diff --git a/ggml/src/ggml-cpu/vec.cpp b/ggml/src/ggml-cpu/vec.cpp
index ac8633e212..be1e3a326e 100644
--- a/ggml/src/ggml-cpu/vec.cpp
+++ b/ggml/src/ggml-cpu/vec.cpp
@@ -414,27 +414,61 @@ void ggml_vec_swiglu_f32(const int n, float * y, const float * x, const float *
 ggml_float ggml_vec_cvar_f32(const int n, float * y, const float * x, const float mean) {
     int i = 0;
     ggml_float sum = 0;
-// TODO: optimize to process the remaining elements in groups using the smaller vector sizes from AVX2 and SSE
-// ref: https://github.com/ggml-org/llama.cpp/pull/15953#pullrequestreview-3310928344
 #if defined(__AVX512F__) && defined(__AVX512DQ__)
+    __m512 sum_v = _mm512_setzero_ps();
+    for (; i + 63 < n; i += 64) {
+        __m512 val1 = _mm512_sub_ps(_mm512_loadu_ps(x + i + 0),  _mm512_set1_ps(mean));
+        __m512 val2 = _mm512_sub_ps(_mm512_loadu_ps(x + i + 16), _mm512_set1_ps(mean));
+        __m512 val3 = _mm512_sub_ps(_mm512_loadu_ps(x + i + 32), _mm512_set1_ps(mean));
+        __m512 val4 = _mm512_sub_ps(_mm512_loadu_ps(x + i + 48), _mm512_set1_ps(mean));
+        _mm512_storeu_ps(y + i + 0,  val1);
+        _mm512_storeu_ps(y + i + 16, val2);
+        _mm512_storeu_ps(y + i + 32, val3);
+        _mm512_storeu_ps(y + i + 48, val4);
+        sum_v = _mm512_fmadd_ps(val1, val1, sum_v);
+        sum_v = _mm512_fmadd_ps(val2, val2, sum_v);
+        sum_v = _mm512_fmadd_ps(val3, val3, sum_v);
+        sum_v = _mm512_fmadd_ps(val4, val4, sum_v);
+    }
     for (; i + 15 < n; i += 16) {
         __m512 val = _mm512_sub_ps(_mm512_loadu_ps(x + i),
                                    _mm512_set1_ps(mean));
         _mm512_storeu_ps(y + i, val);
-        sum += (ggml_float)_mm512_reduce_add_ps(_mm512_mul_ps(val, val));
+        sum_v = _mm512_fmadd_ps(val, val, sum_v);
     }
+    sum += (ggml_float)_mm512_reduce_add_ps(sum_v);
 #elif defined(__AVX2__) && defined(__FMA__)
+    __m256 sum_v1 = _mm256_setzero_ps();
+    __m256 sum_v2 = _mm256_setzero_ps();
+    __m256 sum_v3 = _mm256_setzero_ps();
+    __m256 sum_v4 = _mm256_setzero_ps();
+    for (; i + 31 < n; i += 32) {
+        __m256 val1 = _mm256_sub_ps(_mm256_loadu_ps(x + i + 0),  _mm256_set1_ps(mean));
+        __m256 val2 = _mm256_sub_ps(_mm256_loadu_ps(x + i + 8),  _mm256_set1_ps(mean));
+        __m256 val3 = _mm256_sub_ps(_mm256_loadu_ps(x + i + 16), _mm256_set1_ps(mean));
+        __m256 val4 = _mm256_sub_ps(_mm256_loadu_ps(x + i + 24), _mm256_set1_ps(mean));
+        _mm256_storeu_ps(y + i + 0,  val1);
+        _mm256_storeu_ps(y + i + 8,  val2);
+        _mm256_storeu_ps(y + i + 16, val3);
+        _mm256_storeu_ps(y + i + 24, val4);
+        sum_v1 = _mm256_fmadd_ps(val1, val1, sum_v1);
+        sum_v2 = _mm256_fmadd_ps(val2, val2, sum_v2);
+        sum_v3 = _mm256_fmadd_ps(val3, val3, sum_v3);
+        sum_v4 = _mm256_fmadd_ps(val4, val4, sum_v4);
+    }
     for (; i + 7 < n; i += 8) {
         __m256 val = _mm256_sub_ps(_mm256_loadu_ps(x + i),
                                    _mm256_set1_ps(mean));
         _mm256_storeu_ps(y + i, val);
-        val = _mm256_mul_ps(val,val);
-        __m128 val2 = _mm_add_ps(_mm256_extractf128_ps(val, 1),
-                                 _mm256_castps256_ps128(val));
-        val2 = _mm_add_ps(val2, _mm_movehl_ps(val2, val2));
-        val2 = _mm_add_ss(val2, _mm_movehdup_ps(val2));
-        sum += (ggml_float)_mm_cvtss_f32(val2);
+        sum_v1 = _mm256_fmadd_ps(val, val, sum_v1);
     }
+    sum_v1 = _mm256_add_ps(sum_v1, sum_v2);
+    sum_v1 = _mm256_add_ps(sum_v1, sum_v3);
+    sum_v1 = _mm256_add_ps(sum_v1, sum_v4);
+    __m128 val2 = _mm_add_ps(_mm256_extractf128_ps(sum_v1, 1), _mm256_castps256_ps128(sum_v1));
+    val2 = _mm_add_ps(val2, _mm_movehl_ps(val2, val2));
+    val2 = _mm_add_ss(val2, _mm_movehdup_ps(val2));
+    sum += (ggml_float)_mm_cvtss_f32(val2);
 #elif defined(__SSE2__)
     for (; i + 3 < n; i += 4) {
         __m128 val = _mm_sub_ps(_mm_loadu_ps(x + i),