diff --git a/synapse/storage/databases/state/bg_updates.py b/synapse/storage/databases/state/bg_updates.py
index 5de70f31d294..fa9eadaca7ea 100644
--- a/synapse/storage/databases/state/bg_updates.py
+++ b/synapse/storage/databases/state/bg_updates.py
@@ -195,6 +195,7 @@ class StateBackgroundUpdateStore(StateGroupBackgroundUpdateStore):
     STATE_GROUP_DEDUPLICATION_UPDATE_NAME = "state_group_state_deduplication"
     STATE_GROUP_INDEX_UPDATE_NAME = "state_group_state_type_index"
     STATE_GROUPS_ROOM_INDEX_UPDATE_NAME = "state_groups_room_id_idx"
+    STATE_GROUP_EDGES_UNIQUE_INDEX_UPDATE_NAME = "state_group_edges_unique_idx"
 
     def __init__(
         self,
@@ -217,6 +218,21 @@ def __init__(
             columns=["room_id"],
         )
 
+        # `state_group_edges` can cause severe performance issues if duplicate
+        # rows are introduced, which can accidentally be done by well-meaning
+        # server admins when trying to restore a database dump, etc.
+        # See https://github.com/matrix-org/synapse/issues/11779.
+        # Introduce a unique index to guard against that.
+        self.db_pool.updates.register_background_index_update(
+            self.STATE_GROUP_EDGES_UNIQUE_INDEX_UPDATE_NAME,
+            index_name="state_group_edges_unique_idx",
+            table="state_group_edges",
+            columns=["state_group", "prev_state_group"],
+            unique=True,
+            # The old index was on (state_group) and was not unique.
+            replaces_index="state_group_edges_idx",
+        )
+
     async def _background_deduplicate_state(
         self, progress: dict, batch_size: int
     ) -> int:
diff --git a/synapse/storage/schema/state/delta/70/08_state_group_edges_unique.sql b/synapse/storage/schema/state/delta/70/08_state_group_edges_unique.sql
new file mode 100644
index 000000000000..b8c0ee0fa03e
--- /dev/null
+++ b/synapse/storage/schema/state/delta/70/08_state_group_edges_unique.sql
@@ -0,0 +1,17 @@
+/* Copyright 2022 The Matrix.org Foundation C.I.C
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+INSERT INTO background_updates (ordering, update_name, progress_json) VALUES
+    (7008, 'state_group_edges_unique_idx', '{}');