diff --git a/auto_round/experimental/utils.py b/auto_round/experimental/utils.py
index e90f9c0d5..b38f33d16 100644
--- a/auto_round/experimental/utils.py
+++ b/auto_round/experimental/utils.py
@@ -35,7 +35,12 @@ def update_parameter_data(module: torch.nn.Module, new_val: torch.Tensor, name:
     if hasattr(module, name):
         param = getattr(module, name)
         if isinstance(param, torch.nn.Parameter):
-            param.data.copy_(new_val)
+            if param.shape == new_val.shape:
+                param.data.copy_(new_val)
+            else:
+                # Re-create the parameter when shapes differ (e.g. after offload
+                # cleared it to an empty tensor).
+                module.register_parameter(name, torch.nn.Parameter(new_val.clone(), requires_grad=param.requires_grad))
         else:
             module.register_parameter(name, torch.nn.Parameter(new_val))
     else:
diff --git a/test/test_cpu/schemes/test_auto_scheme.py b/test/test_cpu/schemes/test_auto_scheme.py
index 9bd362bf3..fe7b18511 100644
--- a/test/test_cpu/schemes/test_auto_scheme.py
+++ b/test/test_cpu/schemes/test_auto_scheme.py
@@ -54,3 +54,41 @@ def test_layer_config(self, tiny_opt_model_path):
         avg_bits, _ = compute_avg_bits_for_model(model)
         print(avg_bits)
         assert target_bits - 0.1 < avg_bits <= target_bits + 1e-3
+
+    def test_autoscheme_mxfp_with_static_kv(self, tiny_opt_model_path):
+        """MXFP4+MXFP8 AutoScheme with static_kv_dtype='fp8' should yield
+        non-zero k_scale and v_scale on the first attention layer."""
+        scheme = AutoScheme(
+            avg_bits=5.0,
+            options=("MXFP4", "MXFP8"),
+            nsamples=2,
+            seqlen=8,
+            ignore_scale_zp_bits=True,
+        )
+        ar = AutoRound(
+            tiny_opt_model_path,
+            scheme=scheme,
+            static_kv_dtype="fp8",
+            iters=0,
+            nsamples=2,
+            seqlen=8,
+            disable_opt_rtn=True,
+        )
+        quantized_model, _ = ar.quantize_and_save(
+            format="fake",
+            output_dir=self.save_dir,
+        )
+
+        # After quantize_and_save, the model's attention modules should have
+        # k_scale and v_scale registered as parameters with non-zero values.
+        attn = quantized_model.model.decoder.layers[0].self_attn
+        assert hasattr(attn, "k_scale"), "missing k_scale after quantization"
+        assert hasattr(attn, "v_scale"), "missing v_scale after quantization"
+        k_val = attn.k_scale.item()
+        v_val = attn.v_scale.item()
+        assert k_val != 0.0, (
+            "k_scale is 0.0 — scale was not collected during " "calibration with AutoScheme + static_kv_dtype"
+        )
+        assert v_val != 0.0, (
+            "v_scale is 0.0 — scale was not collected during " "calibration with AutoScheme + static_kv_dtype"
+        )