diff --git a/paddle/fluid/pir/transforms/pd_op_to_kernel_pass.cc b/paddle/fluid/pir/transforms/pd_op_to_kernel_pass.cc
index d6f131cb9d06c4..cbb7e878e04a0b 100644
--- a/paddle/fluid/pir/transforms/pd_op_to_kernel_pass.cc
+++ b/paddle/fluid/pir/transforms/pd_op_to_kernel_pass.cc
@@ -77,6 +77,9 @@ const std::unordered_set<std::string> SpecialLowerOps = {
     pir::YieldOp::name(),
     IfOp::name(),
     WhileOp::name(),
+    pir::CreateStackOp::name(),
+    pir::PushBackOp::name(),
+    pir::PopBackOp::name(),
     "cinn_runtime.jit_kernel"};
 
 static bool NeedFallBackCpu(const pir::Operation* op,
@@ -1017,6 +1020,45 @@ void HandleForSpecialOp(
     }
   }
 
+  if (op_item->isa<::pir::CreateStackOp>() ||
+      op_item->isa<::pir::PushBackOp>()) {
+    for (size_t i = 0; i < op_item->num_operands(); ++i) {
+      auto cur_in = op_item->operand_source(i);
+      if (!cur_in) {
+        vec_inputs.emplace_back();
+        continue;
+      }
+      auto new_in = GetNewInput(
+          cur_in, *map_value_pair, static_cast<int>(i), op_item->name());
+      vec_inputs.push_back(new_in);
+    }
+    for (size_t i = 0; i < op_item->num_results(); ++i) {
+      op_output_types.push_back(op_item->result(i).type());
+    }
+  }
+
+  if (op_item->isa<::pir::PopBackOp>()) {
+    for (size_t i = 0; i < op_item->num_operands(); ++i) {
+      auto cur_in = op_item->operand_source(i);
+      auto new_in = GetNewInput(
+          cur_in, *map_value_pair, static_cast<int>(i), op_item->name());
+      vec_inputs.push_back(new_in);
+    }
+
+    auto pop_back_op = op_item->dyn_cast<::pir::PopBackOp>();
+    for (size_t i = 0; i < op_item->num_results(); ++i) {
+      auto cur_inlet_element = pop_back_op.inlet_element(i);
+      PADDLE_ENFORCE_EQ(map_value_pair->count(cur_inlet_element),
+                        true,
+                        phi::errors::PreconditionNotMet(
+                            "[%d]'s output of [%s] op MUST be in map pair",
+                            i,
+                            op_item->name()));
+      auto new_inlet_element = map_value_pair->at(cur_inlet_element);
+
+      op_output_types.push_back(new_inlet_element.type());
+    }
+  }
   if (op_item->name() == "cinn_runtime.jit_kernel") {
     if (op_item->num_operands() > 0) {
       for (size_t i = 0; i < op_item->num_operands(); ++i) {
@@ -1049,7 +1091,7 @@ void HandleForSpecialOp(
       (*map_value_pair)[op_item->result(i)] = op->result(i);
     }
   }
-  VLOG(6) << "Deep copy a new builtin op: " << op_item->name();
+  VLOG(6) << "Deep copy a new special op: " << op_item->name();
 }
 
 std::vector<pir::Type> BuildOutputs(pir::Operation* op_item,
diff --git a/paddle/pir/dialect/control_flow/ir/cf_op.cc b/paddle/pir/dialect/control_flow/ir/cf_op.cc
index ee34872f54799b..6828701d5961d9 100644
--- a/paddle/pir/dialect/control_flow/ir/cf_op.cc
+++ b/paddle/pir/dialect/control_flow/ir/cf_op.cc
@@ -169,8 +169,10 @@ void PopBackOp::VerifySig() {
              "The pop elements size must equal to push elements size.");
   for (size_t index = 0; index < inlet_size; ++index) {
     IR_ENFORCE(outlet_element(index).type() == inlet_element(index).type(),
-               "The %d element's push type isn't equal to pop type",
-               index);
+               "The %d element's push type (%s) isn't equal to pop type (%s)",
+               index,
+               outlet_element(index).type(),
+               inlet_element(index).type());
   }
   VLOG(4) << "End Verifying for PopBackOp.";
 }
diff --git a/test/cpp/pir/control_flow_dialect/CMakeLists.txt b/test/cpp/pir/control_flow_dialect/CMakeLists.txt
index d295fa37b6b730..9309a8a774b297 100644
--- a/test/cpp/pir/control_flow_dialect/CMakeLists.txt
+++ b/test/cpp/pir/control_flow_dialect/CMakeLists.txt
@@ -5,6 +5,8 @@ cc_test_old(
   DEPS
   pir
   op_dialect_vjp
+  pir_transforms
+  op_dialect
   gtest)
 
 cc_test_old(
@@ -14,4 +16,6 @@ cc_test_old(
   DEPS
   pir
   op_dialect_vjp
+  pir_transforms
+  op_dialect
   gtest)
diff --git a/test/cpp/pir/control_flow_dialect/if_op_test.cc b/test/cpp/pir/control_flow_dialect/if_op_test.cc
index b1b6b3abe005dd..64ccbcdf270224 100644
--- a/test/cpp/pir/control_flow_dialect/if_op_test.cc
+++ b/test/cpp/pir/control_flow_dialect/if_op_test.cc
@@ -14,15 +14,25 @@
 #include <gtest/gtest.h>
 #include <iostream>
 
+#include "paddle/fluid/pir/dialect/kernel/ir/kernel_dialect.h"
 #include "paddle/fluid/pir/dialect/operator/ir/control_flow_op.h"
 #include "paddle/fluid/pir/dialect/operator/ir/op_dialect.h"
 #include "paddle/fluid/pir/dialect/operator/ir/pd_op.h"
+#include "paddle/fluid/pir/transforms/pd_op_to_kernel_pass.h"
+#include "paddle/phi/core/kernel_registry.h"
 #include "paddle/pir/core/builder.h"
 #include "paddle/pir/core/builtin_op.h"
 #include "paddle/pir/core/program.h"
 #include "paddle/pir/dialect/control_flow/ir/cf_dialect.h"
 #include "paddle/pir/dialect/control_flow/ir/cf_op.h"
 
+PD_DECLARE_KERNEL(full, CPU, ALL_LAYOUT);
+PD_DECLARE_KERNEL(add, CPU, ALL_LAYOUT);
+PD_DECLARE_KERNEL(matmul_grad, CPU, ALL_LAYOUT);
+PD_DECLARE_KERNEL(add_grad, CPU, ALL_LAYOUT);
+PD_DECLARE_KERNEL(matmul, CPU, ALL_LAYOUT);
+PD_DECLARE_KERNEL(less_than, CPU, ALL_LAYOUT);
+
 using namespace paddle::dialect;  // NOLINT
 
 TEST(if_op_test, base) {
@@ -99,6 +109,7 @@ TEST(if_op_test, network_with_backward) {
   pir::IrContext* ctx = pir::IrContext::Instance();
   ctx->GetOrRegisterDialect<OperatorDialect>();
   ctx->GetOrRegisterDialect<pir::ControlFlowDialect>();
+  ctx->GetOrRegisterDialect<paddle::dialect::KernelDialect>();
 
   pir::Program program(ctx);
   pir::Block* block = program.block();
@@ -169,4 +180,6 @@ TEST(if_op_test, network_with_backward) {
   builder.SetInsertionPointToEnd(block);
 
   LOG(INFO) << program;
+
+  auto kernel_program = paddle::dialect::PdOpLowerToKernelPass(&program);
 }