diff --git a/jax/_src/lax/lax.py b/jax/_src/lax/lax.py
index 5f9b8778bfdc..b980391193df 100644
--- a/jax/_src/lax/lax.py
+++ b/jax/_src/lax/lax.py
@@ -2113,6 +2113,7 @@ def _naryop_weak_type_rule(name, *avals, **kwargs):
   return all(aval.weak_type for aval in avals)
 
 def naryop(result_dtype, accepted_dtypes, name, translation_rule=None):
+  # TODO(frostig,mattjj): only used with arity > 2 once, simplify
   dtype_rule = partial(naryop_dtype_rule, result_dtype, accepted_dtypes, name)
   shape_rule = partial(_broadcasting_shape_rule, name)
   weak_type_rule = partial(_naryop_weak_type_rule, name)
diff --git a/jax/interpreters/batching.py b/jax/interpreters/batching.py
index 86f6e4553e21..c81edef7948f 100644
--- a/jax/interpreters/batching.py
+++ b/jax/interpreters/batching.py
@@ -331,7 +331,8 @@ def broadcast_batcher(prim, args, dims, **params):
     return (out, (d,) * len(out)) if prim.multiple_results else (out, d)
   else:
     size, = {shape[d] for shape, d in shapes if d is not not_mapped}
-    args = [bdim_at_front(x, d, size) for x, d in zip(args, dims)]
+    args = [bdim_at_front(x, d, size) if np.ndim(x) else x
+            for x, d in zip(args, dims)]
     ndim = max(np.ndim(x) for x in args)  # special-case scalar broadcasting
     args = [_handle_scalar_broadcasting(ndim, x, d) for x, d in zip(args, dims)]
     out = prim.bind(*args, **params)
diff --git a/tests/batching_test.py b/tests/batching_test.py
index 9aec166b9a93..03f463f3d174 100644
--- a/tests/batching_test.py
+++ b/tests/batching_test.py
@@ -21,6 +21,7 @@
 
 import jax
 import jax.numpy as jnp
+import jax.scipy as jsp
 from jax import test_util as jtu
 from jax import lax
 from jax._src.lax import parallel
@@ -1240,5 +1241,13 @@ def testNonJaxTypedOutput(self):
       TypeError, "Output from batched function.*is not a valid JAX type"):
       vmap(lambda x: "hello")(np.arange(5))
 
+  def testIssue6096(self):
+    def f(x):
+      return jsp.special.betainc(jnp.ones(3), 1., x)
+
+    self.assertEquals(f(jnp.ones(3)).shape, (3,))
+    self.assertEquals(jax.vmap(f)(jnp.ones((2, 3))).shape, (2, 3))
+
+
 if __name__ == '__main__':
   absltest.main(testLoader=jtu.JaxTestLoader())