diff --git a/src/accelerate/accelerator.py b/src/accelerate/accelerator.py
index 3bb5e81bff9..d3ef525413c 100755
--- a/src/accelerate/accelerator.py
+++ b/src/accelerate/accelerator.py
@@ -97,6 +97,7 @@
     wait_for_everyone,
 )
 from .utils.constants import FSDP_PYTORCH_VERSION
+from .utils.other import is_compiled_module
 
 
 if is_deepspeed_available():
@@ -1221,7 +1222,12 @@ def prepare(self, *args, device_placement=None):
             for obj in args:
                 if isinstance(obj, torch.nn.Module):
                     model_count += 1
-                    is_type_fsdp = type(obj) == FSDP
+                    # if the model is compiled using PyTorch 2.0,
+                    # check that the wrapped model is FSDP or not;
+                    # else check if it is FSDP or not;
+                    is_type_fsdp = isinstance(obj, FSDP) or (
+                        is_compiled_module(obj) and isinstance(obj._orig_mod, FSDP)
+                    )
                 if isinstance(obj, torch.optim.Optimizer):
                     optimizer_present = True
             if model_count > 1 and optimizer_present:
@@ -1377,7 +1383,7 @@ def prepare_model(self, model: torch.nn.Module, device_placement: bool = None, e
         elif device_placement and not self.verify_device_map(model):
             model = model.to(self.device)
 
-        if self.native_amp and self.distributed_type != DistributedType.FSDP:
+        if self.native_amp:
             model._original_forward = model.forward
             model_forward_func = model.forward.__func__ if hasattr(model.forward, "__func__") else model.forward
             autocast_context = get_mixed_precision_context_manager(self.native_amp, self.autocast_handler)
@@ -1429,7 +1435,13 @@ def prepare_model(self, model: torch.nn.Module, device_placement: bool = None, e
 
                 # Check if the model is already a FSDP model due to `Manual Wrapping` and if so,
                 # don't wrap it again
-                if type(model) != FSDP:
+                # In case the model is already compiled using PyTorch 2.0 and the wrapped model in it
+                # is a FSDP model, don't wrap it again
+                is_type_fsdp = isinstance(model, FSDP) or (
+                    is_compiled_module(model) and isinstance(model._orig_mod, FSDP)
+                )
+
+                if not is_type_fsdp:
                     self.state.fsdp_plugin.set_auto_wrap_policy(model)
                     fsdp_plugin = self.state.fsdp_plugin
                     kwargs = {
@@ -1462,15 +1474,17 @@ def prepare_model(self, model: torch.nn.Module, device_placement: bool = None, e
                             ),
                             auto_wrap_policy=fsdp_plugin.auto_wrap_policy,
                         )
-
+                # if the previous and current models are same, delete the previous one
+                if len(self._models) > 1 and (self._models[-2] is self._models[-1]):
+                    del self._models[-2]
                 self._models[-1] = model
             elif self.distributed_type == DistributedType.MULTI_CPU:
                 kwargs = self.ddp_handler.to_kwargs() if self.ddp_handler is not None else {}
                 model = torch.nn.parallel.DistributedDataParallel(model, **kwargs)
             elif self.distributed_type == DistributedType.TPU and self.state.fork_launched:
                 model = xmp.MpModelWrapper(model).to(self.device)
-        # torch.compile should be called last.
-        if self.state.dynamo_plugin.backend != DynamoBackend.NO:
+        # torch.compile should be called last and only if the model isn't already compiled.
+        if self.state.dynamo_plugin.backend != DynamoBackend.NO and not is_compiled_module(model):
             if not is_torch_version(">=", "2.0"):
                 raise ValueError("Using `torch.compile` requires PyTorch 2.0 or higher.")
             model = torch.compile(model, **self.state.dynamo_plugin.to_kwargs())