diff --git a/invokeai/app/services/shared/graph.py b/invokeai/app/services/shared/graph.py
index e3941d9ca3..cc2ea5cedb 100644
--- a/invokeai/app/services/shared/graph.py
+++ b/invokeai/app/services/shared/graph.py
@@ -1043,23 +1043,32 @@ class GraphExecutionState(BaseModel):
         """Gets the deepest node that is ready to be executed"""
         g = self.execution_graph.nx_graph()
 
-        # Depth-first search with pre-order traversal is a depth-first topological sort
-        sorted_nodes = nx.dfs_preorder_nodes(g)
+        # Perform a topological sort using depth-first search
+        topo_order = list(nx.dfs_postorder_nodes(g))
 
-        next_node = next(
-            (
-                n
-                for n in sorted_nodes
-                if n not in self.executed  # the node must not already be executed...
-                and all((e[0] in self.executed for e in g.in_edges(n)))  # ...and all its inputs must be executed
-            ),
-            None,
-        )
+        # Get all IterateInvocation nodes
+        iterate_nodes = [n for n in topo_order if isinstance(self.execution_graph.nodes[n], IterateInvocation)]
 
-        if next_node is None:
-            return None
+        # Sort the IterateInvocation nodes based on their index attribute
+        iterate_nodes.sort(key=lambda x: self.execution_graph.nodes[x].index)
 
-        return self.execution_graph.nodes[next_node]
+        # Prioritize IterateInvocation nodes and their children
+        for iterate_node in iterate_nodes:
+            if iterate_node not in self.executed and all((e[0] in self.executed for e in g.in_edges(iterate_node))):
+                return self.execution_graph.nodes[iterate_node]
+
+            # Check the children of the IterateInvocation node
+            for child_node in nx.dfs_postorder_nodes(g, iterate_node):
+                if child_node not in self.executed and all((e[0] in self.executed for e in g.in_edges(child_node))):
+                    return self.execution_graph.nodes[child_node]
+
+        # If no IterateInvocation node or its children are ready, return the first ready node in the topological order
+        for node in topo_order:
+            if node not in self.executed and all((e[0] in self.executed for e in g.in_edges(node))):
+                return self.execution_graph.nodes[node]
+
+        # If no node is found, return None
+        return None
 
     def _prepare_inputs(self, node: BaseInvocation):
         input_edges = [e for e in self.execution_graph.edges if e.destination.node_id == node.id]