diff --git a/src/promptflow-core/promptflow/_utils/async_utils.py b/src/promptflow-core/promptflow/_utils/async_utils.py
index afa648e8524..0bec611f936 100644
--- a/src/promptflow-core/promptflow/_utils/async_utils.py
+++ b/src/promptflow-core/promptflow/_utils/async_utils.py
@@ -4,9 +4,11 @@
 
 import asyncio
 import contextvars
+import functools
 from concurrent.futures import ThreadPoolExecutor
 
 from promptflow._utils.utils import set_context
+from promptflow.tracing import ThreadPoolExecutorWithContext
 
 
 def _has_running_loop() -> bool:
@@ -38,3 +40,21 @@ def async_run_allowing_running_loop(async_func, *args, **kwargs):
             return executor.submit(lambda: asyncio.run(async_func(*args, **kwargs))).result()
     else:
         return asyncio.run(async_func(*args, **kwargs))
+
+
+def run_async_function_sync(func):
+    @functools.wraps(func)
+    def wrapper(*args, **kwargs):
+        return async_run_allowing_running_loop(func, *args, **kwargs)
+
+    return wrapper
+
+
+def run_sync_function_async(func):
+    @functools.wraps(func)
+    async def wrapper(*args, **kwargs):
+        with ThreadPoolExecutorWithContext() as executor:
+            partial_func = functools.partial(func, *args, **kwargs)
+            return await asyncio.get_event_loop().run_in_executor(executor, partial_func)
+
+    return wrapper
diff --git a/src/promptflow-core/promptflow/executor/_script_executor.py b/src/promptflow-core/promptflow/executor/_script_executor.py
index 744fa5f6834..bd42cdec1b0 100644
--- a/src/promptflow-core/promptflow/executor/_script_executor.py
+++ b/src/promptflow-core/promptflow/executor/_script_executor.py
@@ -1,4 +1,3 @@
-import asyncio
 import contextlib
 import dataclasses
 import importlib
@@ -14,7 +13,7 @@
 from promptflow._core.log_manager import NodeLogManager
 from promptflow._core.run_tracker import RunTracker
 from promptflow._core.tool_meta_generator import PythonLoadError
-from promptflow._utils.async_utils import async_run_allowing_running_loop
+from promptflow._utils.async_utils import run_async_function_sync, run_sync_function_async
 from promptflow._utils.dataclass_serializer import convert_eager_flow_output_to_dict
 from promptflow._utils.exception_utils import ExceptionPresenter
 from promptflow._utils.logger_utils import logger
@@ -35,7 +34,6 @@
 from promptflow.executor._result import AggregationResult, LineResult
 from promptflow.storage import AbstractRunStorage
 from promptflow.storage._run_storage import DefaultRunStorage
-from promptflow.tracing import ThreadPoolExecutorWithContext
 from promptflow.tracing._trace import _traced
 from promptflow.tracing._tracer import Tracer
 from promptflow.tracing.contracts.trace import TraceType
@@ -135,10 +133,7 @@ def _exec_line(
         line_run_id = run_info.run_id
         try:
             Tracer.start_tracing(line_run_id)
-            if self._is_async:
-                output = asyncio.run(self._func(**inputs))
-            else:
-                output = self._func(**inputs)
+            output = self._func(**inputs)
             output = self._stringify_generator_output(output) if not allow_generator_output else output
             traces = Tracer.end_tracing(line_run_id)
             # Should convert output to dict before storing it to run info, since we will add key 'line_number' to it,
@@ -262,11 +257,7 @@ async def _exec_line_async(
         line_run_id = run_info.run_id
         try:
             Tracer.start_tracing(line_run_id)
-            if self._is_async:
-                output = await self._func(**inputs)
-            else:
-                partial_func = partial(self._func, **inputs)
-                output = await asyncio.get_event_loop().run_in_executor(None, partial_func)
+            output = await self._func_async(**inputs)
             output = self._stringify_generator_output(output) if not allow_generator_output else output
             traces = Tracer.end_tracing(line_run_id)
             output_dict = convert_eager_flow_output_to_dict(output)
@@ -429,14 +420,21 @@ def _initialize_function(self):
             if inspect.ismethod(func):
                 # For class method, the original function is a function reference that not bound to any object,
                 # so we need to pass the instance to it.
+                if func.__qualname__.endswith(".__call__"):
+                    name = func.__qualname__[: -len(".__call__")]
                 func = _traced(
                     partial(getattr(func, "__original_function"), self=func.__self__),
                     trace_type=TraceType.FLOW,
-                    name=func.__qualname__,
+                    name=name,
                 )
             else:
                 func = _traced(getattr(func, "__original_function"), trace_type=TraceType.FLOW)
-        self._func = func
+        if inspect.iscoroutinefunction(func):
+            self._func = run_async_function_sync(func)
+            self._func_async = func
+        else:
+            self._func = func
+            self._func_async = run_sync_function_async(func)
         inputs, _, _, _ = function_to_interface(self._func)
         self._inputs = {k: v.to_flow_input_definition() for k, v in inputs.items()}
         self._is_async = inspect.iscoroutinefunction(self._func)
@@ -453,21 +451,11 @@ def _initialize_aggr_function(self, flow_obj: object):
             if not hasattr(aggr_func, "__original_function"):
                 aggr_func = _traced(aggr_func)
             if inspect.iscoroutinefunction(aggr_func):
-
-                def run_async_function_sync(*args, **kwargs):
-                    return async_run_allowing_running_loop(aggr_func, *args, **kwargs)
-
-                self._aggr_func = run_async_function_sync
+                self._aggr_func = run_async_function_sync(aggr_func)
                 self._aggr_func_async = aggr_func
             else:
-
-                async def run_sync_function_async(*args, **kwargs):
-                    with ThreadPoolExecutorWithContext() as executor:
-                        partial_func = partial(aggr_func, *args, **kwargs)
-                        return await asyncio.get_event_loop().run_in_executor(executor, partial_func)
-
                 self._aggr_func = aggr_func
-                self._aggr_func_async = run_sync_function_async
+                self._aggr_func_async = run_sync_function_async(aggr_func)
             self._aggr_input_name = list(sign.parameters.keys())[0]
 
     def _parse_flow_file(self):