diff --git a/pina/callback/normalizer_data_callback.py b/pina/callback/normalizer_data_callback.py
index ef957b9..faef8a9 100644
--- a/pina/callback/normalizer_data_callback.py
+++ b/pina/callback/normalizer_data_callback.py
@@ -5,7 +5,6 @@ from lightning.pytorch import Callback
 from ..label_tensor import LabelTensor
 from ..utils import check_consistency, is_function
 from ..condition import InputTargetCondition
-from ..data.dataset import PinaGraphDataset
 
 
 class NormalizerDataCallback(Callback):
@@ -122,7 +121,10 @@ class NormalizerDataCallback(Callback):
         """
 
         # Ensure datsets are not graph-based
-        if isinstance(trainer.datamodule.train_dataset, PinaGraphDataset):
+        if any(
+            ds.is_graph_dataset
+            for ds in trainer.datamodule.train_dataset.values()
+        ):
             raise NotImplementedError(
                 "NormalizerDataCallback is not compatible with "
                 "graph-based datasets."
@@ -164,8 +166,8 @@ class NormalizerDataCallback(Callback):
         :param dataset: The `~pina.data.dataset.PinaDataset` dataset.
         """
         for cond in conditions:
-            if cond in dataset.conditions_dict:
-                data = dataset.conditions_dict[cond][self.apply_to]
+            if cond in dataset:
+                data = dataset[cond].data[self.apply_to]
                 shift = self.shift_fn(data)
                 scale = self.scale_fn(data)
                 self._normalizer[cond] = {
@@ -197,25 +199,20 @@ class NormalizerDataCallback(Callback):
 
         :param PinaDataset dataset: The dataset to be normalized.
         """
-        # Initialize update dictionary
-        update_dataset_dict = {}
 
         # Iterate over conditions and apply normalization
         for cond, norm_params in self.normalizer.items():
-            points = dataset.conditions_dict[cond][self.apply_to]
+            update_dataset_dict = {}
+            points = dataset[cond].data[self.apply_to]
             scale = norm_params["scale"]
             shift = norm_params["shift"]
             normalized_points = self._norm_fn(points, scale, shift)
-            update_dataset_dict[cond] = {
-                self.apply_to: (
-                    LabelTensor(normalized_points, points.labels)
-                    if isinstance(points, LabelTensor)
-                    else normalized_points
-                )
-            }
-
-        # Update the dataset in-place
-        dataset.update_data(update_dataset_dict)
+            update_dataset_dict[self.apply_to] = (
+                LabelTensor(normalized_points, points.labels)
+                if isinstance(points, LabelTensor)
+                else normalized_points
+            )
+            dataset[cond].data.update(update_dataset_dict)
 
     @property
     def normalizer(self):
diff --git a/pina/callback/refinement/refinement_interface.py b/pina/callback/refinement/refinement_interface.py
index adc6e4e..c8bafa9 100644
--- a/pina/callback/refinement/refinement_interface.py
+++ b/pina/callback/refinement/refinement_interface.py
@@ -133,13 +133,12 @@ class RefinementInterface(Callback, metaclass=ABCMeta):
 
         :param PINNInterface solver: The solver object.
         """
-        new_points = {}
         for name in self._condition_to_update:
-            current_points = self.dataset.conditions_dict[name]["input"]
-            new_points[name] = {
-                "input": self.sample(current_points, name, solver)
-            }
-        self.dataset.update_data(new_points)
+            new_points = {}
+            current_points = self.dataset[name].data["input"]
+            new_points["input"] = self.sample(current_points, name, solver)
+
+            self.dataset[name].update_data(new_points)
 
     def _compute_population_size(self, conditions):
         """
@@ -150,6 +149,5 @@ class RefinementInterface(Callback, metaclass=ABCMeta):
         :rtype: dict
         """
         return {
-            cond: len(self.dataset.conditions_dict[cond]["input"])
-            for cond in conditions
+            cond: len(self.dataset[cond].data["input"]) for cond in conditions
         }