diff --git a/tests/models/albert/test_modeling_albert.py b/tests/models/albert/test_modeling_albert.py
index 823315bc6785..684a7d62c8cd 100644
--- a/tests/models/albert/test_modeling_albert.py
+++ b/tests/models/albert/test_modeling_albert.py
@@ -326,6 +326,12 @@ def test_model_from_pretrained(self):
             model = AlbertModel.from_pretrained(model_name)
             self.assertIsNotNone(model)
 
+    @unittest.skip(
+        reason="Does not currently support low_cpu_mem_usage - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 @require_torch
 class AlbertModelIntegrationTest(unittest.TestCase):
diff --git a/tests/models/deberta/test_modeling_deberta.py b/tests/models/deberta/test_modeling_deberta.py
index 52758e2222ae..8a5044719abd 100644
--- a/tests/models/deberta/test_modeling_deberta.py
+++ b/tests/models/deberta/test_modeling_deberta.py
@@ -278,6 +278,12 @@ def test_model_from_pretrained(self):
             model = DebertaModel.from_pretrained(model_name)
             self.assertIsNotNone(model)
 
+    @unittest.skip(
+        reason="Does not currently support low_cpu_mem_usage - 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/deberta_v2/test_modeling_deberta_v2.py b/tests/models/deberta_v2/test_modeling_deberta_v2.py
index abfbe7402c93..151c2690b372 100644
--- a/tests/models/deberta_v2/test_modeling_deberta_v2.py
+++ b/tests/models/deberta_v2/test_modeling_deberta_v2.py
@@ -296,6 +296,12 @@ def test_model_from_pretrained(self):
             model = DebertaV2Model.from_pretrained(model_name)
             self.assertIsNotNone(model)
 
+    @unittest.skip(
+        reason="Does not currently support low_cpu_mem_usage - 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/encodec/test_modeling_encodec.py b/tests/models/encodec/test_modeling_encodec.py
index 8f1b06da06c8..c8bd25ce28be 100644
--- a/tests/models/encodec/test_modeling_encodec.py
+++ b/tests/models/encodec/test_modeling_encodec.py
@@ -420,6 +420,12 @@ def test_identity_shortcut(self):
         config.use_conv_shortcut = False
         self.model_tester.create_and_check_model_forward(config, inputs_dict)
 
+    @unittest.skip(
+        reason="Does not currently support low_cpu_mem_usage - TypeError: _weight_norm_interface() missing 1 required positional argument: 'dim'"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 def normalize(arr):
     norm = np.linalg.norm(arr)
diff --git a/tests/models/flava/test_modeling_flava.py b/tests/models/flava/test_modeling_flava.py
index 48a070d9fe31..e0ff3bad3fdc 100644
--- a/tests/models/flava/test_modeling_flava.py
+++ b/tests/models/flava/test_modeling_flava.py
@@ -1256,6 +1256,12 @@ def test_training_gradient_checkpointing_use_reentrant(self):
     def test_training_gradient_checkpointing_use_reentrant_false(self):
         pass
 
+    @unittest.skip(
+        reason="Does not currently support low_cpu_mem_usage - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 # We will verify our results on an image of cute cats
 def prepare_img():
diff --git a/tests/models/fnet/test_modeling_fnet.py b/tests/models/fnet/test_modeling_fnet.py
index 83b84edddccd..948e218b3139 100644
--- a/tests/models/fnet/test_modeling_fnet.py
+++ b/tests/models/fnet/test_modeling_fnet.py
@@ -468,6 +468,12 @@ def test_model_from_pretrained(self):
             model = FNetModel.from_pretrained(model_name)
             self.assertIsNotNone(model)
 
+    @unittest.skip(
+        reason="Does not currently support low_cpu_mem_usage - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 @require_torch
 class FNetModelIntegrationTest(unittest.TestCase):
diff --git a/tests/models/ibert/test_modeling_ibert.py b/tests/models/ibert/test_modeling_ibert.py
index b552cb75a5a6..63847ac14510 100644
--- a/tests/models/ibert/test_modeling_ibert.py
+++ b/tests/models/ibert/test_modeling_ibert.py
@@ -380,8 +380,14 @@ def test_inputs_embeds(self):
                 inputs["inputs_embeds"] = wte(encoder_input_ids)
                 inputs["decoder_inputs_embeds"] = wte(decoder_input_ids)
 
-            with torch.no_grad():
-                model(**inputs)[0]
+        with torch.no_grad():
+            model(**inputs)[0]
+
+    @unittest.skip(
+        reason="Does not currently support low_cpu_mem_usage - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
 
 
 @require_torch
diff --git a/tests/models/lxmert/test_modeling_lxmert.py b/tests/models/lxmert/test_modeling_lxmert.py
index 63d83de36b75..9ca12cd5386c 100644
--- a/tests/models/lxmert/test_modeling_lxmert.py
+++ b/tests/models/lxmert/test_modeling_lxmert.py
@@ -767,6 +767,12 @@ def prepare_tf_inputs_from_pt_inputs(self, pt_inputs_dict):
 
         return tf_inputs_dict
 
+    @unittest.skip(
+        reason="Does not currently support low_cpu_mem_usage - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 @require_torch
 class LxmertModelIntegrationTest(unittest.TestCase):
diff --git a/tests/models/mobilebert/test_modeling_mobilebert.py b/tests/models/mobilebert/test_modeling_mobilebert.py
index e4ebca4b6e5b..2885c7cce293 100644
--- a/tests/models/mobilebert/test_modeling_mobilebert.py
+++ b/tests/models/mobilebert/test_modeling_mobilebert.py
@@ -341,6 +341,12 @@ def test_for_token_classification(self):
         config_and_inputs = self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_mobilebert_for_token_classification(*config_and_inputs)
 
+    @unittest.skip(
+        reason="Does not currently support low_cpu_mem_usage - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 def _long_tensor(tok_lst):
     return torch.tensor(
diff --git a/tests/models/realm/test_modeling_realm.py b/tests/models/realm/test_modeling_realm.py
index 4d6d9fd0ff11..2b3c23c599e7 100644
--- a/tests/models/realm/test_modeling_realm.py
+++ b/tests/models/realm/test_modeling_realm.py
@@ -441,6 +441,12 @@ def test_scorer_from_pretrained(self):
         model = RealmScorer.from_pretrained("google/realm-cc-news-pretrained-scorer")
         self.assertIsNotNone(model)
 
+    @unittest.skip(
+        reason="Does not currently support low_cpu_mem_usage - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 @require_torch
 class RealmModelIntegrationTest(unittest.TestCase):
diff --git a/tests/models/roformer/test_modeling_roformer.py b/tests/models/roformer/test_modeling_roformer.py
index 6c130ae1746c..6b61cd9280c9 100644
--- a/tests/models/roformer/test_modeling_roformer.py
+++ b/tests/models/roformer/test_modeling_roformer.py
@@ -504,6 +504,12 @@ def test_training_gradient_checkpointing_use_reentrant(self):
     def test_training_gradient_checkpointing_use_reentrant_false(self):
         pass
 
+    @unittest.skip(
+        reason="Does not currently support low_cpu_mem_usage - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 @require_torch
 class RoFormerModelIntegrationTest(unittest.TestCase):
diff --git a/tests/models/squeezebert/test_modeling_squeezebert.py b/tests/models/squeezebert/test_modeling_squeezebert.py
index bf86792f57f1..4690af405f8f 100644
--- a/tests/models/squeezebert/test_modeling_squeezebert.py
+++ b/tests/models/squeezebert/test_modeling_squeezebert.py
@@ -281,6 +281,12 @@ def test_model_from_pretrained(self):
             model = SqueezeBertModel.from_pretrained(model_name)
             self.assertIsNotNone(model)
 
+    @unittest.skip(
+        reason="Does not currently support low_cpu_mem_usage - NotImplementedError: Cannot copy out of meta tensor; no data!"
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass
+
 
 @require_sentencepiece
 @require_tokenizers
diff --git a/tests/models/timm_backbone/test_modeling_timm_backbone.py b/tests/models/timm_backbone/test_modeling_timm_backbone.py
index 60ab9e2a217e..c0e4e723df3c 100644
--- a/tests/models/timm_backbone/test_modeling_timm_backbone.py
+++ b/tests/models/timm_backbone/test_modeling_timm_backbone.py
@@ -273,3 +273,9 @@ def test_create_from_modified_config(self):
             model.to(torch_device)
             model.eval()
             result = model(**inputs_dict)
+
+    @unittest.skip(
+        reason="Does not support low_cpu_mem_usage - weights are loaded from timm and not from transformers checkpoint."
+    )
+    def test_save_load_low_cpu_mem_usage(self):
+        pass