diff --git a/pytensor/scan/op.py b/pytensor/scan/op.py
index 2c3f404449..c1ae4db04d 100644
--- a/pytensor/scan/op.py
+++ b/pytensor/scan/op.py
@@ -1647,8 +1647,9 @@ def rval(
             p=p, i=node_input_storage, o=node_output_storage, n=node, allow_gc=allow_gc
         ):
             r = p(n, [x[0] for x in i], o)
-            for o in node.outputs:
-                compute_map[o][0] = True
+            if compute_map is not None:
+                for o in node.outputs:
+                    compute_map[o][0] = True
             if allow_gc:
                 self.fn.free()
             return r
diff --git a/tests/scan/test_basic.py b/tests/scan/test_basic.py
index 351c2e703a..896d131f57 100644
--- a/tests/scan/test_basic.py
+++ b/tests/scan/test_basic.py
@@ -27,6 +27,7 @@
 from pytensor.compile.sharedvalue import shared
 from pytensor.configdefaults import config
 from pytensor.gradient import NullTypeGradError, Rop, disconnected_grad, grad, hessian
+from pytensor.graph import vectorize_graph
 from pytensor.graph.basic import Apply, ancestors, equal_computations
 from pytensor.graph.fg import FunctionGraph
 from pytensor.graph.op import Op
@@ -1178,6 +1179,17 @@ def get_sum_of_grad(input0, input1):
 
         utt.verify_grad(get_sum_of_grad, inputs_test_values, rng=rng)
 
+    def test_blockwise_scan(self):
+        x = pt.tensor("x", shape=())
+        out, _ = scan(lambda x: x + 1, outputs_info=[x], n_steps=10)
+        x_vec = pt.tensor("x_vec", shape=(None,))
+        out_vec = vectorize_graph(out, {x: x_vec})
+
+        fn = function([x_vec], out_vec)
+        o1 = fn([1, 2, 3])
+        o2 = np.arange(2, 12) + np.arange(3).reshape(-1, 1)
+        assert np.allclose(o1, o2)
+
     def test_connection_pattern(self):
         """Test `Scan.connection_pattern` in the presence of recurrent outputs with multiple taps."""