diff --git a/src/metatensor/models/cli/eval.py b/src/metatensor/models/cli/eval.py
index 90f43dc81..f9a46ea13 100644
--- a/src/metatensor/models/cli/eval.py
+++ b/src/metatensor/models/cli/eval.py
@@ -67,6 +67,9 @@ def _add_eval_model_parser(subparser: argparse._SubParsersAction) -> None:
 
 def _eval_targets(model, dataset: Union[Dataset, torch.utils.data.Subset]) -> None:
     """Evaluate an exported model on a dataset and print the RMSEs for each target."""
+    if len(dataset) == 0:
+        logger.info("This dataset is empty. No evaluation will be performed.")
+        return
     # Attach neighbor lists to the systems:
     requested_neighbor_lists = model.requested_neighbors_lists()
     # working around https://github.com/lab-cosmo/metatensor/issues/521
diff --git a/src/metatensor/models/cli/train.py b/src/metatensor/models/cli/train.py
index c38a62d4b..1b2875fd5 100644
--- a/src/metatensor/models/cli/train.py
+++ b/src/metatensor/models/cli/train.py
@@ -255,7 +255,10 @@ def _train_model_hydra(options: DictConfig) -> None:
         train_size -= test_size
 
         if test_size < 0 or test_size >= 1:
-            raise ValueError("Test set split must be between 0 and 1.")
+            raise ValueError(
+                "Test set split must be greater "
+                "than (or equal to) 0 and lesser than 1."
+            )
 
         generator = torch.Generator()
         if options["seed"] is not None:
@@ -304,8 +307,10 @@ def _train_model_hydra(options: DictConfig) -> None:
         validation_size = validation_options
         train_size -= validation_size
 
-        if validation_size < 0 or validation_size >= 1:
-            raise ValueError("Validation set split must be between 0 and 1.")
+        if validation_size <= 0 or validation_size >= 1:
+            raise ValueError(
+                "Validation set split must be greater " "than 0 and lesser than 1."
+            )
 
         generator = torch.Generator()
         if options["seed"] is not None:
diff --git a/tests/cli/test_train_model.py b/tests/cli/test_train_model.py
index f23b8c31e..342a6d4b7 100644
--- a/tests/cli/test_train_model.py
+++ b/tests/cli/test_train_model.py
@@ -135,6 +135,51 @@ def test_train_multiple_datasets(monkeypatch, tmp_path, options):
     train_model(options)
 
 
+def test_empty_training_set(monkeypatch, tmp_path, options):
+    """Test that an error is raised if no training set is provided."""
+    monkeypatch.chdir(tmp_path)
+
+    shutil.copy(DATASET_PATH, "qm9_reduced_100.xyz")
+
+    options["validation_set"] = 0.6
+    options["test_set"] = 0.4
+
+    with pytest.raises(
+        ValueError, match="Fraction of the train set is smaller or equal to 0!"
+    ):
+        train_model(options)
+
+
+def test_empty_validation_set(monkeypatch, tmp_path, options):
+    """Test that an error is raised if no validation set is provided."""
+    monkeypatch.chdir(tmp_path)
+
+    shutil.copy(DATASET_PATH, "qm9_reduced_100.xyz")
+
+    options["validation_set"] = 0.0
+    options["test_set"] = 0.4
+
+    with pytest.raises(ValueError, match="must be greater than 0"):
+        train_model(options)
+
+
+def test_empty_test_set(monkeypatch, tmp_path, options):
+    """Test that no error is raised if no test set is provided."""
+    monkeypatch.chdir(tmp_path)
+
+    shutil.copy(DATASET_PATH, "qm9_reduced_100.xyz")
+
+    options["validation_set"] = 0.4
+    options["test_set"] = 0.0
+
+    train_model(options)
+
+    # check if the logging is correct
+    with open(glob.glob("outputs/*/*/train.log")[0]) as f:
+        log = f.read()
+    assert "This dataset is empty. No evaluation" in log
+
+
 @pytest.mark.parametrize(
     "test_set_file, validation_set_file", [(True, False), (False, True)]
 )