diff --git a/deepspeed/__init__.py b/deepspeed/__init__.py
index 6bc5642ec8ef..eb245b9492c3 100755
--- a/deepspeed/__init__.py
+++ b/deepspeed/__init__.py
@@ -68,10 +68,10 @@ def _parse_version(version_str):
 
 def _mark_initialized(trainobj: Union[torch.nn.Module, Optimizer, _LRScheduler]):
     """Mark a trainobj as initialized by setting the ds_is_inited attribute to True."""
-    # we shouldn't hit the assert below, but just in case
-    assert not hasattr(
-        trainobj, 'ds_is_inited'
-    ), "Model has already been initialized, please make sure to only call deepspeed.initialize on a model once."
+    if hasattr(trainobj, 'ds_is_inited'):
+        assert trainobj.ds_is_inited, "Not expecting the training object has `ds_is_inited` to be False if it exists, make sure you didn't set it to False or called deepspeed.initialize on the model more than once."
+        return
+
     trainobj.ds_is_inited = True
 
 
@@ -79,7 +79,7 @@ def _is_initialized(trainobj: Union[torch.nn.Module, Optimizer, _LRScheduler]):
     """Check if a trainobj has been initialized by checking the ds_is_inited attribute."""
     if hasattr(trainobj, 'ds_is_inited'):
         # we shouldn't hit the assert below, but just in case
-        assert trainobj.ds_is_inited, "Not expecting the model has `ds_is_inited` to be False if it exists, make sure you didn't set it to False or called deepspeed.initialize on the model more than once."
+        assert trainobj.ds_is_inited, "Not expecting the training object has `ds_is_inited` to be False if it exists, make sure you didn't set it to False or called deepspeed.initialize on the model more than once."
         return True
     return False
 
diff --git a/tests/unit/runtime/test_ds_initialize.py b/tests/unit/runtime/test_ds_initialize.py
index 2c9ad701bfff..0da24dc2ba32 100644
--- a/tests/unit/runtime/test_ds_initialize.py
+++ b/tests/unit/runtime/test_ds_initialize.py
@@ -445,17 +445,14 @@ def test_no_repeated_init(self):
         hidden_dim = 10
         model = SimpleModel(hidden_dim)
         client_optimizer = torch.optim.Adam(model.parameters(), lr=0.01)
-
-        model = SimpleModel()
         # Initialize DeepSpeed configurations for fp16
         config_dict = {'train_batch_size': 1}
 
-        client_optimizer = torch.optim.Adam(filter(lambda p: p.requires_grad, model.parameters()), lr=1e-3)
         # Initialize DeepSpeed engine
         _assert_trainobjs_not_inited(model=model, optimizer=client_optimizer, lr_scheduler=None)
-        model_engine, optim, dataloader, scheduler = deepspeed.initialize(model=model,
-                                                                          optimizer=client_optimizer,
-                                                                          config_params=config_dict)
+        model_engine, optim, _, _ = deepspeed.initialize(model=model,
+                                                         optimizer=client_optimizer,
+                                                         config_params=config_dict)
 
         # arguments should be marked as initialized now
         assert _is_initialized(model), "Client model should be marked as initialized"
@@ -464,7 +461,6 @@ def test_no_repeated_init(self):
         # return values should also be marked as initialized
         assert _is_initialized(model_engine), "Model engine should be marked as initialized"
         assert _is_initialized(optim), "Optimizer should be marked as initialized"
-        assert _is_initialized(scheduler), "Scheduler should be marked as initialized"
 
         exception_raised = False
         try:
@@ -473,3 +469,26 @@ def test_no_repeated_init(self):
             exception_raised = True
 
         assert exception_raised, "Repeated initialization should raise an exception"
+
+        exception_raised = False
+        try:
+            deepspeed.initialize(model=model_engine, optimizer=client_optimizer, config_params=config_dict)
+        except ValueError:
+            exception_raised = True
+
+        assert exception_raised, "Initialization on ds types should raise an exception"
+
+        exception_raised = False
+        try:
+            deepspeed.initialize(model=model, optimizer=client_optimizer, config_params=config_dict)
+        except ValueError:
+            exception_raised = True
+
+        assert exception_raised, "Initialization on ds types should raise an exception"
+
+        exception_raised = False
+        try:
+            deepspeed.initialize(model=model_engine, optimizer=client_optimizer, config_params=config_dict)
+        except ValueError:
+            exception_raised = True
+        assert exception_raised, "Initialization on ds types should raise an exception"