diff --git a/nanochat/optim.py b/nanochat/optim.py
index 56e85e14..8ff5a9e1 100644
--- a/nanochat/optim.py
+++ b/nanochat/optim.py
@@ -36,16 +36,23 @@ def adamw_step_fused(
     All in one compiled graph to eliminate Python overhead between ops.
     The 0-D CPU tensors avoid recompilation when hyperparameter values change.
     """
+    # Cast scalar hyperparams to p.dtype. nanochat stores some params (wte,
+    # value_embeds) at COMPUTE_DTYPE (bf16/fp16) to save embedding memory; the
+    # shared scalar tensors here are fp32. CUDA implicitly promotes mixed-dtype
+    # operands but MPS hard-fails ("mps.multiply requires same element type"),
+    # so we cast once up front. No-op when p is already fp32.
+    dtype = p.dtype
+    lr_d, wd_d, beta1_d, beta2_d, eps_d = lr_t.to(dtype), wd_t.to(dtype), beta1_t.to(dtype), beta2_t.to(dtype), eps_t.to(dtype)
     # Weight decay (decoupled, applied before the update)
-    p.mul_(1 - lr_t * wd_t)
+    p.mul_(1 - lr_d * wd_d)
     # Update running averages (lerp_ is cleaner and fuses well)
-    exp_avg.lerp_(grad, 1 - beta1_t)
-    exp_avg_sq.lerp_(grad.square(), 1 - beta2_t)
-    # Bias corrections
+    exp_avg.lerp_(grad, 1 - beta1_d)
+    exp_avg_sq.lerp_(grad.square(), 1 - beta2_d)
+    # Bias corrections (in scalar fp32, then cast back to dtype below)
     bias1 = 1 - beta1_t ** step_t
     bias2 = 1 - beta2_t ** step_t
     # Compute update and apply
-    denom = (exp_avg_sq / bias2).sqrt() + eps_t
+    denom = (exp_avg_sq / bias2.to(dtype)).sqrt() + eps_d
     step_size = lr_t / bias1
     p.add_(exp_avg / denom, alpha=-step_size)
 
@@ -126,7 +133,13 @@ def muon_step_fused(
             A = X @ X.mT
             B = b * A + c * (A @ A)
             X = a * X + B @ X
-    g = X
+    # Cast g back to the parameter dtype: the polar express loop above
+    # intentionally runs in bf16 for speed (X = g.bfloat16()), but the rest
+    # of the function (variance reduction, cautious update) needs g to match
+    # stacked_params and second_momentum_buffer dtypes. CUDA implicitly
+    # promotes mixed-dtype operands; MPS hard-fails. No-op when X.dtype
+    # already matches stacked_params.dtype.
+    g = X.to(stacked_params.dtype)
 
     # Variance reduction
     beta2 = beta2_t.to(g.dtype)
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}"