diff --git a/src/gfn/containers/replay_buffer_manager.py b/src/gfn/containers/replay_buffer_manager.py
index 32e500f3..53465812 100644
--- a/src/gfn/containers/replay_buffer_manager.py
+++ b/src/gfn/containers/replay_buffer_manager.py
@@ -142,10 +142,31 @@ def _apply_baseline_sync(self, msg) -> None:
 
         Sent by a coordinator aggregating local baselines across buffer
         managers.  The manager doesn't need to know who sent it or why.
+
+        A malformed message is an error, not a no-op: the adopted value
+        gates what every assigned worker sends, so a manager that quietly
+        keeps its shard-local threshold filters against a different cutoff
+        from its siblings — the exact condition this message exists to
+        remove, and one that leaves no trace in the run.
         """
-        global_baseline = msg.message_data.get("global_baseline_log_reward")
-        if global_baseline is not None:
-            self._global_baseline = float(global_baseline)
+        if not isinstance(msg.message_data, dict):
+            raise ValueError(
+                "BASELINE_SYNC message_data must be a dict, got "
+                f"{type(msg.message_data).__name__}"
+            )
+        value = msg.message_data.get("global_baseline_log_reward")
+        if value is None:
+            raise ValueError(
+                "BASELINE_SYNC has no usable 'global_baseline_log_reward'; "
+                f"message_data={msg.message_data}"
+            )
+        global_baseline = float(value)
+        if not math.isfinite(global_baseline):
+            raise ValueError(
+                f"BASELINE_SYNC global_baseline_log_reward is {global_baseline}; "
+                "a non-finite baseline keeps every trajectory or none"
+            )
+        self._global_baseline = global_baseline
 
     def _inject_baseline_log_reward(
         self, score_dict: dict[str, float], incoming
diff --git a/testing/test_replay_buffer.py b/testing/test_replay_buffer.py
index 45d0b3fe..2fdefd69 100644
--- a/testing/test_replay_buffer.py
+++ b/testing/test_replay_buffer.py
@@ -790,7 +790,19 @@ def test_manager_baseline_sync_overrides_local(simple_env, trajectories):
     assert score["baseline_log_reward"] == pytest.approx(-7.5)
 
 
-def test_manager_baseline_sync_ignores_missing_payload(simple_env, trajectories):
+@pytest.mark.parametrize(
+    "payload",
+    [
+        {},
+        {"global_baseline_log_reward": None},
+        {"global_baseline_log_reward": float("-inf")},
+        None,
+    ],
+    ids=["missing", "none", "non_finite", "not_a_dict"],
+)
+def test_manager_baseline_sync_rejects_malformed_payload(simple_env, payload):
+    # Keeping the shard-local threshold on a malformed sync is the
+    # inconsistency this message exists to remove, and it leaves no trace.
     mgr = ReplayBufferManager(
         simple_env,
         rank=0,
@@ -798,10 +810,9 @@ def test_manager_baseline_sync_ignores_missing_payload(simple_env, trajectories)
         capacity=5,
         store_locally=False,
     )
-    mgr._apply_baseline_sync(Message(MessageType.BASELINE_SYNC, {}))
-    score: dict = {"score": 0.0}
-    mgr._inject_baseline_log_reward(score, trajectories)
-    assert score["baseline_log_reward"] == pytest.approx(0.0)  # falls back to EMA.
+    with pytest.raises(ValueError, match="BASELINE_SYNC"):
+        mgr._apply_baseline_sync(Message(MessageType.BASELINE_SYNC, payload))
+    assert mgr._global_baseline is None
 
 
 def test_manager_multi_manager_baseline_warning(simple_env):