diff --git a/tests/integration/model_bridge/test_cohere_adapter.py b/tests/integration/model_bridge/test_cohere_adapter.py
index 5e92c1616..3a29c196a 100644
--- a/tests/integration/model_bridge/test_cohere_adapter.py
+++ b/tests/integration/model_bridge/test_cohere_adapter.py
@@ -207,20 +207,36 @@ def test_embed_weight_equals_hf_embed_tokens(
             max_diff < 1e-6
         ), f"embed.W_E was corrupted (possibly by logit_scale fold): max_diff={max_diff:.6f}"
 
-    def test_embed_and_unembed_weights_differ(
-        self, cohere_bridge_processed: TransformerBridge
-    ) -> None:
-        # After the logit_scale fold, embed.W_E and unembed.weight must NOT be identical.
-        # If they are, the untie or fold did not take effect.
-        logit_scale = getattr(cohere_bridge_processed.cfg, "logit_scale")
-        if logit_scale == 1.0:
-            pytest.skip("logit_scale=1.0 — fold is a no-op, skip this check")
-        tl_embed = cohere_bridge_processed.embed.W_E
-        tl_unembed = cohere_bridge_processed.unembed.original_component.weight
-        assert not torch.allclose(tl_embed, tl_unembed), (
-            "embed.W_E and unembed.weight are identical — "
-            "logit_scale fold may not have been applied or untied correctly"
+    @pytest.mark.parametrize("logit_scale", [0.0625, 1.0])
+    def test_embed_and_unembed_weights_differ(self, logit_scale: float) -> None:
+        # After the logit_scale fold, embed.W_E and unembed.weight must NOT be
+        # identical for a non-trivial scale. logit_scale=1.0 is kept as a regression
+        # guard for the no-op case, where the two weights stay tied.
+        #
+        # cfg.logit_scale is set before process_weights so the fold (which reads it
+        # inside preprocess_weights) runs with the parametrized value.
+        bridge = TransformerBridge.boot_transformers(MODEL, device="cpu")
+        bridge.cfg.logit_scale = logit_scale  # type: ignore[attr-defined]
+        bridge.process_weights(
+            fold_ln=False,
+            center_writing_weights=False,
+            center_unembed=False,
+            fold_value_biases=False,
+            refactor_factored_attn_matrices=False,
         )
+        tl_embed = bridge.embed.W_E
+        tl_unembed = bridge.unembed.original_component.weight
+        weights_identical = torch.allclose(tl_embed, tl_unembed)
+        if logit_scale == 1.0:
+            assert weights_identical, (
+                "embed.W_E and unembed.weight should remain tied when logit_scale=1.0 "
+                "(the fold is a no-op)"
+            )
+        else:
+            assert not weights_identical, (
+                "embed.W_E and unembed.weight are identical — "
+                "logit_scale fold may not have been applied or untied correctly"
+            )
 
 
 # ---------------------------------------------------------------------------