diff --git a/torchft/local_sgd.py b/torchft/local_sgd.py
index 1e409a7..de03452 100644
--- a/torchft/local_sgd.py
+++ b/torchft/local_sgd.py
@@ -213,8 +213,14 @@ def __init__(
         self.should_quantize = should_quantize
 
         self._grads: Dict[str, torch.Tensor] = {}
+
+        # Used to save global parameters so that they can be restored in case
+        # commit fails
         self.original_parameters: Dict[str, torch.Tensor] = {}
 
+        # Used to mix the local and global parameters
+        self._local_parameters: Dict[str, torch.Tensor] = {}
+
         for name, p in self._model_fragment.named_parameters():
             if isinstance(p, DTensor):
                 p = extract_local_tensor(p.data)
@@ -237,6 +243,14 @@ def save_parameters(self) -> None:
                 param_to_local = extract_local_tensor(p.data)
                 self.original_parameters[name].copy_(param_to_local, non_blocking=True)
 
+    def _save_local_parameters(self) -> None:
+        """
+        Saves a copy of the model's parameters.
+        """
+        with torch.no_grad():
+            for name, p in self._model_fragment.named_parameters():
+                self._local_parameters[name] = extract_local_tensor(p.data)
+
     @torch.profiler.record_function("torchft::local_sgd::restore_parameters")
     def restore_parameters(self) -> None:
         with torch.no_grad():
@@ -293,6 +307,21 @@ def _set_grads(self) -> None:
                 # No longer needed
                 del self._grads[name]
 
+    def _clear_local_parameters(self) -> None:
+        """
+        Clears the saved copy of the model's parameters
+        """
+        self._local_parameters = {}
+
+    def _merge_parameters(self) -> None:
+        """
+        Merges the local and global parameters.
+        """
+        for name, p in self._model_fragment.named_parameters():
+            torch.lerp(
+                p.data, self._local_parameters[name], 1 - self._fragment_update_alpha
+            )
+
     @torch.profiler.record_function("torchft::local_sgd::wait")
     def wait(self) -> None:
         """
@@ -382,6 +411,8 @@ def perform_sync(self) -> bool:
 
         self.wait()
 
+        # save the parameters so they can be used for merging
+        self._save_local_parameters()
         # Restore the parameters back to the previous state
         self.restore_parameters()
 
@@ -404,8 +435,12 @@ def perform_sync(self) -> bool:
             self._set_grads()
             self._outer_optimizer.step()
             self.save_parameters()
+            self._merge_parameters()
         self._outer_optimizer.zero_grad()
 
+        # free up memory
+        self._clear_local_parameters()
+
         return should_commit
 
     def _average_grads(self) -> None:
@@ -557,12 +592,6 @@ def __init__(
         if fragment_update_alpha < 0 or fragment_update_alpha > 1:
             raise ValueError("fragment_update_alpha must be between 0 and 1")
 
-        # TODO: Support `fragment_update_alpha`
-        if fragment_update_alpha != 0.0:
-            raise ValueError(
-                "Merging local parameters with global parameters is not supported yet"
-            )
-
         super().__init__()
         self._manager = manager