diff --git a/onnxscript/rewriter/_matcher.py b/onnxscript/rewriter/_matcher.py
index 4993fe8232..a007926c37 100644
--- a/onnxscript/rewriter/_matcher.py
+++ b/onnxscript/rewriter/_matcher.py
@@ -183,6 +183,16 @@ def _match_value(
         self, pattern_value: _pattern_ir.ValuePattern, value: ir.Value | None
     ) -> bool:
         """Match an IR value against a ValuePattern instance."""
+        if value is not None and value.graph is not self._graph_or_function:
+            if not isinstance(
+                pattern_value, (_pattern_ir.Var, _pattern_ir.Constant, _pattern_ir.AnyValue)
+            ):
+                # If the pattern value is a Var, Constant, or AnyValue, we allow it to match
+                # values from other graphs. Otherwise, we fail the match.
+                return self.fail(
+                    f"Value {value.name} is not in the graph {self._graph_or_function.name}. "
+                    f"Pattern matches crossing graph boundaries are not supported."
+                )
         if isinstance(pattern_value, _pattern_ir.AnyValue):
             return True
 
@@ -352,6 +362,7 @@ def match(
         complications which require careful consideration.
         """
         self._tracer = tracer
+        self._graph_or_function = graph_or_function[0].graph
         if self.pattern.has_single_output_node:
             self._init_match(verbose)
             return self._match_single_output_node(
diff --git a/onnxscript/rewriter/_rewrite_rule.py b/onnxscript/rewriter/_rewrite_rule.py
index a2ec410e5b..9481ca5077 100644
--- a/onnxscript/rewriter/_rewrite_rule.py
+++ b/onnxscript/rewriter/_rewrite_rule.py
@@ -736,6 +736,18 @@ def _apply_to_graph_or_function(
                 count += 1
                 break
 
+            # Apply rewrite rules to subgraphs of the node.
+            for attr in node.attributes.values():
+                if attr.type == ir.AttributeType.GRAPH:
+                    count += self._apply_to_graph_or_function(
+                        model, attr.value, verbose=verbose, tracer=tracer
+                    )
+                elif attr.type == ir.AttributeType.GRAPHS:
+                    for graph in attr.value:
+                        count += self._apply_to_graph_or_function(
+                            model, graph, verbose=verbose, tracer=tracer
+                        )
+
         for rule in self.rules:
             if rule.graph_post_visitor:
                 rule.graph_post_visitor()