diff --git a/doc/whats_new/v0.23.rst b/doc/whats_new/v0.23.rst
index 05097a4fa9516..e3bce16e96ae2 100644
--- a/doc/whats_new/v0.23.rst
+++ b/doc/whats_new/v0.23.rst
@@ -169,7 +169,7 @@ Changelog
   deprecated. It has no effect. :pr:`11950` by
   :user:`Jeremie du Boisberranger <jeremiedbb>`.
 
-- |API| The ``random_state`` parameter has been added to 
+- |API| The ``random_state`` parameter has been added to
   :class:`cluster.AffinityPropagation`. :pr:`16801` by :user:`rcwoolston`
   and :user:`Chiara Marmo <cmarmo>`.
 
diff --git a/doc/whats_new/v0.24.rst b/doc/whats_new/v0.24.rst
index 00557179ac38b..3cebba4182b1d 100644
--- a/doc/whats_new/v0.24.rst
+++ b/doc/whats_new/v0.24.rst
@@ -166,6 +166,10 @@ Changelog
   :pr:`17603`, :pr:`17604`, :pr:`17606`, :pr:`17608`, :pr:`17609`, :pr:`17633`
   by :user:`Alex Henrie <alexhenrie>`.
 
+- |Enhancement| Avoid converting float32 input to float64 in
+  :class:`neural_network.BernoulliRBM`.
+  :pr:`16352` by :user:`Arthur Imbert <Henley13>`.  
+
 :mod:`sklearn.preprocessing`
 ............................
 
diff --git a/sklearn/neural_network/_rbm.py b/sklearn/neural_network/_rbm.py
index fcb4e90772598..5a41ad01c696c 100644
--- a/sklearn/neural_network/_rbm.py
+++ b/sklearn/neural_network/_rbm.py
@@ -131,7 +131,7 @@ def transform(self, X):
         """
         check_is_fitted(self)
 
-        X = check_array(X, accept_sparse='csr', dtype=np.float64)
+        X = check_array(X, accept_sparse='csr', dtype=(np.float64, np.float32))
         return self._mean_hiddens(X)
 
     def _mean_hiddens(self, v):
@@ -344,16 +344,20 @@ def fit(self, X, y=None):
         self : BernoulliRBM
             The fitted model.
         """
-        X = self._validate_data(X, accept_sparse='csr', dtype=np.float64)
+        X = self._validate_data(
+            X, accept_sparse='csr', dtype=(np.float64, np.float32)
+        )
         n_samples = X.shape[0]
         rng = check_random_state(self.random_state)
 
         self.components_ = np.asarray(
             rng.normal(0, 0.01, (self.n_components, X.shape[1])),
-            order='F')
-        self.intercept_hidden_ = np.zeros(self.n_components, )
-        self.intercept_visible_ = np.zeros(X.shape[1], )
-        self.h_samples_ = np.zeros((self.batch_size, self.n_components))
+            order='F',
+            dtype=X.dtype)
+        self.intercept_hidden_ = np.zeros(self.n_components, dtype=X.dtype)
+        self.intercept_visible_ = np.zeros(X.shape[1], dtype=X.dtype)
+        self.h_samples_ = np.zeros((self.batch_size, self.n_components),
+                                   dtype=X.dtype)
 
         n_batches = int(np.ceil(float(n_samples) / self.batch_size))
         batch_slices = list(gen_even_slices(n_batches * self.batch_size,
diff --git a/sklearn/neural_network/tests/test_rbm.py b/sklearn/neural_network/tests/test_rbm.py
index e319e0e4f3428..22d3b1c75fb01 100644
--- a/sklearn/neural_network/tests/test_rbm.py
+++ b/sklearn/neural_network/tests/test_rbm.py
@@ -1,9 +1,11 @@
 import sys
 import re
+import pytest
 
 import numpy as np
 from scipy.sparse import csc_matrix, csr_matrix, lil_matrix
-from sklearn.utils._testing import (assert_almost_equal, assert_array_equal)
+from sklearn.utils._testing import (assert_almost_equal, assert_array_equal,
+                                    assert_allclose)
 
 from sklearn.datasets import load_digits
 from io import StringIO
@@ -189,3 +191,43 @@ def test_sparse_and_verbose():
                         r" time = (\d|\.)+s", s)
     finally:
         sys.stdout = old_stdout
+
+
+@pytest.mark.parametrize("dtype_in, dtype_out", [
+    (np.float32, np.float32),
+    (np.float64, np.float64),
+    (np.int, np.float64)])
+def test_transformer_dtypes_casting(dtype_in, dtype_out):
+    X = Xdigits[:100].astype(dtype_in)
+    rbm = BernoulliRBM(n_components=16, batch_size=5, n_iter=5,
+                       random_state=42)
+    Xt = rbm.fit_transform(X)
+
+    # dtype_in and dtype_out should be consistent
+    assert Xt.dtype == dtype_out, ('transform dtype: {} - original dtype: {}'
+                                   .format(Xt.dtype, X.dtype))
+
+
+def test_convergence_dtype_consistency():
+    # float 64 transformer
+    X_64 = Xdigits[:100].astype(np.float64)
+    rbm_64 = BernoulliRBM(n_components=16, batch_size=5, n_iter=5,
+                          random_state=42)
+    Xt_64 = rbm_64.fit_transform(X_64)
+
+    # float 32 transformer
+    X_32 = Xdigits[:100].astype(np.float32)
+    rbm_32 = BernoulliRBM(n_components=16, batch_size=5, n_iter=5,
+                          random_state=42)
+    Xt_32 = rbm_32.fit_transform(X_32)
+
+    # results and attributes should be close enough in 32 bit and 64 bit
+    assert_allclose(Xt_64, Xt_32,
+                    rtol=1e-06, atol=0)
+    assert_allclose(rbm_64.intercept_hidden_, rbm_32.intercept_hidden_,
+                    rtol=1e-06, atol=0)
+    assert_allclose(rbm_64.intercept_visible_, rbm_32.intercept_visible_,
+                    rtol=1e-05, atol=0)
+    assert_allclose(rbm_64.components_, rbm_32.components_,
+                    rtol=1e-03, atol=0)
+    assert_allclose(rbm_64.h_samples_, rbm_32.h_samples_)