diff --git a/CHANGELOG.md b/CHANGELOG.md
index b6d0f97f4..92dcfe6cc 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,7 +10,14 @@ Remember to align the itemized text with the first line of an item within a list
 When releasing, please add the new-release-boilerplate to docs/pallas/CHANGELOG.md.
 -->
 
-## jax 0.4.36
+## jax 0.4.37
+
+* Bug fixes
+  * Fix a bug that will throw `index out of range` error in
+    {func}`jax.lax.while_loop` if the user register pytree node class with
+    different aux data for the flatten and flatten_with_path.
+
+## jax 0.4.36 (Dec 5, 2024)
 
 * Breaking Changes
   * This release lands "stackless", an internal change to JAX's tracing
diff --git a/jax/_src/lax/control_flow/loops.py b/jax/_src/lax/control_flow/loops.py
index f62ce2434..9b2d688c3 100644
--- a/jax/_src/lax/control_flow/loops.py
+++ b/jax/_src/lax/control_flow/loops.py
@@ -376,6 +376,9 @@ def _check_carry_type(name, body_fun, in_carry, out_carry_tree, out_avals):
                f'of the carry output is a {thing2}, so {explanation}'
                for path, thing1, thing2, explanation
                in equality_errors(in_carry, out_carry)]
+      if len(diffs) == 0:
+        # The trees may have different aux data but structures are the same.
+        return
       if len(diffs) == 1:
         differences = f'{diffs[0]}.\n'.capitalize()
       else:
@@ -393,6 +396,9 @@ def _check_carry_type(name, body_fun, in_carry, out_carry_tree, out_avals):
              f'{out_aval.str_short()}{_aval_mismatch_extra(in_aval, out_aval)}'
              for path, in_aval, out_aval in zip(paths, in_avals, out_avals)
              if not core.typematch(in_aval, out_aval)]
+    if len(diffs) == 0:
+      # The trees may have different aux data but structures are the same.
+      return
     if len(diffs) == 1:
       differences = f'{diffs[0]}.\n'.capitalize()
     else:
diff --git a/tests/lax_control_flow_test.py b/tests/lax_control_flow_test.py
index d383e4c6a..4b0420fda 100644
--- a/tests/lax_control_flow_test.py
+++ b/tests/lax_control_flow_test.py
@@ -322,6 +322,19 @@ class LaxControlFlowTest(jtu.JaxTestCase):
       lax.while_loop(lambda c: True, lambda c: (True, True),
                      (np.bool_(True), np.float32(0.)))
 
+  def testWhileLoopCustomPytreeDiffAuxData(self):
+    class Node:
+      def __init__(self, x, y):
+        self.x = x
+        self.y = y
+    tree_util.register_pytree_with_keys(
+        Node,
+        lambda o: ((("x", o.x), ("y", o.y)), 'with_keys'),  # flatten_with_keys
+        lambda _, xy: Node(xy[0], xy[1]),   # unflatten (no key involved)
+        lambda o: ((o.x, o.y), 'without_keys'),    # flatten
+    )
+    lax.while_loop(lambda o: o.x > 0., lambda c: Node(0., 0.), Node(1., 1.))
+
   def testNestedWhileWithDynamicUpdateSlice(self):
     num = 5