diff --git a/keras_core/backend/jax/trainer.py b/keras_core/backend/jax/trainer.py
index 77c59eb36..7b605f40d 100644
--- a/keras_core/backend/jax/trainer.py
+++ b/keras_core/backend/jax/trainer.py
@@ -1,3 +1,5 @@
+from functools import partial
+
 import jax
 import numpy as np
 import tree
@@ -237,8 +239,11 @@ def multi_train_steps(state, data):
             train_step = one_train_step
 
         if not self.run_eagerly and self.jit_compile:
-
-            @jax.jit
+            # Note that we mark the state and data to be donated to jax,
+            # so that jax will reuse the memory buffer for outputs.
+            # This will reduce the memory usage of the training function by
+            # half.
+            @partial(jax.jit, donate_argnames="state")
             def compiled_train_step(state, data):
                 return train_step(state, data)
 
@@ -266,8 +271,11 @@ def multi_test_steps(state, data):
             test_step = one_test_step
 
         if not self.run_eagerly and self.jit_compile:
-
-            @jax.jit
+            # Note that we mark the state and data to be donated to jax,
+            # so that jax will reuse the memory buffer for outputs.
+            # This will reduce the memory usage of the training function by
+            # half.
+            @partial(jax.jit, donate_argnames="state")
             def compiled_test_step(state, data):
                 return test_step(state, data)
 
@@ -578,15 +586,18 @@ def evaluate(
             )
             data = self._distribute_data(data)
             logs, state = self.test_function(state, data)
-            # Note that trainable variables are not returned since they're
-            # immutable here.
-            _, non_trainable_variables, metrics_variables = state
+            (
+                trainable_variables,
+                non_trainable_variables,
+                metrics_variables,
+            ) = state
 
             # Setting _jax_state enables callbacks to force a state sync
             # if they need to.
             self._jax_state = {
                 # I wouldn't recommend modifying non-trainable model state
                 # during evaluate(), but it's allowed.
+                "trainable_variables": trainable_variables,
                 "non_trainable_variables": non_trainable_variables,
                 "metrics_variables": metrics_variables,
             }
@@ -764,8 +775,9 @@ def test_on_batch(
         logs, state = self.test_function(state, [data])
 
         # State sync
-        _, non_trainable_variables, metrics_variables = state
+        trainable_variables, non_trainable_variables, metrics_variables = state
         self._jax_state = {
+            "trainable_variables": trainable_variables,
             "non_trainable_variables": non_trainable_variables,
             "metrics_variables": metrics_variables,
         }