[onnx] Add support for autograd function inlining in ONNX_ATEN_FALLBACK mode (#85736)

Solution to #85027

Pull Request resolved: https://github.com/pytorch/pytorch/pull/85736
Approved by: https://github.com/BowenBao
diff --git a/test/onnx/test_autograd_funs.py b/test/onnx/test_autograd_funs.py
index a0980d2..97f0652 100644
--- a/test/onnx/test_autograd_funs.py
+++ b/test/onnx/test_autograd_funs.py
@@ -148,7 +148,7 @@
             operator_export_type=OperatorExportTypes.ONNX_ATEN_FALLBACK,
         )
         iter = graph.nodes()
-        self.assertEqual(next(iter).kind(), "prim::PythonOp")
+        self.assertEqual(next(iter).kind(), "aten::ATen")
 
     def test_inline_and_symbolic(self):
         class Exp(torch.autograd.Function):
diff --git a/torch/csrc/jit/passes/onnx.cpp b/torch/csrc/jit/passes/onnx.cpp
index ea183ae..98f3cb4 100644
--- a/torch/csrc/jit/passes/onnx.cpp
+++ b/torch/csrc/jit/passes/onnx.cpp
@@ -465,7 +465,9 @@
       // 1. The torch.autograd.Function class of this node object has `symbolic`
       // method defined.
       // 2. Custom export symbolic is registered for prim::PythonOp.
-      if (operator_export_type == ::torch::onnx::OperatorExportTypes::ONNX) {
+      if (operator_export_type == ::torch::onnx::OperatorExportTypes::ONNX ||
+          operator_export_type ==
+              ::torch::onnx::OperatorExportTypes::ONNX_ATEN_FALLBACK) {
         try {
           inlineAutograd(op);
         } catch (const std::exception& ex) {