diff --git a/keras_core/backend/torch/optimizers/torch_adadelta.py b/keras_core/backend/torch/optimizers/torch_adadelta.py
new file mode 100644
index 000000000..a05a6cbf1
--- /dev/null
+++ b/keras_core/backend/torch/optimizers/torch_adadelta.py
@@ -0,0 +1,56 @@
+import torch
+
+from keras_core import ops
+from keras_core import optimizers
+from keras_core.backend.torch.optimizers import torch_parallel_optimizer
+
+
+class Adadelta(
+    torch_parallel_optimizer.TorchParallelOptimizer, optimizers.Adadelta
+):
+    def _parallel_update_step(
+        self,
+        grads,
+        variables,
+        learning_rate,
+    ):
+        keras_variables = variables
+        variables = [v.value for v in variables]
+
+        dtype = variables[0].dtype
+        lr = ops.cast(learning_rate, dtype)
+        rho = self.rho
+
+        accumulated_grads = [
+            self._accumulated_grads[self._get_variable_index(variable)].value
+            for variable in keras_variables
+        ]
+        accumulated_delta_vars = [
+            self._accumulated_delta_vars[
+                self._get_variable_index(variable)
+            ].value
+            for variable in keras_variables
+        ]
+        torch._foreach_mul_(accumulated_grads, rho)
+        torch._foreach_add_(
+            accumulated_grads, torch._foreach_mul(grads, grads), alpha=1 - rho
+        )
+
+        def rms(x):
+            return torch._foreach_sqrt(torch._foreach_add(x, self.epsilon))
+
+        delta_vars = torch._foreach_mul(
+            torch._foreach_div(
+                torch._foreach_mul(rms(accumulated_delta_vars), grads),
+                rms(accumulated_grads),
+            ),
+            -1,
+        )
+        torch._foreach_mul_(accumulated_delta_vars, rho)
+        torch._foreach_add_(
+            accumulated_delta_vars,
+            torch._foreach_mul(delta_vars, delta_vars),
+            alpha=1 - rho,
+        )
+
+        torch._foreach_add_(variables, delta_vars, alpha=lr)
diff --git a/keras_core/backend/torch/optimizers/torch_optimizer.py b/keras_core/backend/torch/optimizers/torch_optimizer.py
index 81f5d0f2f..ca83cd84b 100644
--- a/keras_core/backend/torch/optimizers/torch_optimizer.py
+++ b/keras_core/backend/torch/optimizers/torch_optimizer.py
@@ -7,12 +7,14 @@ from keras_core.optimizers.base_optimizer import BaseOptimizer
 class TorchOptimizer(BaseOptimizer):
     def __new__(cls, *args, **kwargs):
         # Import locally to avoid circular imports.
+        from keras_core.backend.torch.optimizers import torch_adadelta
         from keras_core.backend.torch.optimizers import torch_adam
         from keras_core.backend.torch.optimizers import torch_adamw
         from keras_core.backend.torch.optimizers import torch_rmsprop
         from keras_core.backend.torch.optimizers import torch_sgd
 
         OPTIMIZERS = {
+            optimizers.Adadelta: torch_adadelta.Adadelta,
             optimizers.Adam: torch_adam.Adam,
             optimizers.AdamW: torch_adamw.AdamW,
             optimizers.RMSprop: torch_rmsprop.RMSprop,
diff --git a/keras_core/backend/torch/optimizers/torch_rmsprop.py b/keras_core/backend/torch/optimizers/torch_rmsprop.py
index 63b865c15..5b6afb41f 100644
--- a/keras_core/backend/torch/optimizers/torch_rmsprop.py
+++ b/keras_core/backend/torch/optimizers/torch_rmsprop.py
@@ -57,9 +57,8 @@ class RMSprop(
                 self._momentums[self._get_variable_index(variable)].value
                 for variable in keras_variables
             ]
-            momentum_list = torch._foreach_add(
-                increments, momentum_list, alpha=self.momentum
-            )
+            torch._foreach_mul_(momentum_list, self.momentum)
+            torch._foreach_add_(momentum_list, increments)
             torch._foreach_add_(variables, momentum_list, alpha=-1)
         else:
             torch._foreach_add_(variables, increments, alpha=-1)
diff --git a/keras_core/backend/torch/optimizers/torch_sgd.py b/keras_core/backend/torch/optimizers/torch_sgd.py
index 50268c67d..08ba08e17 100644
--- a/keras_core/backend/torch/optimizers/torch_sgd.py
+++ b/keras_core/backend/torch/optimizers/torch_sgd.py
@@ -15,7 +15,7 @@ class SGD(torch_parallel_optimizer.TorchParallelOptimizer, optimizers.SGD):
         variables = [v.value for v in variables]
         if self.momentum != 0:
             bufs = [
-                self.momentums[self._get_variable_index(variable.value)].value
+                self.momentums[self._get_variable_index(variable)].value
                 for variable in keras_variables
             ]
 
diff --git a/keras_core/optimizers/adadelta_test.py b/keras_core/optimizers/adadelta_test.py
index d27b0fd7b..f80236c1f 100644
--- a/keras_core/optimizers/adadelta_test.py
+++ b/keras_core/optimizers/adadelta_test.py
@@ -1,6 +1,7 @@
 import numpy as np
 
 from keras_core import backend
+from keras_core import ops
 from keras_core import testing
 from keras_core.optimizers.adadelta import Adadelta
 
@@ -16,7 +17,7 @@ class AdadeltaTest(testing.TestCase):
 
     def test_single_step(self):
         optimizer = Adadelta(learning_rate=0.5)
-        grads = np.array([1.0, 6.0, 7.0, 2.0])
+        grads = ops.array([1.0, 6.0, 7.0, 2.0])
         vars = backend.Variable([1.0, 2.0, 3.0, 4.0])
         optimizer.apply_gradients(zip([grads], [vars]))
         self.assertAllClose(
@@ -25,7 +26,7 @@ class AdadeltaTest(testing.TestCase):
 
     def test_weight_decay(self):
         grads, var1, var2, var3 = (
-            np.zeros(()),
+            ops.zeros(()),
             backend.Variable(2.0),
             backend.Variable(2.0, name="exclude"),
             backend.Variable(2.0),
@@ -49,8 +50,8 @@ class AdadeltaTest(testing.TestCase):
         optimizer = Adadelta(learning_rate=1.0, rho=0.8, epsilon=1e-6)
 
         x = backend.Variable(np.ones([10]))
-        grads = np.arange(0.1, 1.1, 0.1)
-        first_grads = np.full((10,), 0.01)
+        grads = ops.arange(0.1, 1.1, 0.1)
+        first_grads = ops.full((10,), 0.01)
 
         golden = np.tile(
             [[0.9978], [0.9947], [0.9915], [0.9882], [0.9849]], (1, 10)