diff --git a/tests/models/bert_generation/test_modeling_bert_generation.py b/tests/models/bert_generation/test_modeling_bert_generation.py
index ecd7a459e0ea..4e0e3dc8e1c9 100644
--- a/tests/models/bert_generation/test_modeling_bert_generation.py
+++ b/tests/models/bert_generation/test_modeling_bert_generation.py
@@ -305,6 +305,12 @@ def test_model_from_pretrained(self):
         model = BertGenerationEncoder.from_pretrained("google/bert_for_seq_generation_L-24_bbc_encoder")
         self.assertIsNotNone(model)
 
+    @unittest.skip(
+        "Not currently compatible. Fails with - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 @require_torch
 class BertGenerationEncoderIntegrationTest(unittest.TestCase):
diff --git a/tests/models/fsmt/test_modeling_fsmt.py b/tests/models/fsmt/test_modeling_fsmt.py
index da73b8d41d99..18ee40e471ae 100644
--- a/tests/models/fsmt/test_modeling_fsmt.py
+++ b/tests/models/fsmt/test_modeling_fsmt.py
@@ -329,6 +329,12 @@ def test_tie_model_weights(self):
     def test_resize_embeddings_untied(self):
         pass
 
+    @unittest.skip(
+        "Not currently compatible. Fails with - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 @require_torch
 class FSMTHeadTests(unittest.TestCase):
diff --git a/tests/models/marian/test_modeling_marian.py b/tests/models/marian/test_modeling_marian.py
index 53a67c20459f..e393c7d10325 100644
--- a/tests/models/marian/test_modeling_marian.py
+++ b/tests/models/marian/test_modeling_marian.py
@@ -372,6 +372,12 @@ def test_training_gradient_checkpointing_use_reentrant(self):
     def test_training_gradient_checkpointing_use_reentrant_false(self):
         pass
 
+    @unittest.skip(
+        "Not currently compatible. Fails with - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 def assert_tensors_close(a, b, atol=1e-12, prefix=""):
     """If tensors have different shapes, different values or a and b are not both tensors, raise a nice Assertion error."""
diff --git a/tests/models/musicgen/test_modeling_musicgen.py b/tests/models/musicgen/test_modeling_musicgen.py
index b7952d27a715..284450a00af5 100644
--- a/tests/models/musicgen/test_modeling_musicgen.py
+++ b/tests/models/musicgen/test_modeling_musicgen.py
@@ -1144,6 +1144,10 @@ def test_greedy_generate_stereo_outputs(self):
 
             self.assertNotIn(config.pad_token_id, output_generate)
 
+    @unittest.skip("Fails with - TypeError: _weight_norm_interface() missing 1 required positional argument: 'dim'")
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 def get_bip_bip(bip_duration=0.125, duration=0.5, sample_rate=32000):
     """Produces a series of 'bip bip' sounds at a given frequency."""
diff --git a/tests/models/reformer/test_modeling_reformer.py b/tests/models/reformer/test_modeling_reformer.py
index 11cd7e1a33b4..b1796a6c534d 100644
--- a/tests/models/reformer/test_modeling_reformer.py
+++ b/tests/models/reformer/test_modeling_reformer.py
@@ -687,6 +687,12 @@ def _check_hidden_states_for_generate(
     def test_left_padding_compatibility(self):
         pass
 
+    @unittest.skip(
+        "Not currently compatible. Fails with - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 @require_torch
 class ReformerLSHAttnModelTest(
@@ -848,6 +854,12 @@ def test_past_key_values_format(self):
     def test_left_padding_compatibility(self):
         pass
 
+    @unittest.skip(
+        "Not currently compatible. Fails with - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 @require_torch
 @require_sentencepiece
diff --git a/tests/models/xlm_roberta_xl/test_modeling_xlm_roberta_xl.py b/tests/models/xlm_roberta_xl/test_modeling_xlm_roberta_xl.py
index 828d6a02a6a3..c6513ef79628 100644
--- a/tests/models/xlm_roberta_xl/test_modeling_xlm_roberta_xl.py
+++ b/tests/models/xlm_roberta_xl/test_modeling_xlm_roberta_xl.py
@@ -515,6 +515,12 @@ def test_create_position_ids_from_inputs_embeds(self):
         self.assertEqual(position_ids.shape, expected_positions.shape)
         self.assertTrue(torch.all(torch.eq(position_ids, expected_positions)))
 
+    @unittest.skip(
+        "Not currently compatible. Fails with - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 @require_torch
 class XLMRobertaModelXLIntegrationTest(unittest.TestCase):