diff --git a/py/torch_tensorrt/dynamo/_engine_caching.py b/py/torch_tensorrt/dynamo/_engine_caching.py
index ee5a6ec854..c8ff7aba50 100644
--- a/py/torch_tensorrt/dynamo/_engine_caching.py
+++ b/py/torch_tensorrt/dynamo/_engine_caching.py
@@ -48,7 +48,7 @@ def pack(
         serialized_engine: bytes,
         input_names: List[str],
         output_names: List[str],
-        weight_name_map: Optional[Dict[str, Any]],
+        weight_name_map: Optional[Dict[Any, Any]],
     ) -> bytes:
         """Pack serialized engine, input names, output names, and weight map into a single blob
 
@@ -56,7 +56,7 @@ def pack(
             serialized_engine (bytes): serialized TRT engine
             input_names (List[str]): input names of TRT engine
             output_names (List[str]): output names of TRT engine
-            weight_name_map (Optional[Dict[str, Any]]): weight name map for refitting
+            weight_name_map (Optional[Dict[Any, Any]]): weight name map for refitting
 
         Returns:
             bytes: packed blob
@@ -73,7 +73,7 @@ def pack(
     @staticmethod
     def unpack(
         packed_obj: bytes,
-    ) -> Tuple[bytes, List[str], List[str], Optional[Dict[str, Any]]]:
+    ) -> Tuple[bytes, List[str], List[str], Optional[Dict[Any, Any]]]:
         """Unpack packed blob into serialized engine, input names, output names, and weight map
 
         Args:
diff --git a/py/torch_tensorrt/dynamo/conversion/_TRTInterpreter.py b/py/torch_tensorrt/dynamo/conversion/_TRTInterpreter.py
index c944e8a971..30ce62960e 100644
--- a/py/torch_tensorrt/dynamo/conversion/_TRTInterpreter.py
+++ b/py/torch_tensorrt/dynamo/conversion/_TRTInterpreter.py
@@ -501,7 +501,6 @@ def run(
                     _LOGGER.info(
                         "Found the cached engine that corresponds to this graph. It is directly loaded."
                     )
-                    # TODO: refit the engine here or outside (within convert_module)?
                     return TRTInterpreterResult(
                         serialized_engine,
                         self._input_names,
diff --git a/py/torch_tensorrt/dynamo/conversion/_conversion.py b/py/torch_tensorrt/dynamo/conversion/_conversion.py
index e03c6cf832..5a8f8d62bf 100644
--- a/py/torch_tensorrt/dynamo/conversion/_conversion.py
+++ b/py/torch_tensorrt/dynamo/conversion/_conversion.py
@@ -107,6 +107,36 @@ def interpret_module_to_result(
         compilation_settings=settings,
     )
     interpreter_result = interpreter.run()
+
+    if settings.make_refitable:
+        # Run fast refit even if it's the first compilation.
+        # This is to ensure that the weight name map is correct for future refits.
+        # If the fast refit fails, remove the weight name map.
+        from torch_tensorrt.dynamo._refit import _refit_single_trt_engine_with_gm
+        from torch_tensorrt.logging import TRT_LOGGER
+
+        runtime = trt.Runtime(TRT_LOGGER)
+        refit_test_engine = runtime.deserialize_cuda_engine(
+            interpreter_result.serialized_engine
+        )
+        try:
+            _refit_single_trt_engine_with_gm(
+                new_gm=module,
+                old_engine=refit_test_engine,
+                input_list=inputs,
+                settings=settings,
+                weight_name_map=interpreter_result.weight_name_map,
+            )
+        except AssertionError:
+            # TRTInterpreterResult is a tuple, so we need to create a new one
+            interpreter_result = TRTInterpreterResult(
+                interpreter_result.serialized_engine,
+                interpreter_result.input_names,
+                interpreter_result.output_names,
+                None,
+            )
+            logger.warning("Fast refit test failed. Removing the weight map caching.")
+
     return interpreter_result
 
 
@@ -126,28 +156,6 @@ def convert_module(
         PythonTorchTensorRTModule or TorchTensorRTModule
     """
     interpreter_result = interpret_module_to_result(module, inputs, settings)
-    # Test fast refit:
-    from torch_tensorrt.dynamo._refit import _refit_single_trt_engine_with_gm
-    from torch_tensorrt.logging import TRT_LOGGER
-
-    runtime = trt.Runtime(TRT_LOGGER)
-    refit_test_engine = runtime.deserialize_cuda_engine(
-        interpreter_result.serialized_engine
-    )
-    weight_name_map: Any = None
-    # Do the test refit with cached map if make_refitable is enabled
-    if settings.make_refitable:
-        weight_name_map = interpreter_result.weight_name_map
-        try:
-            _refit_single_trt_engine_with_gm(
-                new_gm=module,
-                old_engine=refit_test_engine,
-                input_list=inputs,
-                settings=settings,
-                weight_name_map=interpreter_result.weight_name_map,
-            )
-        except AssertionError:
-            logger.warning("Fast refit test failed. Removing the weight map caching.")
 
     rt_cls = PythonTorchTensorRTModule
 
@@ -171,5 +179,5 @@ def convert_module(
         output_binding_names=list(interpreter_result.output_names),
         name=name,
         settings=settings,
-        weight_name_map=weight_name_map,
+        weight_name_map=interpreter_result.weight_name_map,
     )