diff --git a/tests/test_optim_bf16.py b/tests/test_optim_bf16.py
new file mode 100644
index 00000000..dd63fdf8
--- /dev/null
+++ b/tests/test_optim_bf16.py
@@ -0,0 +1,71 @@
+"""
+Regression tests for mixed-dtype scalar / parameter handling in optim.py.
+
+These cover the MPS Metal Graph compiler crashes seen with
+NANOCHAT_DTYPE=bfloat16: scalar hyperparams (fp32) being multiplied with
+bf16 params (wte, value_embeds) failed with "mps.multiply requires same
+element type". CUDA implicitly promotes mixed-dtype operands; MPS doesn't.
+"""
+import pytest
+import torch
+
+from nanochat.optim import adamw_step_fused
+
+
+def _device():
+    if torch.backends.mps.is_available():
+        return torch.device("mps")
+    return torch.device("cpu")
+
+
+def _scalars():
+    """0-D fp32 scalar tensors matching what MuonAdamW.__init__ creates."""
+    return [
+        torch.tensor(1.0, dtype=torch.float32),     # step
+        torch.tensor(0.01, dtype=torch.float32),    # lr
+        torch.tensor(0.9, dtype=torch.float32),     # beta1
+        torch.tensor(0.999, dtype=torch.float32),   # beta2
+        torch.tensor(1e-8, dtype=torch.float32),    # eps
+        torch.tensor(0.01, dtype=torch.float32),    # wd
+    ]
+
+
+def _sync(device):
+    if device.type == "mps":
+        torch.mps.synchronize()
+
+
+def _run_adamw(p, grad):
+    exp_avg = torch.zeros_like(p)
+    exp_avg_sq = torch.zeros_like(p)
+    p_before = p.clone()
+    adamw_step_fused(p, grad, exp_avg, exp_avg_sq, *_scalars())
+    _sync(p.device)
+    return p_before
+
+
+def test_adamw_step_fused_bf16_param_with_fp32_scalars():
+    """Regression: adamw_step_fused must not crash when p is bf16 but the
+    scalar hyperparams are fp32. This is the standard nanochat config —
+    wte and value_embeds are cast to COMPUTE_DTYPE (bf16) to save memory,
+    while MuonAdamW's shared scalar tensors remain fp32."""
+    device = _device()
+    torch.manual_seed(0)
+    p = torch.randn(64, 32, dtype=torch.bfloat16, device=device)
+    grad = torch.randn_like(p)
+    p_before = _run_adamw(p, grad)
+    assert torch.isfinite(p).all(), "bf16 update produced non-finite values"
+    assert not torch.equal(p, p_before), "weight did not change after step"
+
+
+def test_adamw_step_fused_fp32_param_unchanged():
+    """The fp32 path must still work and produce a sensible update —
+    the dtype-cast patch should be a no-op when p is already fp32."""
+    device = _device()
+    torch.manual_seed(0)
+    p = torch.randn(64, 32, dtype=torch.float32, device=device)
+    grad = torch.randn_like(p)
+    p_before = _run_adamw(p, grad)
+    assert torch.isfinite(p).all()
+    delta = (p - p_before).norm().item()
+    assert 0 < delta < 10, f"unreasonable update magnitude: {delta}"