diff --git a/src/accelerate/utils/modeling.py b/src/accelerate/utils/modeling.py
index 1e6b1c9c6f6..27aeedc5a8d 100644
--- a/src/accelerate/utils/modeling.py
+++ b/src/accelerate/utils/modeling.py
@@ -1540,7 +1540,7 @@ def get_state_dict_offloaded_model(model: nn.Module):
                 placeholders.add(name + f".{key}")
                 continue
             params = module_state_dict[key]
-            state_dict[name + f".{key}"] = params
+            state_dict[name + f".{key}"] = params.to("cpu")  # move buffers to cpu
     for key in placeholders.copy():
         if key in state_dict:
             placeholders.remove(key)
@@ -1923,7 +1923,7 @@ def align_module_device(module: torch.nn.Module, execution_device: Optional[torc
                 module._hf_hook.execution_device = original_device
 
     elif execution_device is not None:
-        devices = {name: param.device for name, param in module.named_parameters()}
+        devices = {name: param.device for name, param in module.named_parameters(recurse=False)}
         try:
             for name in devices:
                 set_module_tensor_to_device(module, name, execution_device)
diff --git a/tests/test_modeling_utils.py b/tests/test_modeling_utils.py
index 41ce475c6de..4d01c7ef514 100644
--- a/tests/test_modeling_utils.py
+++ b/tests/test_modeling_utils.py
@@ -43,6 +43,7 @@
     convert_file_size_to_int,
     find_tied_parameters,
     get_balanced_memory,
+    get_state_dict_offloaded_model,
     infer_auto_device_map,
     load_checkpoint_in_model,
     load_state_dict,
@@ -66,6 +67,15 @@ def forward(self, x):
         return self.linear2(self.batchnorm(self.linear1(x)))
 
 
+class NestedModelForTest(nn.Module):
+    def __init__(self):
+        super().__init__()
+        self.model = ModelForTest()
+
+    def forward(self, x):
+        return self.model(x)
+
+
 class LinearWithNonPersistentBuffers(nn.Module):
     def __init__(self, in_features: int, out_features: int, bias: bool = True, device=None, dtype=None) -> None:
         factory_kwargs = {"device": device, "dtype": dtype}
@@ -788,6 +798,19 @@ def test_convert_file_size(self):
         with self.assertRaises(ValueError):
             convert_file_size_to_int("-1GB")
 
+    def test_get_state_dict_offloaded_model(self):
+        for model_cls in (ModelForTest, NestedModelForTest):
+            model = model_cls()
+            execution_device = torch.device(torch_device)
+            original_state_dict = model.state_dict()
+
+            cpu_offload(model, execution_device=execution_device)
+            state_dict = get_state_dict_offloaded_model(model)
+
+            assert original_state_dict.keys() == state_dict.keys()
+            for key in original_state_dict:
+                assert torch.equal(original_state_dict[key], state_dict[key])
+
     def test_align_module_device_simple(self):
         model = ModelForTest()
         execution_device = torch.device(torch_device)
@@ -834,3 +857,13 @@ def test_align_module_device_offloaded(self):
         assert model.linear1.weight.device == offload_device
         assert model.batchnorm.weight.device == offload_device
         assert model.linear2.weight.device == offload_device
+
+    def test_align_module_device_offloaded_nested(self):
+        model = NestedModelForTest()
+        execution_device = torch.device(torch_device)
+        align_device = torch.device("cpu")
+        cpu_offload(model, execution_device=execution_device)
+        for module in model.modules():
+            with align_module_device(module, align_device):
+                for param in model.parameters(recurse=False):
+                    assert param.device == align_device