diff --git a/src/inspect_robots/approver.py b/src/inspect_robots/approver.py
index 6aaa51b9..90bbebf1 100644
--- a/src/inspect_robots/approver.py
+++ b/src/inspect_robots/approver.py
@@ -252,14 +252,18 @@ def rewind_reference(store: dict[str, Any], pose: npt.NDArray[np.float64]) -> No
         the limiter measures subsequent deltas from the pose that actually ran.
         If the limiter has not established a reference, this is a no-op.
         """
-        if _LAST_APPROVED_KEY in store:
+        if _LAST_APPROVED_KEY in store and bool(np.all(np.isfinite(pose))):
             store[_LAST_APPROVED_KEY] = pose.copy()
 
     def review(self, action: Action, store: dict[str, Any]) -> Action:
         """Limit per-step change, retaining absolute-mode history in trial state."""
         data = np.asarray(action.data, dtype=np.float64)
-        if bool(np.isnan(data).any()):
-            raise SafetyAbort("DeltaLimitApprover: action contains NaN; refusing to pass it on")
+        if not bool(np.all(np.isfinite(data))):
+            raise SafetyAbort(
+                "DeltaLimitApprover: action contains NaN or non-finite values; "
+                "refusing to pass it on"
+            )
+
         if self._absolute:
             reference = store.get(_LAST_APPROVED_KEY)
             if reference is None:
diff --git a/tests/test_approvers.py b/tests/test_approvers.py
index 8741e491..b4a20c58 100644
--- a/tests/test_approvers.py
+++ b/tests/test_approvers.py
@@ -208,6 +208,16 @@ def test_rewind_reference_uses_the_limiter_store_key() -> None:
     assert np.array_equal(reference, np.array([0.3, 0.4]))
 
 
+def test_delta_limit_approver_rejects_inf() -> None:
+    approver = DeltaLimitApprover(_abs_space(), max_delta=0.1)
+    store: dict[str, object] = {}
+    with pytest.raises(SafetyAbort, match="non-finite"):
+        approver.review(Action(data=np.array([float("inf"), 0.0])), store)
+
+    with pytest.raises(SafetyAbort, match="non-finite"):
+        approver.review(Action(data=np.array([0.0, float("-inf")])), store)
+
+
 def test_substitution_rewinds_the_next_delta_reference() -> None:
     held = Action(data=np.array([0.0, 0.0]))