diff --git a/test/scan/test_scan.py b/test/scan/test_scan.py
index b61d8648fa2d..6023f302e8e9 100644
--- a/test/scan/test_scan.py
+++ b/test/scan/test_scan.py
@@ -75,12 +75,16 @@ def run_test(self,
             if v is not None else 0, tree_leaves(t)), torch.tensor(0.0))
     dupe = lambda v: v.detach().clone().requires_grad_(v.requires_grad)
 
+    def _requires_grad(tensors):
+      return any(tree_flatten(tree_map(lambda v: v.requires_grad, tensors))[0])
+
     # Actual output
     init_scan = tree_map(dupe, init)
     xs_scan = tree_map(dupe, xs)
     final_carry, ys = scan(fn, init_scan, xs_scan, partition_fn=partition_fn)
     # Add up all leaves and `backward()` once.
-    (squish(final_carry) + squish(ys)).backward()
+    if _requires_grad(final_carry) or _requires_grad(ys):
+      (squish(final_carry) + squish(ys)).backward()
     torch_xla.sync()
 
     # Expected output
@@ -88,7 +92,8 @@ def run_test(self,
     xs_loop = tree_map(dupe, xs)
     expected_final_carry, expected_ys = _loopy_scan(fn, init_loop, xs_loop)
     # Add up all leaves and `backward()` once.
-    (squish(expected_final_carry) + squish(expected_ys)).backward()
+    if _requires_grad(expected_final_carry) or _requires_grad(expected_ys):
+      (squish(expected_final_carry) + squish(expected_ys)).backward()
     torch_xla.sync()
 
     # Compare values
@@ -126,6 +131,31 @@ def step_fn(carry, x):
     self.compare_pytree(expected_final_carry, final_carry)
     self.compare_pytree(expected_ys, ys)
 
+  def test_scan_long_tensor(self):
+    """This test uses `scan` to implement `torch.cumsum`."""
+
+    def step_fn(carry, x):
+      new_carry = carry + x
+      y = new_carry
+      return new_carry, y
+
+    init = torch.tensor([0.0, 0.0],
+                        requires_grad=False,
+                        device=self.device,
+                        dtype=torch.long)
+    xs = torch.tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]],
+                      requires_grad=False,
+                      dtype=torch.long,
+                      device=self.device)
+    final_carry, ys = self.run_test(step_fn, init, xs)
+
+    # Also ensure that our loop-based scan is correct, with manual checks
+    # that replicate the step_fn.
+    expected_final_carry = torch.sum(xs, dim=0) + init
+    expected_ys = torch.cumsum(xs, dim=0)
+    self.compare_pytree(expected_final_carry, final_carry)
+    self.compare_pytree(expected_ys, ys)
+
   def test_scan_fn_not_callable(self):
     init = torch.tensor([1.0, 1.0], device=self.device)
     xs = torch.tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]], device=self.device)
diff --git a/torch_xla/experimental/scan.py b/torch_xla/experimental/scan.py
index c517e252c163..df4d6c3fa543 100644
--- a/torch_xla/experimental/scan.py
+++ b/torch_xla/experimental/scan.py
@@ -229,7 +229,8 @@ def make_fake_tensor(v: torch.Tensor, requires_grad=True) -> torch.Tensor:
     return torch.empty_like(
         v, dtype=v.dtype, device=v.device, requires_grad=requires_grad)
 
-  fake_carry_pytree = tree_map(make_fake_tensor, init)
+  fake_carry_pytree = tree_map(
+      lambda v: make_fake_tensor(v, requires_grad=v.is_floating_point()), init)
   fake_x_pytree = tree_map(
       lambda v: make_fake_tensor(v[0], requires_grad=v.requires_grad), xs)
 
@@ -261,11 +262,15 @@ def fn_no_output_aliasing(*args):
     # intermediate activations.
     num_out = len(list(tree_iter(out)))
     # Capture the backward.
-    out, unflatten_fwd_out = tree_flatten_none(out)
-    torch.autograd.backward(out, tree_map(lambda v: torch.ones_like(v), out))
+    flat_out, unflatten_fwd_out = tree_flatten_none(out)
+    out_with_grad = list(filter(lambda v: v.requires_grad, flat_out))
+    if len(out_with_grad) > 0:
+      torch.autograd.backward(
+          out_with_grad, tree_map(lambda v: torch.ones_like(v), out_with_grad))
 
   fwd_graph = get_fwd()
-  bwd_graph = get_bwd()
+  if len(out_with_grad) > 0:
+    bwd_graph = get_bwd()
 
   # Figure out which activations are aliases to the inputs. We don't need to
   # pass them through the scan logic unchanged. That would use more memory.
@@ -320,6 +325,8 @@ def alias_input(partial_activations, xs):
     return tuple(activations)
 
   def backward(carry, x):
+    if len(out_with_grad) == 0:
+      return None, None
     grad_new_carry, _ = tree_flatten(carry)
     (grad_y, activations) = x
     grad_y, _ = tree_flatten_none(grad_y)