diff --git a/opacus/optimizers/ddpoptimizer.py b/opacus/optimizers/ddpoptimizer.py
index d0f16d73..1b4e472d 100644
--- a/opacus/optimizers/ddpoptimizer.py
+++ b/opacus/optimizers/ddpoptimizer.py
@@ -70,8 +70,12 @@ def reduce_gradients(self):
     def step(
         self, closure: Optional[Callable[[], float]] = None
     ) -> Optional[torch.Tensor]:
+        if closure is not None:
+            with torch.enable_grad():
+                closure()
+
         if self.pre_step():
             self.reduce_gradients()
-            return self.original_optimizer.step(closure)
+            return self.original_optimizer.step()
         else:
             return None
diff --git a/opacus/optimizers/optimizer.py b/opacus/optimizers/optimizer.py
index 1afb3ce5..2522a9de 100644
--- a/opacus/optimizers/optimizer.py
+++ b/opacus/optimizers/optimizer.py
@@ -491,6 +491,11 @@ def pre_step(
             closure: A closure that reevaluates the model and
                 returns the loss. Optional for most optimizers.
         """
+        # The corner case when the optimizer has no trainable parameters.
+        # Essentially the DPOptimizer act as a normal optimizer
+        if self.grad_samples is None or len(self.grad_samples) == 0:
+            return True
+
         self.clip_and_accumulate()
         if self._check_skip_next_step():
             self._is_last_step_skipped = True