diff --git a/optax/tree_utils/_tree_math.py b/optax/tree_utils/_tree_math.py
index 96636ec4b..0d671acad 100644
--- a/optax/tree_utils/_tree_math.py
+++ b/optax/tree_utils/_tree_math.py
@@ -152,7 +152,7 @@ def tree_vdot(tree_x: Any, tree_y: Any) -> chex.Numeric:
   numerical issues.
   """
   vdots = jtu.tree_map(_vdot_safe, tree_x, tree_y)
-  return jtu.tree_reduce(operator.add, vdots)
+  return jtu.tree_reduce(operator.add, vdots, 0)
 
 
 def tree_sum(tree: Any) -> chex.Numeric:
@@ -165,7 +165,7 @@ def tree_sum(tree: Any) -> chex.Numeric:
     a scalar value.
   """
   sums = jtu.tree_map(jnp.sum, tree)
-  return jtu.tree_reduce(operator.add, sums)
+  return jtu.tree_reduce(operator.add, sums, 0)
 
 
 def _square(leaf):
diff --git a/optax/tree_utils/_tree_math_test.py b/optax/tree_utils/_tree_math_test.py
index 792e32e33..574c02769 100644
--- a/optax/tree_utils/_tree_math_test.py
+++ b/optax/tree_utils/_tree_math_test.py
@@ -232,6 +232,12 @@ def test_bias_correction_bf16(self):
             tu.tree_bias_correction(m, decay, count),
             custom_message=f'failed with decay={decay}, count={count}')
 
+  def test_empty_tree_reduce(self):
+    # assert False
+    for tree in [{}, (), [], None, {'key': [None, [None]]}]:
+      self.assertEqual(tu.tree_sum(tree), 0)
+      self.assertEqual(tu.tree_vdot(tree, tree), 0)
+
 
 if __name__ == '__main__':
   absltest.main()