diff --git a/tests/models/gemma/test_modeling_gemma.py b/tests/models/gemma/test_modeling_gemma.py
index 6385e4cbf5..1b32f1b16e 100644
--- a/tests/models/gemma/test_modeling_gemma.py
+++ b/tests/models/gemma/test_modeling_gemma.py
@@ -298,6 +298,10 @@ class GemmaModelTest(ModelTesterMixin, GenerationTesterMixin, PipelineTesterMixi
     test_headmasking = False
     test_pruning = False
 
+    # Need to remove 0.9 in `test_cpu_offload`
+    # This is because we are hitting edge cases with the causal_mask buffer
+    model_split_percents = [0.5, 0.6]
+
     # TODO (ydshieh): Check this. See https://app.circleci.com/pipelines/github/huggingface/transformers/79245/workflows/9490ef58-79c2-410d-8f51-e3495156cf9c/jobs/1012146
     def is_pipeline_test_to_skip(
         self, pipeline_test_casse_name, config_class, model_architecture, tokenizer_name, processor_name
diff --git a/tests/models/llama/test_modeling_llama.py b/tests/models/llama/test_modeling_llama.py
index 02c649c39a..9c5eccd2d2 100644
--- a/tests/models/llama/test_modeling_llama.py
+++ b/tests/models/llama/test_modeling_llama.py
@@ -302,6 +302,10 @@ class LlamaModelTest(ModelTesterMixin, GenerationTesterMixin, PipelineTesterMixi
     test_pruning = False
     fx_compatible = True
 
+    # Need to use `0.8` instead of `0.9` for `test_cpu_offload`
+    # This is because we are hitting edge cases with the causal_mask buffer
+    model_split_percents = [0.5, 0.7, 0.8]
+
     def setUp(self):
         self.model_tester = LlamaModelTester(self)
         self.config_tester = ConfigTester(self, config_class=LlamaConfig, hidden_size=37)