diff --git a/paddle/fluid/framework/op_info.h b/paddle/fluid/framework/op_info.h
index 5ce39d0c3a334c7fb61576040c6f920c0a7e884b..e1bc5be8c64f9ec31d2b585be461a2a0b9bef826 100644
--- a/paddle/fluid/framework/op_info.h
+++ b/paddle/fluid/framework/op_info.h
@@ -97,6 +97,8 @@ class OpInfo {
     return grad_op_maker_ != nullptr && !use_empty_grad_op_desc_maker_;
   }
 
+  bool HasEmptyGradOpMaker() const { return use_empty_grad_op_desc_maker_; }
+
   const DygraphGradOpMakerFN& DygraphGradOpMaker() const {
     // Normally, proto_ should not be null, except some special operators, such
     // as LeaklyReluDoubleGrad op.
diff --git a/paddle/fluid/operators/generator/templates/operator_utils.c.j2 b/paddle/fluid/operators/generator/templates/operator_utils.c.j2
index 16f0ecaa642f3a77667a176bfcff4408e5b7e99a..f762eedf3bffb0906804b03ac6880e1da937c58c 100644
--- a/paddle/fluid/operators/generator/templates/operator_utils.c.j2
+++ b/paddle/fluid/operators/generator/templates/operator_utils.c.j2
@@ -477,6 +477,7 @@ REGISTER_OPERATOR({{name}}, ops::{{name | to_pascal_case}}Op,
   {% set backward_name = op["backward"] %}
                   ops::{{backward_name | to_pascal_case}}OpMaker<paddle::framework::OpDesc>,
                   ops::{{backward_name | to_pascal_case}}OpMaker<paddle::imperative::OpBase>,
+{% elif "forward" in op %}
 {% else %}
                   paddle::framework::EmptyGradOpMaker<paddle::framework::OpDesc>,
                   paddle::framework::EmptyGradOpMaker<paddle::imperative::OpBase>,
diff --git a/paddle/fluid/pybind/pybind.cc b/paddle/fluid/pybind/pybind.cc
index a9b1bf398f84e6a08b278a3b1a33875cf0363fbe..34bb746c48ed6bc2ad990e0d6f7164c08949e950 100644
--- a/paddle/fluid/pybind/pybind.cc
+++ b/paddle/fluid/pybind/pybind.cc
@@ -1327,8 +1327,7 @@ All parameter, weight, gradient are variables in Paddle.
           if ((grad_op_maker == nullptr) && (grad_comp_op_maker == nullptr)) {
             // Normally, proto_ should not be null, except some special
             // operators, such as LeaklyReluDoubleGrad op.
-            std::string type =
-                op_info.proto_ ? op_info.proto_->type() : "unknown";
+            std::string type = op_desc.Type();
             PADDLE_THROW(platform::errors::NotFound(
                 "Neither operator %s's GradOpMaker nor CompGradOpMaker has "
                 "been registered.\nPlease check whether (%s) operator has "
@@ -1350,7 +1349,8 @@ All parameter, weight, gradient are variables in Paddle.
           VLOG(3) << "need skip: " << need_skip << std::endl;
           if (paddle::prim::PrimCommonUtils::IsBwdPrimEnabled()) {
             if ((grad_comp_op_maker != nullptr) && (!need_skip)) {
-              VLOG(3) << "Runing composite fun for " << op_desc.Type();
+              VLOG(3) << "Prim Flag Open: Runing composite grad fun for "
+                      << op_desc.Type();
               grad_op_descs = grad_comp_op_maker(op_desc,
                                                  no_grad_set,
                                                  &grad_to_var,
@@ -1362,9 +1362,13 @@ All parameter, weight, gradient are variables in Paddle.
             }
           } else {
             if (grad_op_maker != nullptr) {
+              VLOG(3) << "Prim Flag Close: Runing origin grad fun for "
+                      << op_desc.Type();
               grad_op_descs = grad_op_maker(
                   op_desc, no_grad_set, &grad_to_var, grad_sub_block);
             } else {
+              VLOG(3) << "Prim Flag Close: Runing composite grad fun for "
+                      << op_desc.Type();
               grad_op_descs = grad_comp_op_maker(op_desc,
                                                  no_grad_set,
                                                  &grad_to_var,
@@ -1392,6 +1396,9 @@ All parameter, weight, gradient are variables in Paddle.
         .Get(op_type)
         .HasNonEmptyGradOpMaker();
   });
+  m.def("has_empty_grad_op_maker", [](const std::string op_type) {
+    return framework::OpInfoMap::Instance().Get(op_type).HasEmptyGradOpMaker();
+  });
   m.def("has_infer_inplace", [](const std::string op_type) {
     return framework::OpInfoMap::Instance().Get(op_type).HasInferInplace();
   });
diff --git a/python/paddle/fluid/backward.py b/python/paddle/fluid/backward.py
index 51fe6294a5077abfe495ea00f956100e948a1fed..f7b8531aee4d94b1fdadc9d0564251c684a7fd01 100755
--- a/python/paddle/fluid/backward.py
+++ b/python/paddle/fluid/backward.py
@@ -2348,7 +2348,7 @@ def _find_op_path_(
         for i, op in enumerate(block.ops):
             if _some_in_set_(
                 op.desc.input_arg_names(), input_names
-            ) and core.has_non_empty_grad_op_maker(op.type):
+            ) and not core.has_empty_grad_op_maker(op.type):
                 for name in op.desc.output_arg_names():
                     if name not in no_grad_set:
                         input_names.add(name)
@@ -2367,7 +2367,7 @@ def _find_op_path_(
 
         if _some_in_set_(
             op.desc.output_arg_names(), output_names
-        ) and core.has_non_empty_grad_op_maker(op.type):
+        ) and not core.has_empty_grad_op_maker(op.type):
             for name in op.desc.input_arg_names():
                 if name not in no_grad_set:
                     output_names.add(name)
@@ -2382,7 +2382,7 @@ def _find_op_path_(
                 op.desc.output_arg_names(), output_names
             ):
                 relevant_op_flags[i] = True
-                if core.has_non_empty_grad_op_maker(op.type):
+                if not core.has_empty_grad_op_maker(op.type):
                     for name in op.desc.input_arg_names():
                         if name not in no_grad_set:
                             output_names.add(name)
diff --git a/test/autograd/test_autograd_functional_static.py b/test/autograd/test_autograd_functional_static.py
index 38c27c5e2384e7a8cbd05005c04cc7400e36993f..8786515d2699a126ec547586fed262f38df35cd1 100644
--- a/test/autograd/test_autograd_functional_static.py
+++ b/test/autograd/test_autograd_functional_static.py
@@ -466,7 +466,7 @@ class TestHessianFloat32(unittest.TestCase):
     def test_square(self):
         def pd_f(x):
             """Input is a square matrix."""
-            return paddle.matmul(x, x.T).flatten().sum()
+            return paddle.matmul(x, x.T).sum()
 
         def np_hess(x):
             dim = x.shape[0]
diff --git a/tools/check_file_diff_approvals.sh b/tools/check_file_diff_approvals.sh
index 3215f9d5072225046a8b599423a8edddb1055df0..f2fb9d86cdfdafd302cd023cdb5f2207467380a9 100644
--- a/tools/check_file_diff_approvals.sh
+++ b/tools/check_file_diff_approvals.sh
@@ -81,6 +81,7 @@ API_FILES=("CMakeLists.txt"
            "paddle/phi/core/kernel_context.h"
            "paddle/phi/core/infermeta_utils.h"
            "paddle/fluid/prim/api/composite_backward/composite_backward_api.h"
+           "paddle/fluid/prim/api/composite_backward/composite_double_backward_api.h"
            "paddle/fluid/prim/api/manual_prim/prim_manual_api.h"
            "paddle/fluid/prim/api/api.yaml"
            "python/paddle/incubate/autograd/composite_rules.py"
@@ -207,7 +208,7 @@ for API_FILE in ${API_FILES[*]}; do
       elif [ "${API_FILE}" == "paddle/phi/api/include/tensor.h" ] || [ "${API_FILE}" == "paddle/phi/core/tensor_base.h" ] || [ "${API_FILE}" == "paddle/phi/core/dense_tensor.h" ] || [ "${API_FILE}" == "paddle/phi/core/meta_tensor.h" ] || [ "${API_FILE}" == "paddle/phi/core/tensor_meta.h" ] || [ "${API_FILE}" == "paddle/phi/core/attribute.h" ] || [ "${API_FILE}" == "paddle/phi/core/device_context.h" ] || [ "${API_FILE}" == "paddle/phi/core/kernel_utils.h" ] || [ "${API_FILE}" == "paddle/phi/core/kernel_registry.h" ] || [ "${API_FILE}" == "paddle/phi/core/kernel_factory.h" ] || [ "${API_FILE}" == "paddle/phi/core/kernel_context.h" ] || [ "${API_FILE}" == "paddle/phi/core/infermeta_utils.h" ]; then
             echo_line="You must have one RD (chenwhql, phlrain, zyfncg, YuanRisheng) approval for changing ${API_FILE} , which manages the underlying code for PaddlePaddle PHI Library.\n"
             check_approval chenwhql phlrain zyfncg YuanRisheng
-      elif [ "${API_FILE}" == "paddle/fluid/prim/api/composite_backward/composite_backward_api.h" ] || [ "${API_FILE}" == "paddle/fluid/prim/api/manual_prim/prim_manual_api.h" ] || [ "${API_FILE}" == "paddle/fluid/prim/api/api.yaml" ]; then
+      elif [ "${API_FILE}" == "paddle/fluid/prim/api/composite_backward/composite_backward_api.h" ] || [ "${API_FILE}" == "paddle/fluid/prim/api/manual_prim/prim_manual_api.h" ] || [ "${API_FILE}" == "paddle/fluid/prim/api/api.yaml" ] || [ "${API_FILE}" == "paddle/fluid/prim/api/composite_backward/composite_double_backward_api.h" ]; then
             echo_line="You must have one RD (JiabinYang, cxxly(chenxiaoxu) , xiaoguoguo626807(wangruting)) approval for changing ${API_FILE} , which manages the code for PaddlePaddle Composite Bacward Prim API.\n"
             check_approval 1 JiabinYang cxxly xiaoguoguo626807
       elif [ "${API_FILE}" == "python/paddle/incubate/autograd/primitives.py" ] || [ "${API_FILE}" == "python/paddle/incubate/autograd/composite_rules.py" ]; then