diff --git a/comfy_execution/graph.py b/comfy_execution/graph.py
index b53e10f3..0b5bf189 100644
--- a/comfy_execution/graph.py
+++ b/comfy_execution/graph.py
@@ -99,30 +99,44 @@ class TopologicalSort:
         self.add_strong_link(from_node_id, from_socket, to_node_id)
 
     def add_strong_link(self, from_node_id, from_socket, to_node_id):
-        self.add_node(from_node_id)
-        if to_node_id not in self.blocking[from_node_id]:
-            self.blocking[from_node_id][to_node_id] = {}
-            self.blockCount[to_node_id] += 1
-        self.blocking[from_node_id][to_node_id][from_socket] = True
+        if not self.is_cached(from_node_id):
+            self.add_node(from_node_id)
+            if to_node_id not in self.blocking[from_node_id]:
+                self.blocking[from_node_id][to_node_id] = {}
+                self.blockCount[to_node_id] += 1
+            self.blocking[from_node_id][to_node_id][from_socket] = True
 
-    def add_node(self, unique_id, include_lazy=False, subgraph_nodes=None):
-        if unique_id in self.pendingNodes:
-            return
-        self.pendingNodes[unique_id] = True
-        self.blockCount[unique_id] = 0
-        self.blocking[unique_id] = {}
+    def add_node(self, node_unique_id, include_lazy=False, subgraph_nodes=None):
+        node_ids = [node_unique_id]
+        links = []
 
-        inputs = self.dynprompt.get_node(unique_id)["inputs"]
-        for input_name in inputs:
-            value = inputs[input_name]
-            if is_link(value):
-                from_node_id, from_socket = value
-                if subgraph_nodes is not None and from_node_id not in subgraph_nodes:
-                    continue
-                input_type, input_category, input_info = self.get_input_info(unique_id, input_name)
-                is_lazy = input_info is not None and "lazy" in input_info and input_info["lazy"]
-                if include_lazy or not is_lazy:
-                    self.add_strong_link(from_node_id, from_socket, unique_id)
+        while len(node_ids) > 0:
+            unique_id = node_ids.pop()
+            if unique_id in self.pendingNodes:
+                continue
+
+            self.pendingNodes[unique_id] = True
+            self.blockCount[unique_id] = 0
+            self.blocking[unique_id] = {}
+
+            inputs = self.dynprompt.get_node(unique_id)["inputs"]
+            for input_name in inputs:
+                value = inputs[input_name]
+                if is_link(value):
+                    from_node_id, from_socket = value
+                    if subgraph_nodes is not None and from_node_id not in subgraph_nodes:
+                        continue
+                    input_type, input_category, input_info = self.get_input_info(unique_id, input_name)
+                    is_lazy = input_info is not None and "lazy" in input_info and input_info["lazy"]
+                    if (include_lazy or not is_lazy) and not self.is_cached(from_node_id):
+                        node_ids.append(from_node_id)
+                        links.append((from_node_id, from_socket, unique_id))
+                        
+        for link in links:
+            self.add_strong_link(*link)
+
+    def is_cached(self, node_id):
+        return False
 
     def get_ready_nodes(self):
         return [node_id for node_id in self.pendingNodes if self.blockCount[node_id] == 0]
@@ -146,11 +160,8 @@ class ExecutionList(TopologicalSort):
         self.output_cache = output_cache
         self.staged_node_id = None
 
-    def add_strong_link(self, from_node_id, from_socket, to_node_id):
-        if self.output_cache.get(from_node_id) is not None:
-            # Nothing to do
-            return
-        super().add_strong_link(from_node_id, from_socket, to_node_id)
+    def is_cached(self, node_id):
+        return self.output_cache.get(node_id) is not None
 
     def stage_node_execution(self):
         assert self.staged_node_id is None