diff --git a/ops.h b/ops.h
index 8f92d82..1919ac9 100644
--- a/ops.h
+++ b/ops.h
@@ -362,12 +362,30 @@ static HWY_NOINLINE HWY_MAYBE_UNUSED void RMSNorm(
 static HWY_NOINLINE HWY_MAYBE_UNUSED void RMSNorm(
     const float* HWY_RESTRICT x, const hwy::bfloat16_t* HWY_RESTRICT weight,
     float* HWY_RESTRICT out, size_t size) {
+  namespace hn = hwy::HWY_NAMESPACE;
+
   constexpr float eps = 1e-6f;
-  float ss = SquaredL2(x, size);
-  ss = 1.0f / sqrtf(ss / StaticCast<float>(size) + eps);
-  for (size_t j = 0; j < size; j++) {
-    // Note 1.0f centering here
-    out[j] = (1.0f + hwy::F32FromBF16(weight[j])) * (ss * x[j]);
+  constexpr size_t unroll_size = 2;
+
+  const hn::ScalableTag<hwy::bfloat16_t> dbf;
+  const hn::Repartition<float, decltype(dbf)> df32;
+  const size_t N32 = hn::Lanes(df32);
+
+  const float ss = SquaredL2(x, size);
+  const auto vss =
+      hn::Set(df32, 1.0f / sqrtf(ss / StaticCast<float>(size) + eps));
+
+  HWY_DASSERT(size % (unroll_size * MaxLanes(df32)) == 0);
+  for (size_t i = 0; i < size; i += unroll_size * N32) {
+    const hn::Vec<decltype(dbf)> w16 = hn::LoadU(dbf, weight + i);
+    const auto w0 = hn::PromoteLowerTo(df32, w16);
+    const auto w1 = hn::PromoteUpperTo(df32, w16);
+    const auto m0 = hn::Mul(vss, hn::LoadU(df32, x + i));
+    const auto m1 = hn::Mul(vss, hn::LoadU(df32, x + i + N32));
+
+    // (1+weight) * m = m + weight*m = one FMA.
+    hn::StoreU(hn::MulAdd(m0, w0, m0), df32, out + i);
+    hn::StoreU(hn::MulAdd(m1, w1, m1), df32, out + i + N32);
   }
 }