diff --git a/paddle/fluid/inference/analysis/data_flow_graph.h b/paddle/fluid/inference/analysis/data_flow_graph.h
index 1c60d5de21538043962cc58a6f508aea635fe8c4..bc1875f4d851c5d28d290357d94528fe3303f631 100644
--- a/paddle/fluid/inference/analysis/data_flow_graph.h
+++ b/paddle/fluid/inference/analysis/data_flow_graph.h
@@ -36,6 +36,8 @@ namespace analysis {
 
 /*
  * DataFlowGraph - A container of Value and Function Nodes.
+ *
+ * This is the base graph for any other type of graphs, such as SSA or CFG.
  */
 struct DataFlowGraph {
   NodeMap nodes;
diff --git a/paddle/fluid/inference/analysis/fluid_to_data_flow_graph_pass.cc b/paddle/fluid/inference/analysis/fluid_to_data_flow_graph_pass.cc
index 496921db9eabce1b1e40c7cb13089446ca93321c..88fdf8c9cb4ce5369d70d416bbcfe6a4c7f23a98 100644
--- a/paddle/fluid/inference/analysis/fluid_to_data_flow_graph_pass.cc
+++ b/paddle/fluid/inference/analysis/fluid_to_data_flow_graph_pass.cc
@@ -40,6 +40,8 @@ void FluidToDataFlowGraphPass::Run(DataFlowGraph *graph) {
   PADDLE_ENFORCE(graph);
   PADDLE_ENFORCE(desc_);
   // insert vars
+  // The `var2id` keeps a map from a variable's name to its Node-id, the Node-id
+  // will keep updating to its latest alias during the graph-building.
   std::unordered_map<std::string, size_t> var2id;
   auto &main_block = desc_->blocks(framework::kRootBlockIndex);
   for (int i = 0; i < main_block.vars_size(); i++) {
@@ -51,6 +53,15 @@ void FluidToDataFlowGraphPass::Run(DataFlowGraph *graph) {
     var2id[var.name()] = v->id();
   }
 
+  // The variables in a SSA can only write once, so if a variable is written
+  // multiple times(quite common in our ProgramDesc design), multiple alias
+  // Nodes of this variable will be created, and each will just write once.
+
+  // An set that keep all the names of the variables(the original, not alias)
+  // that have been written(as outputs). Once an Op's output variable hit the
+  // set, it should create a new alias and update the global alias for this
+  // variable. And that make a Data Flow Graph a SSA.
+  std::unordered_set<Node *> unique_written_vars;
   for (int i = 0; i < main_block.ops_size(); i++) {
     const auto &op = main_block.ops(i);
     auto *o = graph->nodes.Create(Node::Type::kFunction);
@@ -62,33 +73,33 @@ void FluidToDataFlowGraphPass::Run(DataFlowGraph *graph) {
     o->SetPbMsg(op.SerializeAsString());
 
     // set inputs and outputs
-    std::unordered_set<Node *> inlinks;
     for (int j = 0; j < op.inputs_size(); j++) {
       auto &in_var = op.inputs(j);
       for (int k = 0; k < in_var.arguments_size(); k++) {
         auto *in = graph->nodes.GetMutable(var2id.at(in_var.arguments(k)));
         in->outlinks.push_back(o);
         o->inlinks.push_back(in);
-        inlinks.insert(in);
       }
     }
     for (int j = 0; j < op.outputs_size(); j++) {
       auto &out_var = op.outputs(j);
       for (int k = 0; k < out_var.arguments_size(); k++) {
         auto *out = graph->nodes.GetMutable(var2id[out_var.arguments(k)]);
-        if (inlinks.count(out)) {
+        if (unique_written_vars.count(out)) {
           // Loop found, for example, a = op(a), use SSA, change to a1 = op(a).
           auto *out_alias = graph->nodes.Create(Node::Type::kValue);
           out_alias->SetName(out->name());
           out_alias->SetPbDesc(out->pb_desc());
           out_alias->SetPbMsg(out->pb_msg());
-          var2id[out_alias->name()] = out_alias->id();  // update a -> a0
+          var2id[out_alias->name()] =
+              out_alias->id();  // update variable's alias Node
           LOG(INFO) << "loop found in graph, create SSA alias node ["
                     << out_alias->repr() << "] for [" << out->repr() << "]";
           out = out_alias;
         }
         out->inlinks.push_back(o);
         o->outlinks.push_back(out);
+        unique_written_vars.insert(out);
       }
     }
   }
diff --git a/paddle/fluid/inference/analysis/fluid_to_data_flow_graph_pass.h b/paddle/fluid/inference/analysis/fluid_to_data_flow_graph_pass.h
index da8463b63bd0bb1633bfcb9d7d41a884ddd632c7..fb948bf2242abcbc1e841fd3b8457e63358782c5 100644
--- a/paddle/fluid/inference/analysis/fluid_to_data_flow_graph_pass.h
+++ b/paddle/fluid/inference/analysis/fluid_to_data_flow_graph_pass.h
@@ -30,7 +30,7 @@ namespace inference {
 namespace analysis {
 
 /*
- * Transform a FluidDesc to a data flow graph.
+ * Transform a FluidDesc to a SSA.
  */
 class FluidToDataFlowGraphPass final : public DataFlowGraphPass {
  public: