diff --git a/trl/trainer/grpo_trainer.py b/trl/trainer/grpo_trainer.py
index 0f400e14fcd..caa7cf378c1 100644
--- a/trl/trainer/grpo_trainer.py
+++ b/trl/trainer/grpo_trainer.py
@@ -2174,6 +2174,15 @@ def _generate_and_score_completions(
         all_process_advantages = advantages.clone()  # keep the aggregated advantages for logging
         advantages = advantages[process_slice]
 
+        # Mask out completions from groups with zero reward std (all rewards identical).
+        # When std=0, advantages are 0, so the policy loss contribution is already zero.
+        # However, the KL penalty term (beta * per_token_kl) still produces gradients that
+        # pull the model toward the reference policy without any reward signal. Zeroing
+        # the completion mask for these groups eliminates the spurious KL gradients.
+        # See https://huggingface.co/papers/2505.22257 (Section 3.2).
+        is_std_zero_local = is_std_zero[process_slice]
+        completion_mask = completion_mask * (~is_std_zero_local).unsqueeze(1).int()
+
         # Calculate mean reward per function, but only for samples where the function was applied (non-NaN values)
         for i, reward_func_name in enumerate(self.reward_func_names):
             mean_rewards = torch.nanmean(rewards_per_func[:, i]).item()