diff --git a/skyrl/backends/skyrl_train/utils/ppo_utils.py b/skyrl/backends/skyrl_train/utils/ppo_utils.py
index 64606b26a7..8a173a13e0 100644
--- a/skyrl/backends/skyrl_train/utils/ppo_utils.py
+++ b/skyrl/backends/skyrl_train/utils/ppo_utils.py
@@ -119,7 +119,9 @@ def compute_approx_kl(
         raise ValueError(f"Invalid KL estimator type: {kl_estimator_type}")
 
     if loss_mask is not None:
-        kld = kld * loss_mask
+        # Multiplying by `loss_mask` can leak `nan` from masked positions,
+        # so route masked positions to 0.0 directly while keeping mask scaling elsewhere
+        kld = torch.where(loss_mask.bool(), kld * loss_mask, 0.0)
     return kld
 
 
diff --git a/tests/backends/skyrl_train/utils/test_ppo_utils.py b/tests/backends/skyrl_train/utils/test_ppo_utils.py
index 6a34e93de5..81055debda 100644
--- a/tests/backends/skyrl_train/utils/test_ppo_utils.py
+++ b/tests/backends/skyrl_train/utils/test_ppo_utils.py
@@ -26,6 +26,7 @@
     register_advantage_estimator,
     register_policy_loss,
 )
+from skyrl.backends.skyrl_train.utils.torch_utils import masked_mean
 
 
 @pytest.fixture
@@ -66,6 +67,29 @@ def test_compute_approx_kl(dummy_data):
     assert torch.allclose(kl_k3, expected_k3, atol=1e-4), "k3 estimator is not correct"
 
 
+@pytest.mark.parametrize("kl_estimator_type", ["k1", "k2", "k3", "abs"])
+def test_compute_approx_kl_applies_loss_mask(kl_estimator_type: str) -> None:
+    """Scales kept positions; masked positions become 0.0, even when their inputs are nan/inf."""
+    log_probs = torch.tensor([[0.2, 0.3, 0.5, 0.7]])
+    # Position 3: nan input + mask=0.0; assertions below check the nan doesn't leak
+    log_probs_base = torch.tensor([[0.1, 0.2, 0.4, float("nan")]])
+    mask = torch.tensor([[1.0, 0.5, 0.25, 0.0]])
+
+    kld = compute_approx_kl(log_probs, log_probs_base, mask, kl_estimator_type=kl_estimator_type)
+
+    # A masked position must contribute nothing, even when its input is non-finite
+    assert torch.isfinite(kld).all(), f"{kl_estimator_type}: kld leaked non-finite values: {kld}"
+    assert kld[0, 3].item() == 0.0, f"{kl_estimator_type}: masked position not zeroed"
+    assert torch.isfinite(masked_mean(kld, mask)), f"{kl_estimator_type}: masked_mean is non-finite"
+
+    # Soft-mask values scale each kept position multiplicatively
+    unmasked = compute_approx_kl(log_probs, log_probs_base, None, kl_estimator_type=kl_estimator_type)
+    expected_kept = unmasked[:, :3] * mask[:, :3]
+    assert torch.allclose(
+        kld[:, :3], expected_kept, atol=1e-6
+    ), f"{kl_estimator_type}: soft mask scaling not preserved: {kld[:, :3]} vs {expected_kept}"
+
+
 def test_compute_reinforce_plus_plus_outcome_advantage_returns_and_masking():
     """REINFORCE++ returns should be discounted sums with reset after EOS; advantages masked."""
     token_level_rewards = torch.tensor([[1.0, 2.0, 3.0]])