diff --git a/tensordict/nn/params.py b/tensordict/nn/params.py
index 20b945241..221f50718 100644
--- a/tensordict/nn/params.py
+++ b/tensordict/nn/params.py
@@ -1164,7 +1164,12 @@ def _apply(self, fn, recurse=True):
         self._param_td._erase_cache()
         param_td = self._param_td
         self._param_td = param_td.copy()
+        # Keep a list of buffers to update .data only
+        bufs = dict(self._buffers)
         out: TensorDictBase = super()._apply(fn, recurse=recurse)
+        for key, val in bufs.items():
+            val.data = self._buffers[key].data
+            self._buffers[key] = val
         # Check device and shape
         cbs = out._check_batch_size(raise_exception=False)
         if not cbs: