diff --git a/faiss/utils/distances.cpp b/faiss/utils/distances.cpp
index 0eb2ab5e04..90bac9b998 100644
--- a/faiss/utils/distances.cpp
+++ b/faiss/utils/distances.cpp
@@ -361,7 +361,212 @@ void exhaustive_L2sqr_blas(
     exhaustive_L2sqr_blas_default_impl(x, y, d, nx, ny, res);
 }
 
-#ifdef __AVX2__
+#if defined(__AVX512F__)
+void exhaustive_L2sqr_blas_cmax_avx512(
+        const float* x,
+        const float* y,
+        size_t d,
+        size_t nx,
+        size_t ny,
+        Top1BlockResultHandler<CMax<float, int64_t>>& res,
+        const float* y_norms) {
+    // BLAS does not like empty matrices
+    if (nx == 0 || ny == 0) {
+        return;
+    }
+
+    /* block sizes */
+    const size_t bs_x = distance_compute_blas_query_bs;
+    const size_t bs_y = distance_compute_blas_database_bs;
+    std::unique_ptr<float[]> ip_block(new float[bs_x * bs_y]);
+    std::unique_ptr<float[]> x_norms(new float[nx]);
+    std::unique_ptr<float[]> del2;
+
+    fvec_norms_L2sqr(x_norms.get(), x, d, nx);
+
+    if (!y_norms) {
+        float* y_norms2 = new float[ny];
+        del2.reset(y_norms2);
+        fvec_norms_L2sqr(y_norms2, y, d, ny);
+        y_norms = y_norms2;
+    }
+
+    for (size_t i0 = 0; i0 < nx; i0 += bs_x) {
+        size_t i1 = i0 + bs_x;
+        if (i1 > nx) {
+            i1 = nx;
+        }
+
+        res.begin_multiple(i0, i1);
+
+        for (size_t j0 = 0; j0 < ny; j0 += bs_y) {
+            size_t j1 = j0 + bs_y;
+            if (j1 > ny) {
+                j1 = ny;
+            }
+            /* compute the actual dot products */
+            {
+                float one = 1, zero = 0;
+                FINTEGER nyi = j1 - j0, nxi = i1 - i0, di = d;
+                sgemm_("Transpose",
+                       "Not transpose",
+                       &nyi,
+                       &nxi,
+                       &di,
+                       &one,
+                       y + j0 * d,
+                       &di,
+                       x + i0 * d,
+                       &di,
+                       &zero,
+                       ip_block.get(),
+                       &nyi);
+            }
+#pragma omp parallel for
+            for (int64_t i = i0; i < i1; i++) {
+                float* ip_line = ip_block.get() + (i - i0) * (j1 - j0);
+
+                _mm_prefetch((const char*)ip_line, _MM_HINT_NTA);
+                _mm_prefetch((const char*)(ip_line + 16), _MM_HINT_NTA);
+
+                // constant
+                const __m512 mul_minus2 = _mm512_set1_ps(-2);
+
+                // Track 16 min distances + 16 min indices.
+                // All the distances tracked do not take x_norms[i]
+                // into account in order to get rid of extra
+                // _mm512_add_ps(x_norms[i], ...) instructions
+                // in distance computations.
+                __m512 min_distances =
+                        _mm512_set1_ps(res.dis_tab[i] - x_norms[i]);
+
+                // these indices are local and are relative to j0.
+                // so, value 0 means j0.
+                __m512i min_indices = _mm512_set1_epi32(0);
+
+                __m512i current_indices = _mm512_setr_epi32(
+                        0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15);
+                const __m512i indices_delta = _mm512_set1_epi32(16);
+
+                // current j index
+                size_t idx_j = 0;
+                size_t count = j1 - j0;
+
+                // process 32 elements per loop
+                for (; idx_j < (count / 32) * 32; idx_j += 32, ip_line += 32) {
+                    _mm_prefetch((const char*)(ip_line + 32), _MM_HINT_NTA);
+                    _mm_prefetch((const char*)(ip_line + 48), _MM_HINT_NTA);
+
+                    // load values for norms
+                    const __m512 y_norm_0 =
+                            _mm512_loadu_ps(y_norms + idx_j + j0 + 0);
+                    const __m512 y_norm_1 =
+                            _mm512_loadu_ps(y_norms + idx_j + j0 + 16);
+
+                    // load values for dot products
+                    const __m512 ip_0 = _mm512_loadu_ps(ip_line + 0);
+                    const __m512 ip_1 = _mm512_loadu_ps(ip_line + 16);
+
+                    // compute dis = y_norm[j] - 2 * dot(x_norm[i], y_norm[j]).
+                    // x_norm[i] was dropped off because it is a constant for a
+                    // given i. We'll deal with it later.
+                    __m512 distances_0 =
+                            _mm512_fmadd_ps(ip_0, mul_minus2, y_norm_0);
+                    __m512 distances_1 =
+                            _mm512_fmadd_ps(ip_1, mul_minus2, y_norm_1);
+
+                    // compare the new distances to the min distances
+                    // for each of the first group of 16 AVX512 components.
+                    const __mmask16 comparison_0 = _mm512_cmp_ps_mask(
+                            min_distances, distances_0, _CMP_LE_OS);
+
+                    // update min distances and indices with closest vectors if
+                    // needed.
+                    min_distances = _mm512_mask_blend_ps(
+                            comparison_0, distances_0, min_distances);
+                    min_indices = _mm512_mask_blend_epi32(
+                            comparison_0, current_indices, min_indices);
+                    current_indices =
+                            _mm512_add_epi32(current_indices, indices_delta);
+
+                    // compare the new distances to the min distances
+                    // for each of the second group of 16 AVX512 components.
+                    const __mmask16 comparison_1 = _mm512_cmp_ps_mask(
+                            min_distances, distances_1, _CMP_LE_OS);
+
+                    // update min distances and indices with closest vectors if
+                    // needed.
+                    min_distances = _mm512_mask_blend_ps(
+                            comparison_1, distances_1, min_distances);
+                    min_indices = _mm512_mask_blend_epi32(
+                            comparison_1, current_indices, min_indices);
+                    current_indices =
+                            _mm512_add_epi32(current_indices, indices_delta);
+                }
+
+                // dump values and find the minimum distance / minimum index
+                float min_distances_scalar[16];
+                uint32_t min_indices_scalar[16];
+                _mm512_storeu_ps(min_distances_scalar, min_distances);
+                _mm512_storeu_si512(
+                        (__m512i*)(min_indices_scalar), min_indices);
+
+                float current_min_distance = res.dis_tab[i];
+                uint32_t current_min_index = res.ids_tab[i];
+
+                // This unusual comparison is needed to maintain the behavior
+                // of the original implementation: if two indices are
+                // represented with equal distance values, then
+                // the index with the min value is returned.
+                for (size_t jv = 0; jv < 16; jv++) {
+                    // add missing x_norms[i]
+                    float distance_candidate =
+                            min_distances_scalar[jv] + x_norms[i];
+
+                    // negative values can occur for identical vectors
+                    //    due to roundoff errors.
+                    if (distance_candidate < 0) {
+                        distance_candidate = 0;
+                    }
+
+                    int64_t index_candidate = min_indices_scalar[jv] + j0;
+
+                    if (current_min_distance > distance_candidate) {
+                        current_min_distance = distance_candidate;
+                        current_min_index = index_candidate;
+                    } else if (
+                            current_min_distance == distance_candidate &&
+                            current_min_index > index_candidate) {
+                        current_min_index = index_candidate;
+                    }
+                }
+
+                // process leftovers
+                for (; idx_j < count; idx_j++, ip_line++) {
+                    float ip = *ip_line;
+                    float dis = x_norms[i] + y_norms[idx_j + j0] - 2 * ip;
+                    // negative values can occur for identical vectors
+                    //    due to roundoff errors.
+                    if (dis < 0) {
+                        dis = 0;
+                    }
+
+                    if (current_min_distance > dis) {
+                        current_min_distance = dis;
+                        current_min_index = idx_j + j0;
+                    }
+                }
+
+                res.add_result(i, current_min_distance, current_min_index);
+            }
+        }
+        // Does nothing for SingleBestResultHandler, but
+        // keeping the call for the consistency.
+        res.end_multiple();
+        InterruptCallback::check();
+    }
+}
+#elif defined(__AVX2__)
 void exhaustive_L2sqr_blas_cmax_avx2(
         const float* x,
         const float* y,
@@ -761,7 +966,17 @@ void exhaustive_L2sqr_blas<Top1BlockResultHandler<CMax<float, int64_t>>>(
         size_t ny,
         Top1BlockResultHandler<CMax<float, int64_t>>& res,
         const float* y_norms) {
-#if defined(__AVX2__)
+#if defined(__AVX512F__)
+    // use a faster fused kernel if available
+    if (exhaustive_L2sqr_fused_cmax(x, y, d, nx, ny, res, y_norms)) {
+        // the kernel is available and it is complete, we're done.
+        return;
+    }
+
+    // run the specialized AVX512 implementation
+    exhaustive_L2sqr_blas_cmax_avx512(x, y, d, nx, ny, res, y_norms);
+
+#elif defined(__AVX2__)
     // use a faster fused kernel if available
     if (exhaustive_L2sqr_fused_cmax(x, y, d, nx, ny, res, y_norms)) {
         // the kernel is available and it is complete, we're done.