output probabilities for each input observation.
+   */
+  void Probability(const DataType& x, DataType& probabilities) const
+  {
+    probabilities = Probability(x);
+  }
+
+  /**
+    * Calculates the log of normal probability density function for each
+    * data point (column) in the given matrix.
+    *
+    * @param x The observation matrix.
+    * @param probabilities Output log probabilities for each input observation.
+    */
+  void LogProbability(const DataType& x, DataType& probabilities) const
+  {
+    probabilities = LogProbability(x);
+  }
+
+  /**
+   * Return a randomly generated observation according to the probability
+   * distribution defined by this object.
+   *
+   * @return Random observation from this Normal distribution.
+   */
+  DataType Sample() const;
+
+  //! Get the mean.
+  const DataType& Mean() const { return mean; }
+
+  //! Modify the mean.
+  DataType& Mean() { return mean; }
+
+  //! Get the standard deviation.
+  const DataType& StandardDeviation() const { return sigma; }
+
+  //! Modify the standard deviation.
+  DataType& StandardDeviation() { return sigma; }
+
+  //! Return the dimensionality of this distribution.
+  size_t Dimensionality() const { return mean.n_elem; }
+
+  /**
+   * Serialize the distribution.
+   */
+  template<typename Archive>
+  void serialize(Archive& ar, const unsigned int /* version */);
+
+ private:
+  //! Mean of the distribution.
+  DataType mean;
+
+  //! Standard deviation of the distribution.
+  DataType sigma;
+}; // class NormalDistribution
+
+} // namespace ann
+} // namespace mlpack
+
+// Include implementation.
+#include "normal_distribution_impl.hpp"
+
+#endif
diff --git a/src/mlpack/methods/ann/dists/normal_distribution_impl.hpp b/src/mlpack/methods/ann/dists/normal_distribution_impl.hpp
new file mode 100644
index 0000000000..4212f30b70
--- /dev/null
+++ b/src/mlpack/methods/ann/dists/normal_distribution_impl.hpp
@@ -0,0 +1,78 @@
+/**
+ * @file normal_distribution_impl.hpp
+ * @author xiaohong ji
+ * @author Nishant Kumar
+ *
+ * Implementation of the Normal Distribution class.
+ *
+ * mlpack is free software; you may redistribute it and/or modify it under the
+ * terms of the 3-clause BSD license.  You should have received a copy of the
+ * 3-clause BSD license along with mlpack.  If not, see
+ * http://www.opensource.org/licenses/BSD-3-Clause for more information.
+ */
+#ifndef MLPACK_METHODS_ANN_DISTRIBUTIONS_NORMAL_DISTRIBUTION_IMPL_HPP
+#define MLPACK_METHODS_ANN_DISTRIBUTIONS_NORMAL_DISTRIBUTION_IMPL_HPP
+
+// In case it hasn't yet been included.
+#include "normal_distribution.hpp"
+
+namespace mlpack {
+namespace ann /** Artificial Neural Network. */ {
+
+template<typename DataType>
+NormalDistribution<DataType>::NormalDistribution()
+{
+  // Nothing to do here.
+}
+
+template<typename DataType>
+NormalDistribution<DataType>::NormalDistribution(
+    const DataType& mean,
+    const DataType& sigma) :
+    mean(mean),
+    sigma(sigma)
+{
+  // Nothing to do here.
+}
+
+template<typename DataType>
+DataType NormalDistribution<DataType>::Sample() const
+{
+  return sigma * arma::randn<DataType>(mean.n_elem) + mean;
+}
+
+template<typename DataType>
+DataType NormalDistribution<DataType>::LogProbability(
+    const DataType& observation) const
+{
+  const DataType v1 = arma::log(sigma) + std::log(std::sqrt(2 * M_PI));
+  const DataType v2 = arma::square(observation - mean) /
+                      (2 * arma::square(sigma));
+  return  (-v1 - v2);
+}
+
+template<typename DataType>
+void NormalDistribution<DataType>::ProbBackward(
+    const DataType& observation,
+    DataType& dmu,
+    DataType& dsigma) const
+{
+  dmu = (observation - mean) / (arma::square(sigma)) % Probability(observation);
+  dsigma = (- 1.0 / sigma +
+            (arma::square(observation - mean) / arma::pow(sigma, 3)))
+            % Probability(observation);
+}
+
+template<typename DataType>
+template<typename Archive>
+void NormalDistribution<DataType>::serialize(Archive& ar,
+                                             const unsigned int /* version */)
+{
+  ar & BOOST_SERIALIZATION_NVP(mean);
+  ar & BOOST_SERIALIZATION_NVP(sigma);
+}
+
+} // namespace ann
+} // namespace mlpack
+
+#endif
diff --git a/src/mlpack/tests/ann_dist_test.cpp b/src/mlpack/tests/ann_dist_test.cpp
index 6c6dad1371..face8565bd 100644
--- a/src/mlpack/tests/ann_dist_test.cpp
+++ b/src/mlpack/tests/ann_dist_test.cpp
@@ -1,6 +1,7 @@
 /**
  * @file ann_dist_test.cpp
  * @author Atharva Khandait
+ * @author Nishant Kumar
  *
  * Tests the ann distributions.
  *
@@ -12,6 +13,7 @@
 #include <mlpack/core.hpp>
 
 #include <mlpack/methods/ann/dists/bernoulli_distribution.hpp>
+#include <mlpack/methods/ann/dists/normal_distribution.hpp>
 #include <mlpack/methods/ann/init_rules/random_init.hpp>
 
 #include <boost/test/unit_test.hpp>
@@ -127,4 +129,174 @@ BOOST_AUTO_TEST_CASE(JacobianBernoulliDistributionLogisticTest)
   }
 }
 
+/**
+ * Normal Distribution module test.
+ */
+BOOST_AUTO_TEST_CASE(NormalDistributionTest)
+{
+  arma::vec mu = {1.1, 1.2, 1.5, 1.7};
+  arma::vec sigma = {0.1, 0.11, 0.5, 0.23};
+
+  ann::NormalDistribution<> normalDist(mu, sigma);
+
+  arma::vec x = {1.05, 1.1, 1.7, 2.5};
+
+  arma::vec prob;
+  normalDist.LogProbability(x, prob);
+
+  // Testing output of log probability for some random mu, sigma and x.
+  BOOST_REQUIRE_CLOSE(prob[0], 1.2586464, 1e-3);
+  BOOST_REQUIRE_CLOSE(prob[1], 0.8751131, 1e-3);
+  BOOST_REQUIRE_CLOSE(prob[2], -0.30579138, 1e-3);
+  BOOST_REQUIRE_CLOSE(prob[3], -5.498411, 1e-3);
+
+  arma::vec dmu, dsigma;
+  normalDist.ProbBackward(x, dmu, dsigma);
+
+  // Testing output of dmu and dsigma for some random mu, sigma and x.
+  BOOST_REQUIRE_CLOSE(dmu[0], -17.603287, 1e-3);
+  BOOST_REQUIRE_CLOSE(dsigma[0], -26.40487, 1e-3);
+  BOOST_REQUIRE_CLOSE(dmu[1], -19.827663, 1e-3);
+  BOOST_REQUIRE_CLOSE(dsigma[1], -3.7852707, 1e-3);
+  BOOST_REQUIRE_CLOSE(dmu[2], 0.5892323, 1e-3);
+  BOOST_REQUIRE_CLOSE(dsigma[2], -1.2373875, 1e-3);
+  BOOST_REQUIRE_CLOSE(dmu[3], 0.061901994, 1e-3);
+  BOOST_REQUIRE_CLOSE(dsigma[3], 0.19751444, 1e-3);
+}
+
+/**
+ * Jacobian Normal Distribution module test for mean.
+ */
+BOOST_AUTO_TEST_CASE(JacobianNormalDistributionMeanTest)
+{
+  for (size_t i = 0; i < 5; i++)
+  {
+    const size_t targetElements = math::RandInt(2, 1000);
+
+    arma::mat mu;
+    mu.randn(targetElements, 1);
+
+    arma::mat sigma;
+    sigma.randu(targetElements, 1);
+
+    arma::mat x;
+    x.randn(targetElements, 1);
+
+    NormalDistribution<> module(mu, sigma);
+
+    const double perturbation = 1e-6;
+    arma::mat output, outputA, outputB, jacobianA, jacobianB;
+
+    // Initialize the jacobian matrix.
+    module.Probability(x, output);
+    jacobianA = arma::zeros(x.n_elem, output.n_elem);
+
+    for (size_t j = 0; j < x.n_elem; ++j)
+    {
+      double original = module.Mean()(j);
+      module.Mean()(j) = original - perturbation;
+      module.Probability(x, outputA);
+      module.Mean()(j) = original + perturbation;
+      module.Probability(x, outputB);
+      module.Mean()(j) = original;
+
+      outputB -= outputA;
+      outputB /= 2 * perturbation;
+      jacobianA.row(j) = outputB.t();
+    }
+
+    // Initialize the derivative parameter.
+    arma::mat deriv = arma::zeros(output.n_rows, output.n_cols);
+
+    // Share the derivative parameter.
+    arma::mat derivTemp = arma::mat(deriv.memptr(), deriv.n_rows, deriv.n_cols,
+        false, false);
+
+    // Initialize the jacobian matrix.
+    jacobianB = arma::zeros(mu.n_elem, output.n_elem);
+
+    for (size_t k = 0; k < derivTemp.n_elem; ++k)
+    {
+      deriv.zeros();
+      derivTemp(k) = 1;
+
+      arma::mat deltaMu, deltaSigma;
+      module.ProbBackward(x, deltaMu, deltaSigma);
+
+      jacobianB.col(k) = deltaMu % deriv;
+    }
+
+    BOOST_REQUIRE_LE(arma::max(arma::max(arma::abs(jacobianA - jacobianB))),
+        5e-3);
+  }
+}
+
+/**
+ * Jacobian Normal Distribution module test for standard deviation.
+ */
+BOOST_AUTO_TEST_CASE(JacobianNormalDistributionStandardDeviationTest)
+{
+  for (size_t i = 0; i < 5; i++)
+  {
+    const size_t targetElements = math::RandInt(2, 1000);
+
+    arma::mat mu;
+    mu.randn(targetElements, 1);
+
+    arma::mat sigma;
+    sigma.randu(targetElements, 1);
+
+    arma::mat x;
+    x.randn(targetElements, 1);
+
+    NormalDistribution<> module(mu, sigma);
+
+    const double perturbation = 1e-6;
+    arma::mat output, outputA, outputB, jacobianA, jacobianB;
+
+    // Initialize the jacobian matrix.
+    module.Probability(x, output);
+    jacobianA = arma::zeros(x.n_elem, output.n_elem);
+
+    for (size_t j = 0; j < x.n_elem; ++j)
+    {
+      double original = module.StandardDeviation()(j);
+      module.StandardDeviation()(j) = original - perturbation;
+      module.Probability(x, outputA);
+      module.StandardDeviation()(j) = original + perturbation;
+      module.Probability(x, outputB);
+      module.StandardDeviation()(j) = original;
+
+      outputB -= outputA;
+      outputB /= 2 * perturbation;
+      jacobianA.row(j) = outputB.t();
+    }
+
+    // Initialize the derivative parameter.
+    arma::mat deriv = arma::zeros(output.n_rows, output.n_cols);
+
+    // Share the derivative parameter.
+    arma::mat derivTemp = arma::mat(deriv.memptr(), deriv.n_rows, deriv.n_cols,
+        false, false);
+
+    // Initialize the jacobian matrix.
+    jacobianB = arma::zeros(sigma.n_elem, output.n_elem);
+
+    for (size_t k = 0; k < derivTemp.n_elem; ++k)
+    {
+      deriv.zeros();
+      derivTemp(k) = 1;
+
+      arma::mat deltaMu, deltaSigma;
+      module.ProbBackward(x, deltaMu, deltaSigma);
+
+      jacobianB.col(k) = deltaSigma % deriv;
+    }
+
+    BOOST_REQUIRE_LE(arma::max(arma::max(arma::abs(jacobianA - jacobianB))),
+        5e-3);
+  }
+}
+
+
 BOOST_AUTO_TEST_SUITE_END();