diff --git a/cinn/poly/ast_gen.cc b/cinn/poly/ast_gen.cc
index f4af440255a34..e175fc8db2dad 100644
--- a/cinn/poly/ast_gen.cc
+++ b/cinn/poly/ast_gen.cc
@@ -3,17 +3,22 @@
 namespace cinn {
 namespace poly {
 
-isl::ast_node AstGen::operator()(const std::vector<Element> &elements, const Scheduler &scheduler) {
-  // Collect domains.
-  auto sets = utils::Map<std::vector<Element>, isl::set>(elements, [](const Element &e) { return e.domain(); });
-  isl::union_set domain = SetsToUnionSet(sets);
+isl::union_set AstGen::domain() {
+  CHECK(!poly_elements_.empty());
+  auto sets = utils::Map<std::vector<Element>, isl::set>(poly_elements_, [](const Element &e) { return e.domain(); });
+  return SetsToUnionSet(sets);
+}
 
-  isl::ctx ctx = elements.front().domain().ctx();
+isl::ctx AstGen::ctx() const {
+  CHECK(!poly_elements_.empty());
+  return poly_elements_.front().domain().ctx();
+}
 
+isl::ast_node AstGen::Build() {
   // Collect schedule from scheduler.
-  auto schedules = scheduler.BuildSchedule();
+  auto schedules = scheduler_.BuildSchedule();
   std::vector<isl::map> maps;
-  for (auto &ele : elements) {
+  for (auto &ele : poly_elements_) {
     auto it = schedules.find(ele.id());
     CHECK(it != std::end(schedules));
     maps.push_back(it->second);
@@ -21,18 +26,41 @@ isl::ast_node AstGen::operator()(const std::vector<Element> &elements, const Sch
   auto schedule = MapsToUnionMap(maps);
 
   // Build it.
-  auto build = isl::ast_build::from_context(context_);
+  auto ast_build = isl::ast_build::from_context(context_);
   // Set iterators.
   if (!iterator_names_.empty()) {
-    auto iterator_names = scheduler.WrapIteratorNames(iterator_names_);
-    isl::id_list ids    = isl::manage(isl_id_list_alloc(ctx.get(), iterator_names.size()));
+    auto iterator_names = scheduler_.WrapIteratorNames(iterator_names_);
+    isl::id_list ids    = isl::manage(isl_id_list_alloc(ctx().get(), iterator_names.size()));
     for (int i = 0; i < iterator_names.size(); i++) {
-      ids = isl::manage(isl_id_list_add(ids.release(), isl_id_alloc(ctx.get(), iterator_names[i].c_str(), nullptr)));
+      ids = isl::manage(isl_id_list_add(ids.release(), isl_id_alloc(ctx().get(), iterator_names[i].c_str(), nullptr)));
     }
-    build = isl::manage(isl_ast_build_set_iterators(build.release(), ids.release()));
+    ast_build = isl::manage(isl_ast_build_set_iterators(ast_build.release(), ids.release()));
   }
 
-  auto ast = build.node_from_schedule_map(schedule.intersect_domain(domain));
+  // collect iterator map
+  auto get_domain_by_name = [this](const std::string &name) -> isl::set {
+    auto ele_it = std::find_if(
+        poly_elements_.begin(), poly_elements_.end(), [&name](const Element &ele) { return ele.id() == name; });
+    CHECK(ele_it != std::end(poly_elements_));
+    return ele_it->domain();
+  };
+
+  auto collect = [&](isl::ast_node node, isl::ast_build build) -> isl::ast_node {
+    auto tuple_name                     = detail::GetTupleName(node.get());
+    auto indice_map                     = ExtractIslTransformedIndiceMap(get_domain_by_name(tuple_name), build.get());
+    transformed_indice_map_[tuple_name] = indice_map;
+    return node;
+  };
+
+  ast_build = ast_build.set_at_each_domain(collect);
+
+  isl::union_map transformed_schedule = transform().apply_range(schedule);
+  auto schedule_domain                = transformed_schedule.intersect_domain(domain());
+  VLOG(4) << "domain: " << domain();
+  VLOG(4) << "transform schedule " << poly_elements()[0].schedule();
+  VLOG(4) << "schedule: " << schedule;
+  VLOG(4) << "schedule_domain: " << schedule_domain;
+  auto ast = ast_build.node_from_schedule_map(schedule_domain);
   VLOG(2) << "\n" << isl_ast_node_to_C_str(ast.get());
   return ast;
 }
@@ -42,5 +70,77 @@ AstGen &AstGen::SetIteratorNames(const std::vector<std::string> &names) {
   return *this;
 }
 
+isl::ast_expr CreateIslAstIndexExpression(isl_ast_build *build, const isl::map &access);
+
+std::map<std::string, isl::ast_expr> AstGen::ExtractIslTransformedIndiceMap(const isl::set &iterator_domain,
+                                                                            isl_ast_build *build) {
+  std::map<std::string, isl::ast_expr> iterator_map;
+  isl::map identity = isl::manage(isl_set_identity(iterator_domain.copy()));
+  isl::map schedule = identity;
+
+  identity                = identity.apply_domain(schedule);
+  isl::ast_expr idx_expr  = CreateIslAstIndexExpression(build, identity);
+  isl::space domain_space = iterator_domain.space();
+
+  for (int i = 1; i < isl_ast_expr_get_op_n_arg(idx_expr.get()); i++) {
+    if (isl_space_has_dim_name(domain_space.get(), isl_dim_set, i - 1)) {
+      std::string original_idx_name   = isl_space_get_dim_name(domain_space.get(), isl_dim_set, i - 1);
+      isl::ast_expr transformed_index = isl::manage(isl_ast_expr_get_op_arg(idx_expr.get(), i));
+      iterator_map.emplace(original_idx_name, transformed_index);
+    }
+  }
+
+  return iterator_map;
+}
+
+const std::map<std::string, isl::ast_expr> &AstGen::axis2ast(const std::string &tuple_name) const {
+  auto it = transformed_indice_map_.find(tuple_name);
+  CHECK(it != transformed_indice_map_.end()) << "no id " << tuple_name;
+  return it->second;
+}
+
+isl::ast_expr CreateIslAstIndexExpression(isl_ast_build *build, const isl::map &access) {
+  CHECK(build);
+  isl::map schedule = isl::manage(isl_map_from_union_map(isl_ast_build_get_schedule(build)));
+
+  // get identity access from schedule.
+  auto statement       = isl_map_get_statement_repr(schedule.get(), isl_dim_in);
+  auto statement_set   = isl::manage(isl_set_read_from_str(isl_map_get_ctx(schedule.get()),
+                                                         utils::StringFormat("{ %s : }", statement.c_str()).c_str()));
+  auto identity_access = isl::manage(isl_set_identity(statement_set.release()));
+  isl::map map         = isl::manage(isl_map_reverse(schedule.copy()));
+
+  isl::pw_multi_aff iterator_map = isl::manage(isl_pw_multi_aff_from_map(map.copy()));
+  isl::pw_multi_aff index_aff    = isl::manage(isl_pw_multi_aff_from_map(identity_access.copy()));
+
+  isl::space model2        = iterator_map.space();
+  index_aff                = isl::manage(isl_pw_multi_aff_align_params(index_aff.copy(), model2.copy()));
+  isl::space model         = index_aff.space();
+  iterator_map             = isl::manage(isl_pw_multi_aff_align_params(iterator_map.copy(), model.copy()));
+  iterator_map             = isl::manage(isl_pw_multi_aff_pullback_pw_multi_aff(index_aff.copy(), iterator_map.copy()));
+  isl::ast_expr index_expr = isl::manage(isl_ast_build_access_from_pw_multi_aff(build, iterator_map.copy()));
+
+  return index_expr;
+}
+
+isl::union_map AstGen::transform() {
+  std::vector<isl::map> transforms;
+  for (auto &ele : poly_elements()) {
+    transforms.push_back(ele.schedule());
+  }
+  return MapsToUnionMap(transforms);
+}
+
+namespace detail {
+
+std::string GetTupleName(isl_ast_node *node) {
+  auto expr = isl::manage(isl_ast_node_user_get_expr(node));
+  auto arg  = isl::manage(isl_ast_expr_get_op_arg(expr.get(), 0));
+  auto name = isl_id_get_name(isl_ast_expr_get_id(arg.get()));
+  return name;
+}
+
+}  // namespace detail
+
 }  // namespace poly
 }  // namespace cinn
diff --git a/cinn/poly/ast_gen.h b/cinn/poly/ast_gen.h
index 2f70e9b5e701d..eae55d678c844 100644
--- a/cinn/poly/ast_gen.h
+++ b/cinn/poly/ast_gen.h
@@ -1,6 +1,9 @@
 #pragma once
 #include <isl/cpp.h>
 
+#include <map>
+#include <string>
+
 #include "cinn/poly/element.h"
 #include "cinn/poly/isl_utils.h"
 #include "cinn/poly/schedule.h"
@@ -11,7 +14,8 @@ namespace poly {
 
 class AstGen {
  public:
-  AstGen(const isl::set& context) : context_(context) {}
+  AstGen(const isl::set& context, const std::vector<Element>& elements, const Scheduler& scheduler)
+      : context_(context), poly_elements_(elements), scheduler_(scheduler) {}
 
   /**
    * Set forloop iterator names.
@@ -20,12 +24,42 @@ class AstGen {
    */
   AstGen& SetIteratorNames(const std::vector<std::string>& names);
 
-  isl::ast_node operator()(const std::vector<Element>& elements, const Scheduler& scheduler);
+  isl::ctx ctx() const;
+
+  isl::ast_node Build();
+
+  const std::vector<Element>& poly_elements() const { return poly_elements_; }
+
+  const std::map<std::string, isl::ast_expr>& axis2ast(const std::string& tuple_name) const;
+
+ private:
+  //! Return a domain composed of all the elements.
+  isl::union_set domain();
+
+  //! Return a map composed of all the transforms.
+  isl::union_map transform();
+
+  //! Replace the Expr with the transformed indices.
+  //! e.g. Stage's expr is C[i,j] ...
+  //! e.g. with ISL transformed statement S0(c0+1, c1*2), the expr will turn to C[c0+1, c1*2]
+  static std::map<std::string, isl::ast_expr> ExtractIslTransformedIndiceMap(const isl::set& iterator_domain,
+                                                                             isl_ast_build* build);
 
  private:
   isl::set context_;
+  std::vector<Element> poly_elements_;
+  const Scheduler& scheduler_;
   std::vector<std::string> iterator_names_;
+  //! tuple name -> { axis -> isl_ast }
+  std::map<std::string, std::map<std::string, isl::ast_expr>> transformed_indice_map_;
 };
 
+namespace detail {
+
+//! Get tuple name of a ast node.
+std::string GetTupleName(isl_ast_node* node);
+
+}  // namespace detail
+
 }  // namespace poly
 }  // namespace cinn
diff --git a/cinn/poly/ast_gen_test.cc b/cinn/poly/ast_gen_test.cc
index 20e49b3bb6a23..9d7b987bb48a2 100644
--- a/cinn/poly/ast_gen_test.cc
+++ b/cinn/poly/ast_gen_test.cc
@@ -10,14 +10,25 @@ TEST(ast_gen, basic) {
   Element A(isl::set(ctx, "{ A[i,j,k]: 0<i,j,k<100 }"));
   Element B(isl::set(ctx, "{ B[i,j,k]: 0<i,j,k<100 }"));
 
+  Iterator A_i0, A_i1;
+  Iterator B_i0, B_i1;
+
+  std::tie(A_i0, A_i1) = A.Split(Iterator("i"), 4);
+  std::tie(B_i0, B_i1) = B.Split(Iterator("i"), 4);
+
   Scheduler scheduler;
   scheduler.RegisterElement(A);
   scheduler.RegisterElement(B);
-  scheduler.After(A, B, 2);
+  scheduler.After(A, B, 3);
+
+  AstGen gen(isl::set(ctx, "{:}"), {A, B}, scheduler);
+  gen.SetIteratorNames({"i.outer", "i.inner", "j", "k"});
+  gen.Build();
 
-  AstGen gen(isl::set(ctx, "{:}"));
-  gen.SetIteratorNames({"i", "j", "k"});
-  gen({A, B}, scheduler);
+  auto iters = gen.axis2ast("A");
+  for (auto& x : iters) {
+    LOG(INFO) << x.first << " " << x.second;
+  }
 }
 
 }  // namespace poly
diff --git a/cinn/poly/element.cc b/cinn/poly/element.cc
index d81a2f7a967d1..eb392871c9f67 100644
--- a/cinn/poly/element.cc
+++ b/cinn/poly/element.cc
@@ -33,7 +33,6 @@ void Element::InitSchedule() {
 Element::Element(const isl::set &domain) : domain_(domain) {
   CHECK(!domain_.is_null());
   CHECK(!domain_.is_empty());
-
   InitSchedule();
 }
 
diff --git a/cinn/poly/isl_utils.cc b/cinn/poly/isl_utils.cc
index e6a8b93c3c4ed..4823c76938146 100644
--- a/cinn/poly/isl_utils.cc
+++ b/cinn/poly/isl_utils.cc
@@ -3,6 +3,8 @@
 #include <glog/logging.h>
 #include <isl/cpp.h>
 
+#include "cinn/utils/string.h"
+
 namespace cinn {
 namespace poly {
 
@@ -58,5 +60,16 @@ isl::union_set SetsToUnionSet(const std::vector<isl::set> &sets) {
   return uset;
 }
 
+std::string isl_map_get_statement_repr(__isl_keep isl_map *map, isl_dim_type type) {
+  CHECK(map);
+  auto tuple_name = isl_map_get_tuple_name(map, type);
+  std::vector<std::string> dims;
+
+  for (int i = 0; i < isl_map_dim(map, type); i++) {
+    dims.push_back(isl_map_get_dim_name(map, type, i));
+  }
+  return utils::StringFormat("%s[%s]", tuple_name, utils::Join(dims, ", ").c_str());
+}
+
 }  // namespace poly
 }  // namespace cinn
diff --git a/cinn/poly/isl_utils.h b/cinn/poly/isl_utils.h
index 4632f99eeddce..f93f6f80ed0d9 100644
--- a/cinn/poly/isl_utils.h
+++ b/cinn/poly/isl_utils.h
@@ -21,5 +21,8 @@ void SetDimNames(isl::map* map, isl_dim_type dim_type, const std::vector<std::st
 isl::union_map MapsToUnionMap(const std::vector<isl::map>& maps);
 isl::union_set SetsToUnionSet(const std::vector<isl::set>& sets);
 
+//! Get a representation of the tuple in the map.
+std::string isl_map_get_statement_repr(__isl_keep isl_map* map, isl_dim_type type);
+
 }  // namespace poly
 }  // namespace cinn