diff --git a/tests/compile/test_config.py b/tests/compile/test_config.py
index 7465ea442c..2d4ef13e33 100644
--- a/tests/compile/test_config.py
+++ b/tests/compile/test_config.py
@@ -70,6 +70,37 @@ def test_get_raw_stream_patch():
         assert get_raw_stream is _cuda_getCurrentRawStream
 
 
+# Inductor can initialize CUDA even for CPU inputs.
+@pytest.mark.forked
+@pytest.mark.parametrize("use_v2", [False, True])
+def test_e8m0_custom_op_fullgraph(use_v2, use_fresh_inductor_cache):
+    """E8M0 inputs must not prevent mutable custom-op decomposition."""
+    with torch.library._scoped_library("test_e8m0", "FRAGMENT") as lib:
+        lib.define("scale_(Tensor(a!) out, Tensor scale) -> ()")
+
+        @torch.library.impl(lib, "scale_", "CPU")
+        def scale_impl(out, scale):
+            out.mul_(scale.float())
+
+        @torch.library.register_fake("test_e8m0::scale_", lib=lib)
+        def scale_fake(out, scale):
+            return None
+
+        def forward(x, scale):
+            out = x.clone()
+            torch.ops.test_e8m0.scale_(out, scale)
+            return out
+
+        x = torch.randn(4, 4)
+        scale = torch.full((4,), 128, dtype=torch.uint8).view(torch.float8_e8m0fnu)
+        compiled = torch.compile(
+            forward,
+            fullgraph=True,
+            options={"enable_auto_functionalized_v2": use_v2},
+        )
+        torch.testing.assert_close(compiled(x, scale), x * 2)
+
+
 def test_copy_pass():
     vllm_config = VllmConfig()
     inductor_pass = FixFunctionalizationPass(vllm_config)
diff --git a/vllm/env_override.py b/vllm/env_override.py
index 87501eb469..bfcdfa7af2 100644
--- a/vllm/env_override.py
+++ b/vllm/env_override.py
@@ -916,6 +916,58 @@ def _patch_inductor_fallback_allow_list() -> None:
 
 _patch_inductor_fallback_allow_list()
 
+
+def _apply_inductor_pattern_matcher_patch() -> None:
+    """Allow custom ops and functionalization wrappers with unsupported dtypes."""
+    from torch._inductor import pattern_matcher
+    from torch._inductor.lowering import fallback_node_due_to_unsupported_type
+
+    def fallback_for_builtin(node, allow_cpu_inputs=True):
+        return (
+            isinstance(node.target, torch._ops.OpOverload)
+            and torch._library.utils.is_builtin(node.target)
+            and fallback_node_due_to_unsupported_type(node, allow_cpu_inputs)
+        )
+
+    pattern_matcher.fallback_node_due_to_unsupported_type = fallback_for_builtin
+
+
+def _patch_inductor_pattern_matcher() -> None:
+    """Apply the backport when Inductor imports its pattern matcher."""
+    import sys
+
+    target_name = "torch._inductor.pattern_matcher"
+    if target_name in sys.modules:
+        _apply_inductor_pattern_matcher_patch()
+        return
+
+    import importlib.abc
+
+    class _PatternMatcherPatchFinder(importlib.abc.MetaPathFinder):
+        def find_spec(self, fullname, path, target=None):
+            if fullname != target_name:
+                return None
+            sys.meta_path.remove(self)
+            spec = importlib.util.find_spec(fullname)
+            if spec is None or spec.loader is None:
+                return None
+            original_exec = spec.loader.exec_module
+
+            def _exec_then_patch(module):
+                original_exec(module)
+                _apply_inductor_pattern_matcher_patch()
+
+            spec.loader.exec_module = _exec_then_patch  # type: ignore[method-assign]
+            return spec
+
+    sys.meta_path.insert(0, _PatternMatcherPatchFinder())
+
+
+# Remove once the minimum supported torch includes
+# https://github.com/pytorch/pytorch/pull/196013.
+if not is_torch_equal_or_newer("2.16.0.dev"):
+    _patch_inductor_pattern_matcher()
+
 # ============================================================
 # Triton Autotuner determinism
 # ============================================================