diff --git a/keras_core/random/random_test.py b/keras_core/random/random_test.py
index 27007892b..009de3798 100644
--- a/keras_core/random/random_test.py
+++ b/keras_core/random/random_test.py
@@ -1,6 +1,8 @@
 import numpy as np
+import pytest
 from absl.testing import parameterized
 
+import keras_core
 from keras_core import testing
 from keras_core.operations import numpy as knp
 from keras_core.random import random
@@ -61,3 +63,23 @@ class RandomTest(testing.TestCase, parameterized.TestCase):
         x_res = random.dropout(x, rate=0.8, seed=0)
         self.assertGreater(knp.max(x_res), knp.max(x))
         self.assertGreater(knp.sum(x_res == 0), 2)
+
+    @pytest.mark.skipif(
+        keras_core.backend.backend() != "jax",
+        reason="This test requires `jax` as the backend.",
+    )
+    def test_dropout_jax_jit_stateless(self):
+        import jax
+        import jax.numpy as jnp
+
+        x = knp.ones(3)
+
+        @jax.jit
+        def train_step(x):
+            with keras_core.backend.StatelessScope():
+                x = keras_core.layers.Dropout(rate=0.1)(x, training=True)
+            return x
+
+        keras_core.utils.traceback_utils.disable_traceback_filtering()
+        x = train_step(x)
+        assert isinstance(x, jnp.ndarray)
diff --git a/keras_core/random/seed_generator.py b/keras_core/random/seed_generator.py
index 645070e35..f94b104c7 100644
--- a/keras_core/random/seed_generator.py
+++ b/keras_core/random/seed_generator.py
@@ -16,7 +16,10 @@ class SeedGenerator:
             )
 
         def seed_initializer(*args, **kwargs):
-            return [seed, 0]
+            from keras_core.backend import convert_to_tensor
+
+            dtype = kwargs.get("dtype", None)
+            return convert_to_tensor([seed, 0], dtype=dtype)
 
         self.state = Variable(
             seed_initializer,