diff --git a/src/transformers/generation/utils.py b/src/transformers/generation/utils.py
index 6349eb67e75a3d..177afef836918f 100644
--- a/src/transformers/generation/utils.py
+++ b/src/transformers/generation/utils.py
@@ -1344,13 +1344,18 @@ def _get_static_cache(self, max_batch_size: int, max_cache_len: int) -> StaticCa
                 cache_dtype = self.config._pre_quantization_dtype
             else:
                 cache_dtype = self.dtype
-            self._static_cache = StaticCache(
-                config=self.config,
-                max_batch_size=max_batch_size,
-                max_cache_len=max_cache_len,
-                device=self.device,
-                dtype=cache_dtype,
-            )
+            try:
+                self._static_cache = StaticCache(
+                    config=self.config,
+                    max_batch_size=max_batch_size,
+                    max_cache_len=max_cache_len,
+                    device=self.device,
+                    dtype=cache_dtype,
+                )
+            except AttributeError:
+                raise ValueError(
+                    f"This model's class ({self.__class__.__name__}) does not support static cache for generation."
+                )
         else:
             self._static_cache.reset()  # reset the cache for a new generation
         return self._static_cache
diff --git a/src/transformers/models/dbrx/configuration_dbrx.py b/src/transformers/models/dbrx/configuration_dbrx.py
index b03d2c17b09e07..61c1a8ced4ccf9 100644
--- a/src/transformers/models/dbrx/configuration_dbrx.py
+++ b/src/transformers/models/dbrx/configuration_dbrx.py
@@ -249,6 +249,7 @@ def __init__(
         self.use_cache = use_cache
         self.initializer_range = initializer_range
         self.output_router_logits = output_router_logits
+        self.num_key_value_heads = self.attn_config.kv_n_heads
 
         tie_word_embeddings = kwargs.pop("tie_word_embeddings", False)
         if tie_word_embeddings:
diff --git a/tests/generation/test_utils.py b/tests/generation/test_utils.py
index c605a165840464..bb55e417882a8c 100644
--- a/tests/generation/test_utils.py
+++ b/tests/generation/test_utils.py
@@ -1655,6 +1655,7 @@ def test_new_cache_format(self, num_beams, do_sample):
 
     @require_torch_gpu
     @slow
+    @is_flaky()  # compilation may result in equivalent (!= same) FP ops, causing the argmax in generate to be flaky
     def test_generate_compile_fullgraph(self):
         """Tests that `.generate` is compatible with torch.compile without graph breaks, keeping the same results"""
         for model_class in self.all_generative_model_classes:
diff --git a/tests/models/dbrx/test_modeling_dbrx.py b/tests/models/dbrx/test_modeling_dbrx.py
index 4c6b74a4d7baf2..cf07ea63a85835 100644
--- a/tests/models/dbrx/test_modeling_dbrx.py
+++ b/tests/models/dbrx/test_modeling_dbrx.py
@@ -355,6 +355,10 @@ def test_model_from_pretrained(self):
     def test_tied_weights_keys(self):
         pass
 
+    @unittest.skip("Dbrx does not support `torch.compile` with `fullgraph=True`.")
+    def test_generate_compile_fullgraph(self):
+        pass
+
 
 @require_torch
 class DbrxModelIntegrationTest(unittest.TestCase):
diff --git a/tests/models/jamba/test_modeling_jamba.py b/tests/models/jamba/test_modeling_jamba.py
index ffe859bb59d62e..ab463f451c36d2 100644
--- a/tests/models/jamba/test_modeling_jamba.py
+++ b/tests/models/jamba/test_modeling_jamba.py
@@ -644,6 +644,10 @@ def test_flash_attn_2_inference_equivalence_right_padding(self):
     def test_new_cache_format(self, num_beams, do_sample):
         pass
 
+    @unittest.skip("Jamba has its own special cache type")
+    def test_generate_compile_fullgraph(self):
+        pass
+
 
 @require_torch
 class JambaModelIntegrationTest(unittest.TestCase):