diff --git a/aesara/tensor/extra_ops.py b/aesara/tensor/extra_ops.py
index 03e6fffbf3..28b54ba75c 100644
--- a/aesara/tensor/extra_ops.py
+++ b/aesara/tensor/extra_ops.py
@@ -23,6 +23,7 @@
 from aesara.raise_op import Assert
 from aesara.scalar import int32 as int_t
 from aesara.scalar import upcast
+from aesara.scalar.basic import Composite
 from aesara.tensor import basic as at
 from aesara.tensor import get_vector_length
 from aesara.tensor.exceptions import NotScalarConstantError
@@ -1552,16 +1553,29 @@ def broadcast_shape_iter(
                     # be broadcastable or equal to the one non-broadcastable
                     # constant `const_nt_shape_var`.
                     assert_dim = Assert("Could not broadcast dimensions")
+
+                    scalar_nonconst_nb_shapes = [
+                        at.scalar_from_tensor(s) if isinstance(s, TensorVariable) else s
+                        for s in nonconst_nb_shapes
+                    ]
+
+                    dummy_nonconst_nb_shapes = [
+                        v.type() for v in scalar_nonconst_nb_shapes
+                    ]
                     assert_cond = reduce(
                         aes.and_,
                         (
                             aes.or_(
                                 aes.eq(nbv, one_at), aes.eq(nbv, const_nt_shape_var)
                             )
-                            for nbv in nonconst_nb_shapes
+                            for nbv in dummy_nonconst_nb_shapes
                         ),
                     )
-                    bcast_dim = assert_dim(const_nt_shape_var, assert_cond)
+                    assert_cond_op = Composite(dummy_nonconst_nb_shapes, [assert_cond])
+
+                    bcast_dim = assert_dim(
+                        const_nt_shape_var, assert_cond_op(*scalar_nonconst_nb_shapes)
+                    )
                 else:
                     bcast_dim = const_nt_shape_var
             else:
@@ -1579,21 +1593,36 @@ def broadcast_shape_iter(
                     result_dims.append(maybe_non_bcast_shapes[0])
                     continue
 
+                scalar_maybe_non_bcast_shapes = [
+                    at.scalar_from_tensor(s) if isinstance(s, TensorVariable) else s
+                    for s in maybe_non_bcast_shapes
+                ]
+                dummy_maybe_non_bcast_shapes = [
+                    v.type() for v in scalar_maybe_non_bcast_shapes
+                ]
                 non_bcast_vec = [
                     aes.switch(aes.eq(nbv, 1), -one_at, nbv)
-                    for nbv in maybe_non_bcast_shapes
+                    for nbv in dummy_maybe_non_bcast_shapes
                 ]
                 dim_max = aes.abs(reduce(aes.scalar_maximum, non_bcast_vec))
+                dim_max_op = Composite(dummy_maybe_non_bcast_shapes, [dim_max])
+
+                dummy_dim_max = dim_max_op(*dummy_maybe_non_bcast_shapes)
 
                 assert_dim = Assert("Could not broadcast dimensions")
                 assert_cond = reduce(
                     aes.and_,
                     (
-                        aes.or_(aes.eq(nbv, -one_at), aes.eq(nbv, dim_max))
+                        aes.or_(aes.eq(nbv, -one_at), aes.eq(nbv, dummy_dim_max))
                         for nbv in non_bcast_vec
                     ),
                 )
-                bcast_dim = assert_dim(dim_max, assert_cond)
+                assert_cond_op = Composite(dummy_maybe_non_bcast_shapes, [assert_cond])
+
+                bcast_dim = assert_dim(
+                    dim_max_op(*scalar_maybe_non_bcast_shapes),
+                    assert_cond_op(*scalar_maybe_non_bcast_shapes),
+                )
 
             result_dims.append(bcast_dim)