diff --git a/CHANGES.md b/CHANGES.md
index 4ffd2b82d..b81b3eadd 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -20,6 +20,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - The behavior of method `net.get_params` changed to make it more consistent with sklearn: it will no longer return "learned" attributes like `module_`; therefore, functions like `sklearn.base.clone`, when called with a fitted net, will no longer return a fitted net but instead an uninitialized net; if you want a copy of a fitted net, use `copy.deepcopy` instead;`net.get_params` is used under the hood by many sklearn functions and classes, such as `GridSearchCV`, whose behavior may thus be affected by the change. (#521, #527)
 - Raise `FutureWarning` when using `CyclicLR` scheduler, because the default behavior has changed from taking a step every batch to taking a step every epoch. (#626)
 - Set train/validation on criterion if it's a PyTorch module (#621)
+- Don't pass `y=None` to `NeuralNet.train_split` to enable the direct use of split functions without positional `y` in their signatures. This is useful when working with unsupervised data (#605).
 
 ### Fixed
 
diff --git a/skorch/net.py b/skorch/net.py
index aa6c9e1d9..ac82813c9 100644
--- a/skorch/net.py
+++ b/skorch/net.py
@@ -1210,12 +1210,16 @@ def get_split_datasets(self, X, y=None, **fit_params):
 
         """
         dataset = self.get_dataset(X, y)
-        if self.train_split:
-            dataset_train, dataset_valid = self.train_split(
-                dataset, y, **fit_params)
-        else:
-            dataset_train, dataset_valid = dataset, None
-        return dataset_train, dataset_valid
+        if not self.train_split:
+            return dataset, None
+
+        # After a change in (#646),
+        # `y` is no longer passed to `self.train_split` if it is `None`.
+        # To revert to the previous behavior, remove the following two lines:
+        if y is None:
+            return self.train_split(dataset, **fit_params)
+
+        return self.train_split(dataset, y, **fit_params)
 
     def get_iterator(self, dataset, training=False):
         """Get an iterator that allows to loop over the batches of the
diff --git a/skorch/tests/callbacks/test_scoring.py b/skorch/tests/callbacks/test_scoring.py
index 5764f0dd3..ce8959695 100644
--- a/skorch/tests/callbacks/test_scoring.py
+++ b/skorch/tests/callbacks/test_scoring.py
@@ -401,13 +401,16 @@ def __init__(self, X, y):
         class MySkorchDataset(skorch.dataset.Dataset):
             pass
 
-        rawsplit = lambda ds, _: (ds, ds)
+        rawsplit = lambda ds: (ds, ds)
         cvsplit = CVSplit(2, random_state=0)
 
+        def split_ignore_y(ds, y):
+            return rawsplit(ds)
+
         table = [
             # Test a split where type(input) == type(output) is guaranteed
-            (data, rawsplit, np.ndarray, False),
-            (data, rawsplit, skorch.dataset.Dataset, True),
+            (data, split_ignore_y, np.ndarray, False),
+            (data, split_ignore_y, skorch.dataset.Dataset, True),
             ((MyTorchDataset(*data), None), rawsplit, MyTorchDataset, False),
             ((MyTorchDataset(*data), None), rawsplit, MyTorchDataset, True),
             ((MySkorchDataset(*data), None), rawsplit, np.ndarray, False),
diff --git a/skorch/tests/test_net.py b/skorch/tests/test_net.py
index 78ba9741b..6d07ed2ed 100644
--- a/skorch/tests/test_net.py
+++ b/skorch/tests/test_net.py
@@ -2490,6 +2490,48 @@ def initialize_module(self, *args, **kwargs):
         hidden_units = net.mymodule_.state_dict()['sequential.3.weight'].shape[1]
         assert hidden_units == 99
 
+    @pytest.mark.parametrize("needs_y, train_split, raises", [
+        (False, None, ExitStack()),  # ExitStack = does not raise
+        (True, None, ExitStack()),
+        (False, "default", ExitStack()),  # Default parameters for NeuralNet
+        (True, "default", ExitStack()),  # Default parameters for NeuralNet
+        (False, lambda x: (x, x), ExitStack()),  # Earlier this was not allowed
+        (True, lambda x, y: (x, x), ExitStack()),  # Works for custom split
+        (True, lambda x: (x, x), pytest.raises(TypeError)),  # Raises an error
+    ])
+    def test_passes_y_to_train_split_when_not_none(
+            self, needs_y, train_split, raises):
+        from skorch.net import NeuralNet
+        from skorch.toy import MLPModule
+
+        # By default, `train_split=CVSplit(5)` in the `NeuralNet` definition
+        kwargs = {} if train_split == 'default' else {
+            'train_split': train_split}
+
+        # Dummy loss that ignores y_true
+        class UnsupervisedLoss(torch.nn.NLLLoss):
+            def forward(self, y_pred, _):
+                return y_pred.mean()
+
+        # Generate the dummy dataset
+        n_samples, n_features = 128, 10
+        X = np.random.rand(n_samples, n_features).astype(np.float32)
+        y = np.random.binomial(n=1, p=0.5, size=n_samples) if needs_y else None
+
+        # The `NeuralNetClassifier` or `NeuralNetRegressor` always require `y`
+        # Only `NeuralNet` can transfer `y=None` to `train_split` method.
+        net = NeuralNet(
+            MLPModule,  # Any model, it's not important here
+            module__input_units=n_features,
+            max_epochs=2,  # Run train loop twice to detect possible errors
+            criterion=UnsupervisedLoss,
+            **kwargs,
+        )
+
+        # Check if the code should fail or not
+        with raises:
+            net.fit(X, y)
+
 
 class TestNetSparseInput:
     @pytest.fixture(scope='module')
diff --git a/skorch/utils.py b/skorch/utils.py
index e37d6de6a..1624a90d5 100644
--- a/skorch/utils.py
+++ b/skorch/utils.py
@@ -475,7 +475,7 @@ def get_step(self):
         return self.step
 
 
-def _make_split(X, y, valid_ds, **kwargs):
+def _make_split(X, valid_ds, **kwargs):
     """Used by ``predefined_split`` to allow for pickling"""
     return X, valid_ds