diff --git a/tests/algorithm/kl_fn_test.py b/tests/algorithm/kl_fn_test.py
new file mode 100644
index 0000000000..f3771c5f7c
--- /dev/null
+++ b/tests/algorithm/kl_fn_test.py
@@ -0,0 +1,131 @@
+# -*- coding: utf-8 -*-
+"""Test for KL functions"""
+
+import unittest
+
+import torch
+
+from trinity.algorithm.kl_fn.kl_fn import KL_FN
+
+
+class KLFnTest(unittest.TestCase):
+    def setUp(self):
+        seed = 42
+        torch.manual_seed(seed)
+        torch.cuda.manual_seed(seed)
+        torch.cuda.manual_seed_all(seed)
+        torch.backends.cudnn.deterministic = True
+        torch.backends.cudnn.benchmark = False
+
+        shape = (4, 10)
+        self.logprob = 2 * torch.rand(shape) - 1
+        self.ref_logprob = 2 * torch.rand(shape) - 1
+        self.old_logprob = 2 * torch.rand(shape) - 1
+        self.response_mask = torch.rand(shape) > 0.5
+
+    def test_k1_kl_fn(self):
+        kl_fn_cls = KL_FN.get("k1")
+        kl_fn = kl_fn_cls(kl_coef=0.01)
+        kl = kl_fn.calculate_kl(self.logprob, self.ref_logprob)
+        expected_kl = self.logprob - self.ref_logprob
+        self.assertTrue(torch.allclose(kl, expected_kl))
+
+    def test_k2_kl_fn(self):
+        kl_fn_cls = KL_FN.get("k2")
+        kl_fn = kl_fn_cls(kl_coef=0.01)
+        kl = kl_fn.calculate_kl(self.logprob, self.ref_logprob)
+        expected_kl = (self.logprob - self.ref_logprob).square() * 0.5
+        self.assertTrue(torch.allclose(kl, expected_kl))
+
+    def test_k3_kl_fn(self):
+        kl_fn_cls = KL_FN.get("k3")
+        kl_fn = kl_fn_cls(kl_coef=0.01)
+        kl = kl_fn.calculate_kl(self.logprob, self.ref_logprob)
+        logr = self.ref_logprob - self.logprob
+        expected_kl = logr.exp() - 1 - logr
+        self.assertTrue(torch.allclose(kl, expected_kl))
+
+    def test_abs_kl_fn(self):
+        kl_fn_cls = KL_FN.get("abs")
+        kl_fn = kl_fn_cls(kl_coef=0.01)
+        kl = kl_fn.calculate_kl(self.logprob, self.ref_logprob)
+        expected_kl = torch.abs(self.logprob - self.ref_logprob)
+        self.assertTrue(torch.allclose(kl, expected_kl))
+
+    def test_low_var_kl_fn(self):
+        kl_fn_cls = KL_FN.get("low_var_kl")
+        kl_fn = kl_fn_cls(kl_coef=0.01)
+        kl = kl_fn.calculate_kl(self.logprob, self.ref_logprob)
+        kl_intermediate = self.ref_logprob - self.logprob
+        kl_intermediate = torch.clamp(kl_intermediate, min=-20, max=20)
+        ratio = torch.exp(kl_intermediate)
+        expected_kl = torch.clamp((ratio - kl_intermediate - 1).contiguous(), min=-10, max=10)
+        self.assertTrue(torch.allclose(kl, expected_kl))
+
+    def test_dummy_kl_fn(self):
+        kl_fn_cls = KL_FN.get("none")
+        kl_fn = kl_fn_cls(kl_coef=0.01)
+        kl = kl_fn.calculate_kl(self.logprob, self.ref_logprob)
+        expected_kl = torch.zeros_like(self.logprob)
+        self.assertTrue(torch.allclose(kl, expected_kl))
+
+    def test_corrected_k3_fallback(self):
+        k3_fn = KL_FN.get("k3")(kl_coef=0.01)
+        corrected_k3_fn = KL_FN.get("corrected_k3")(kl_coef=0.01)
+        kl_standard = k3_fn.calculate_kl(self.logprob, self.ref_logprob)
+        kl_corrected_no_old = corrected_k3_fn.calculate_kl(
+            self.logprob, self.ref_logprob, old_logprob=None
+        )
+        self.assertTrue(torch.allclose(kl_standard, kl_corrected_no_old))
+
+    def test_corrected_k3_with_old_logprob(self):
+        corrected_k3_fn = KL_FN.get("corrected_k3")(kl_coef=0.01)
+        kl_corrected = corrected_k3_fn.calculate_kl(
+            self.logprob, self.ref_logprob, self.old_logprob
+        )
+        logr = self.ref_logprob - self.logprob
+        kl_standard = logr.exp() - 1 - logr
+        log_ratio_is = self.logprob - self.old_logprob
+        ratio_is = log_ratio_is.exp()
+        ratio_is = torch.clamp(ratio_is, min=0.0, max=2.0)
+        expected_kl = ratio_is * kl_standard
+        self.assertTrue(torch.allclose(kl_corrected, expected_kl))
+
+    def test_corrected_k3_same_policy(self):
+        k3_fn = KL_FN.get("k3")(kl_coef=0.01)
+        corrected_k3_fn = KL_FN.get("corrected_k3")(kl_coef=0.01)
+        kl_standard = k3_fn.calculate_kl(self.logprob, self.ref_logprob)
+        kl_corrected = corrected_k3_fn.calculate_kl(self.logprob, self.ref_logprob, self.logprob)
+        self.assertTrue(torch.allclose(kl_standard, kl_corrected, rtol=1e-4, atol=1e-6))
+
+    def test_corrected_k3_loss(self):
+        corrected_k3_fn = KL_FN.get("corrected_k3")(kl_coef=0.01)
+        kl_loss, metrics = corrected_k3_fn.calculate_kl_loss(
+            logprob=self.logprob,
+            ref_logprob=self.ref_logprob,
+            response_mask=self.response_mask,
+            loss_agg_mode="token-mean",
+            old_logprob=self.old_logprob,
+        )
+        self.assertEqual(kl_loss.dim(), 0)
+        self.assertIn("kl_loss", metrics)
+        self.assertIn("kl_coef", metrics)
+        self.assertEqual(metrics["kl_coef"], 0.01)
+
+    def test_kl_loss_aggregation_modes(self):
+        corrected_k3_fn = KL_FN.get("corrected_k3")(kl_coef=0.01)
+        kl_loss_mean, _ = corrected_k3_fn.calculate_kl_loss(
+            logprob=self.logprob,
+            ref_logprob=self.ref_logprob,
+            response_mask=self.response_mask,
+            loss_agg_mode="token-mean",
+            old_logprob=self.old_logprob,
+        )
+        kl_loss_sum, _ = corrected_k3_fn.calculate_kl_loss(
+            logprob=self.logprob,
+            ref_logprob=self.ref_logprob,
+            response_mask=self.response_mask,
+            loss_agg_mode="seq-mean-token-sum",
+            old_logprob=self.old_logprob,
+        )
+        self.assertGreater(kl_loss_sum.item(), kl_loss_mean.item())
diff --git a/trinity/algorithm/kl_fn/kl_fn.py b/trinity/algorithm/kl_fn/kl_fn.py
index 49c59f2367..54e1639608 100644
--- a/trinity/algorithm/kl_fn/kl_fn.py
+++ b/trinity/algorithm/kl_fn/kl_fn.py
@@ -82,9 +82,18 @@ def calculate_kl_loss(
         ref_logprob: torch.Tensor,
         response_mask: torch.Tensor,
         loss_agg_mode: str,
+        old_logprob: Optional[torch.Tensor] = None,
     ) -> Tuple[torch.Tensor, Dict]:
-        """Compute KL loss."""
-        kl = self.calculate_kl(logprob, ref_logprob)
+        """Compute KL loss.
+
+        Args:
+            logprob: Log probabilities from current policy
+            ref_logprob: Log probabilities from reference policy
+            response_mask: Mask for valid response tokens
+            loss_agg_mode: Loss aggregation mode
+            old_logprob: Log probabilities from old policy (for importance sampling)
+        """
+        kl = self.calculate_kl(logprob, ref_logprob, old_logprob)
         kl_loss = aggregate_loss(kl, response_mask, loss_agg_mode=loss_agg_mode)
         metrics = {
             "kl_loss": kl_loss.detach().item(),
@@ -93,8 +102,19 @@ def calculate_kl_loss(
         return kl_loss * self.kl_coef, metrics
 
     @abstractmethod
-    def calculate_kl(self, logprob: torch.Tensor, ref_logprob: torch.Tensor) -> torch.Tensor:
-        """Compute KL divergence between logprob and ref_logprob."""
+    def calculate_kl(
+        self,
+        logprob: torch.Tensor,
+        ref_logprob: torch.Tensor,
+        old_logprob: Optional[torch.Tensor] = None,
+    ) -> torch.Tensor:
+        """Compute KL divergence between logprob and ref_logprob.
+
+        Args:
+            logprob: Log probabilities from current policy
+            ref_logprob: Log probabilities from reference policy
+            old_logprob: Log probabilities from old policy (for importance sampling)
+        """
 
     @classmethod
     def default_args(cls):
@@ -108,7 +128,12 @@ class DummyKLFn(KLFn):
     Dummy KL function.
     """
 
-    def calculate_kl(self, logprob: torch.Tensor, ref_logprob: torch.Tensor) -> torch.Tensor:
+    def calculate_kl(
+        self,
+        logprob: torch.Tensor,
+        ref_logprob: torch.Tensor,
+        old_logprob: Optional[torch.Tensor] = None,
+    ) -> torch.Tensor:
         return torch.zeros_like(logprob)
 
     def apply_kl_penalty_to_reward(self, experiences: Any) -> Tuple[Any, Dict]:
@@ -121,6 +146,7 @@ def calculate_kl_loss(
         ref_logprob: torch.Tensor,
         response_mask: torch.Tensor,
         loss_agg_mode: str,
+        old_logprob: Optional[torch.Tensor] = None,
     ) -> Tuple[torch.Tensor, Dict]:
         # return a zero tensor
         return torch.tensor(0.0), {}
@@ -132,7 +158,12 @@ class K1Fn(KLFn):
     KL K1 function.
     """
 
-    def calculate_kl(self, logprob: torch.Tensor, ref_logprob: torch.Tensor) -> torch.Tensor:
+    def calculate_kl(
+        self,
+        logprob: torch.Tensor,
+        ref_logprob: torch.Tensor,
+        old_logprob: Optional[torch.Tensor] = None,
+    ) -> torch.Tensor:
         return logprob - ref_logprob
 
 
@@ -142,7 +173,12 @@ class K2Fn(KLFn):
     KL K2 function.
     """
 
-    def calculate_kl(self, logprob: torch.Tensor, ref_logprob: torch.Tensor) -> torch.Tensor:
+    def calculate_kl(
+        self,
+        logprob: torch.Tensor,
+        ref_logprob: torch.Tensor,
+        old_logprob: Optional[torch.Tensor] = None,
+    ) -> torch.Tensor:
         return (logprob - ref_logprob).square() * 0.5
 
 
@@ -152,7 +188,12 @@ class K3Fn(KLFn):
     KL K3 function.
     """
 
-    def calculate_kl(self, logprob: torch.Tensor, ref_logprob: torch.Tensor) -> torch.Tensor:
+    def calculate_kl(
+        self,
+        logprob: torch.Tensor,
+        ref_logprob: torch.Tensor,
+        old_logprob: Optional[torch.Tensor] = None,
+    ) -> torch.Tensor:
         logr = ref_logprob - logprob
         return logr.exp() - 1 - logr
 
@@ -163,7 +204,12 @@ class LowVarKLFn(KLFn):
     Low Variance KL function.
     """
 
-    def calculate_kl(self, logprob: torch.Tensor, ref_logprob: torch.Tensor) -> torch.Tensor:
+    def calculate_kl(
+        self,
+        logprob: torch.Tensor,
+        ref_logprob: torch.Tensor,
+        old_logprob: Optional[torch.Tensor] = None,
+    ) -> torch.Tensor:
         kl = ref_logprob - logprob
         kl = torch.clamp(kl, min=-20, max=20)
         ratio = torch.exp(kl)
@@ -177,5 +223,66 @@ class AbsFn(KLFn):
     KL Abs function.
     """
 
-    def calculate_kl(self, logprob: torch.Tensor, ref_logprob: torch.Tensor) -> torch.Tensor:
+    def calculate_kl(
+        self,
+        logprob: torch.Tensor,
+        ref_logprob: torch.Tensor,
+        old_logprob: Optional[torch.Tensor] = None,
+    ) -> torch.Tensor:
         return torch.abs(logprob - ref_logprob)
+
+
+@KL_FN.register_module("corrected_k3")
+class CorrectedK3Fn(KLFn):
+    """
+    Corrected K3 function with importance sampling.
+
+    This method applies importance sampling correction to the standard K3 KL divergence.
+    The corrected KL is computed as:
+
+        KL_corrected = (π_θ / π_old) * KL_standard(π_ref || π_θ)
+
+    where:
+        - π_θ: current policy
+        - π_old: old policy (from rollout)
+        - π_ref: reference policy
+        - KL_standard: exp(log(π_ref/π_θ)) - log(π_ref/π_θ) - 1
+
+    If old_logprob is not provided, it falls back to standard K3.
+    """
+
+    def calculate_kl(
+        self,
+        logprob: torch.Tensor,
+        ref_logprob: torch.Tensor,
+        old_logprob: Optional[torch.Tensor] = None,
+    ) -> torch.Tensor:
+        """Compute corrected K3 KL divergence with importance sampling.
+
+        Args:
+            logprob: Log probabilities from current policy (log π_θ)
+            ref_logprob: Log probabilities from reference policy (log π_ref)
+            old_logprob: Log probabilities from old policy (log π_old), optional
+
+        Returns:
+            KL divergence tensor with same shape as input
+        """
+        # Standard K3 KL term: exp(log_ratio) - log_ratio - 1
+        # where log_ratio = log(π_ref / π_θ) = ref_logprob - logprob
+        logr = ref_logprob - logprob
+        kl_term = logr.exp() - 1 - logr
+
+        if old_logprob is None:
+            # Fall back to standard K3 if old_logprob is not provided
+            return kl_term
+
+        # Compute importance sampling ratio: π_θ / π_old
+        log_ratio_is = logprob - old_logprob
+        ratio_is = log_ratio_is.exp()
+        # Clamp ratio for numerical stability, range [0, 2]
+        ratio_is = torch.clamp(ratio_is, min=0.0, max=2.0)
+
+        # Corrected KL with importance sampling
+        corrected_kl = ratio_is * kl_term
+
+        return corrected_kl
diff --git a/trinity/trainer/verl/dp_actor.py b/trinity/trainer/verl/dp_actor.py
index 0d571ed497..2d1258b9cb 100644
--- a/trinity/trainer/verl/dp_actor.py
+++ b/trinity/trainer/verl/dp_actor.py
@@ -162,6 +162,7 @@ def update_policy(self, data: DataProto):  # noqa: C901
                         ref_logprob=model_inputs.get("ref_log_prob", None),
                         response_mask=response_mask,
                         loss_agg_mode=self.loss_agg_mode,
+                        old_logprob=model_inputs.get("old_log_probs", None),
                     )
                     prefix_metrics(
                         src_metrics=kl_loss_metrics,
diff --git a/trinity/trainer/verl/megatron_actor.py b/trinity/trainer/verl/megatron_actor.py
index 4e9183609f..48849c9037 100644
--- a/trinity/trainer/verl/megatron_actor.py
+++ b/trinity/trainer/verl/megatron_actor.py
@@ -210,6 +210,7 @@ def loss_func(output, data, meta_info):
                     ref_logprob=data.get("ref_log_prob", None),
                     response_mask=response_mask,
                     loss_agg_mode=self.loss_agg_mode,
+                    old_logprob=data.get("old_log_probs", None),
                 )
                 prefix_metrics(
                     src_metrics=kl_loss_metrics,