diff --git a/faiss/impl/HNSW.cpp b/faiss/impl/HNSW.cpp
index cd7f9a0d91..24455fa877 100644
--- a/faiss/impl/HNSW.cpp
+++ b/faiss/impl/HNSW.cpp
@@ -16,6 +16,15 @@
 #include <faiss/impl/IDSelector.h>
 #include <faiss/utils/prefetch.h>
 
+#include <faiss/impl/platform_macros.h>
+
+#ifdef __AVX2__
+#include <immintrin.h>
+
+#include <limits>
+#include <type_traits>
+#endif
+
 namespace faiss {
 
 /**************************************************************
@@ -1010,17 +1019,105 @@ void HNSW::MinimaxHeap::clear() {
     nvalid = k = 0;
 }
 
+#ifdef __AVX2__
+int HNSW::MinimaxHeap::pop_min(float* vmin_out) {
+    assert(k > 0);
+    static_assert(
+            std::is_same<storage_idx_t, int32_t>::value,
+            "This code expects storage_idx_t to be int32_t");
+
+    int32_t min_idx = -1;
+    float min_dis = std::numeric_limits<float>::infinity();
+
+    size_t iii = 0;
+
+    __m256i min_indices = _mm256_setr_epi32(-1, -1, -1, -1, -1, -1, -1, -1);
+    __m256 min_distances =
+            _mm256_set1_ps(std::numeric_limits<float>::infinity());
+    __m256i current_indices = _mm256_setr_epi32(0, 1, 2, 3, 4, 5, 6, 7);
+    __m256i offset = _mm256_set1_epi32(8);
+
+    // The baseline version is available in non-AVX2 branch.
+
+    // The following loop tracks the rightmost index with the min distance.
+    // -1 index values are ignored.
+    const int k8 = (k / 8) * 8;
+    for (; iii < k8; iii += 8) {
+        __m256i indices =
+                _mm256_loadu_si256((const __m256i*)(ids.data() + iii));
+        __m256 distances = _mm256_loadu_ps(dis.data() + iii);
+
+        // This mask filters out -1 values among indices.
+        __m256i m1mask = _mm256_cmpgt_epi32(_mm256_setzero_si256(), indices);
+
+        __m256i dmask = _mm256_castps_si256(
+                _mm256_cmp_ps(min_distances, distances, _CMP_LT_OS));
+        __m256 finalmask = _mm256_castsi256_ps(_mm256_or_si256(m1mask, dmask));
+
+        const __m256i min_indices_new = _mm256_castps_si256(_mm256_blendv_ps(
+                _mm256_castsi256_ps(current_indices),
+                _mm256_castsi256_ps(min_indices),
+                finalmask));
+
+        const __m256 min_distances_new =
+                _mm256_blendv_ps(distances, min_distances, finalmask);
+
+        min_indices = min_indices_new;
+        min_distances = min_distances_new;
+
+        current_indices = _mm256_add_epi32(current_indices, offset);
+    }
+
+    // Vectorizing is doable, but is not practical
+    int32_t vidx8[8];
+    float vdis8[8];
+    _mm256_storeu_ps(vdis8, min_distances);
+    _mm256_storeu_si256((__m256i*)vidx8, min_indices);
+
+    for (size_t j = 0; j < 8; j++) {
+        if (min_dis > vdis8[j] || (min_dis == vdis8[j] && min_idx < vidx8[j])) {
+            min_idx = vidx8[j];
+            min_dis = vdis8[j];
+        }
+    }
+
+    // process last values. Vectorizing is doable, but is not practical
+    for (; iii < k; iii++) {
+        if (ids[iii] != -1 && dis[iii] <= min_dis) {
+            min_dis = dis[iii];
+            min_idx = iii;
+        }
+    }
+
+    if (min_idx == -1) {
+        return -1;
+    }
+
+    if (vmin_out) {
+        *vmin_out = min_dis;
+    }
+    int ret = ids[min_idx];
+    ids[min_idx] = -1;
+    --nvalid;
+    return ret;
+}
+
+#else
+
+// baseline non-vectorized version
 int HNSW::MinimaxHeap::pop_min(float* vmin_out) {
     assert(k > 0);
     // returns min. This is an O(n) operation
     int i = k - 1;
     while (i >= 0) {
-        if (ids[i] != -1)
+        if (ids[i] != -1) {
             break;
+        }
         i--;
     }
-    if (i == -1)
+    if (i == -1) {
         return -1;
+    }
     int imin = i;
     float vmin = dis[i];
     i--;
@@ -1031,14 +1128,16 @@ int HNSW::MinimaxHeap::pop_min(float* vmin_out) {
         }
         i--;
     }
-    if (vmin_out)
+    if (vmin_out) {
         *vmin_out = vmin;
+    }
     int ret = ids[imin];
     ids[imin] = -1;
     --nvalid;
 
     return ret;
 }
+#endif
 
 int HNSW::MinimaxHeap::count_below(float thresh) {
     int n_below = 0;
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index ecf45cde50..d5b6084432 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -28,6 +28,7 @@ set(FAISS_TEST_SRC
   test_distances_simd.cpp
   test_heap.cpp
   test_code_distance.cpp
+  test_hnsw.cpp
 )
 
 add_executable(faiss_test ${FAISS_TEST_SRC})
diff --git a/tests/test_hnsw.cpp b/tests/test_hnsw.cpp
new file mode 100644
index 0000000000..9d90cf25e8
--- /dev/null
+++ b/tests/test_hnsw.cpp
@@ -0,0 +1,192 @@
+/**
+ * Copyright (c) Facebook, Inc. and its affiliates.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ */
+
+#include <gtest/gtest.h>
+
+#include <cstddef>
+#include <cstdint>
+#include <limits>
+#include <random>
+#include <unordered_set>
+#include <vector>
+
+#include <faiss/impl/HNSW.h>
+
+int reference_pop_min(faiss::HNSW::MinimaxHeap& heap, float* vmin_out) {
+    assert(heap.k > 0);
+    // returns min. This is an O(n) operation
+    int i = heap.k - 1;
+    while (i >= 0) {
+        if (heap.ids[i] != -1)
+            break;
+        i--;
+    }
+    if (i == -1)
+        return -1;
+    int imin = i;
+    float vmin = heap.dis[i];
+    i--;
+    while (i >= 0) {
+        if (heap.ids[i] != -1 && heap.dis[i] < vmin) {
+            vmin = heap.dis[i];
+            imin = i;
+        }
+        i--;
+    }
+    if (vmin_out)
+        *vmin_out = vmin;
+    int ret = heap.ids[imin];
+    heap.ids[imin] = -1;
+    --heap.nvalid;
+
+    return ret;
+}
+
+void test_popmin(int heap_size, int amount_to_put) {
+    // create a heap
+    faiss::HNSW::MinimaxHeap mm_heap(heap_size);
+
+    using storage_idx_t = faiss::HNSW::storage_idx_t;
+
+    std::default_random_engine rng(123 + heap_size * amount_to_put);
+    std::uniform_int_distribution<storage_idx_t> u(0, 65536);
+    std::uniform_real_distribution<float> uf(0, 1);
+
+    // generate random unique indices
+    std::unordered_set<storage_idx_t> indices;
+    while (indices.size() < amount_to_put) {
+        const storage_idx_t index = u(rng);
+        indices.insert(index);
+    }
+
+    // put ones into the heap
+    for (const auto index : indices) {
+        float distance = uf(rng);
+        if (distance >= 0.7f) {
+            // add infinity values from time to time
+            distance = std::numeric_limits<float>::infinity();
+        }
+        mm_heap.push(index, distance);
+    }
+
+    // clone the heap
+    faiss::HNSW::MinimaxHeap cloned_mm_heap = mm_heap;
+
+    // takes ones out one by one
+    while (mm_heap.size() > 0) {
+        // compare heaps
+        ASSERT_EQ(mm_heap.n, cloned_mm_heap.n);
+        ASSERT_EQ(mm_heap.k, cloned_mm_heap.k);
+        ASSERT_EQ(mm_heap.nvalid, cloned_mm_heap.nvalid);
+        ASSERT_EQ(mm_heap.ids, cloned_mm_heap.ids);
+        ASSERT_EQ(mm_heap.dis, cloned_mm_heap.dis);
+
+        // use the reference pop_min for the cloned heap
+        float cloned_vmin_dis = std::numeric_limits<float>::quiet_NaN();
+        storage_idx_t cloned_vmin_idx =
+                reference_pop_min(cloned_mm_heap, &cloned_vmin_dis);
+
+        float vmin_dis = std::numeric_limits<float>::quiet_NaN();
+        storage_idx_t vmin_idx = mm_heap.pop_min(&vmin_dis);
+
+        // compare returns
+        ASSERT_EQ(vmin_dis, cloned_vmin_dis);
+        ASSERT_EQ(vmin_idx, cloned_vmin_idx);
+    }
+
+    // compare heaps again
+    ASSERT_EQ(mm_heap.n, cloned_mm_heap.n);
+    ASSERT_EQ(mm_heap.k, cloned_mm_heap.k);
+    ASSERT_EQ(mm_heap.nvalid, cloned_mm_heap.nvalid);
+    ASSERT_EQ(mm_heap.ids, cloned_mm_heap.ids);
+    ASSERT_EQ(mm_heap.dis, cloned_mm_heap.dis);
+}
+
+void test_popmin_identical_distances(
+        int heap_size,
+        int amount_to_put,
+        const float distance) {
+    // create a heap
+    faiss::HNSW::MinimaxHeap mm_heap(heap_size);
+
+    using storage_idx_t = faiss::HNSW::storage_idx_t;
+
+    std::default_random_engine rng(123 + heap_size * amount_to_put);
+    std::uniform_int_distribution<storage_idx_t> u(0, 65536);
+
+    // generate random unique indices
+    std::unordered_set<storage_idx_t> indices;
+    while (indices.size() < amount_to_put) {
+        const storage_idx_t index = u(rng);
+        indices.insert(index);
+    }
+
+    // put ones into the heap
+    for (const auto index : indices) {
+        mm_heap.push(index, distance);
+    }
+
+    // clone the heap
+    faiss::HNSW::MinimaxHeap cloned_mm_heap = mm_heap;
+
+    // takes ones out one by one
+    while (mm_heap.size() > 0) {
+        // compare heaps
+        ASSERT_EQ(mm_heap.n, cloned_mm_heap.n);
+        ASSERT_EQ(mm_heap.k, cloned_mm_heap.k);
+        ASSERT_EQ(mm_heap.nvalid, cloned_mm_heap.nvalid);
+        ASSERT_EQ(mm_heap.ids, cloned_mm_heap.ids);
+        ASSERT_EQ(mm_heap.dis, cloned_mm_heap.dis);
+
+        // use the reference pop_min for the cloned heap
+        float cloned_vmin_dis = std::numeric_limits<float>::quiet_NaN();
+        storage_idx_t cloned_vmin_idx =
+                reference_pop_min(cloned_mm_heap, &cloned_vmin_dis);
+
+        float vmin_dis = std::numeric_limits<float>::quiet_NaN();
+        storage_idx_t vmin_idx = mm_heap.pop_min(&vmin_dis);
+
+        // compare returns
+        ASSERT_EQ(vmin_dis, cloned_vmin_dis);
+        ASSERT_EQ(vmin_idx, cloned_vmin_idx);
+    }
+
+    // compare heaps again
+    ASSERT_EQ(mm_heap.n, cloned_mm_heap.n);
+    ASSERT_EQ(mm_heap.k, cloned_mm_heap.k);
+    ASSERT_EQ(mm_heap.nvalid, cloned_mm_heap.nvalid);
+    ASSERT_EQ(mm_heap.ids, cloned_mm_heap.ids);
+    ASSERT_EQ(mm_heap.dis, cloned_mm_heap.dis);
+}
+
+TEST(HNSW, Test_popmin) {
+    std::vector<size_t> sizes = {1, 2, 3, 4, 5, 7, 9, 11, 16, 27, 32, 64, 128};
+    for (const size_t size : sizes) {
+        for (size_t amount = size; amount > 0; amount /= 2) {
+            test_popmin(size, amount);
+        }
+    }
+}
+
+TEST(HNSW, Test_popmin_identical_distances) {
+    std::vector<size_t> sizes = {1, 2, 3, 4, 5, 7, 9, 11, 16, 27, 32};
+    for (const size_t size : sizes) {
+        for (size_t amount = size; amount > 0; amount /= 2) {
+            test_popmin_identical_distances(size, amount, 1.0f);
+        }
+    }
+}
+
+TEST(HNSW, Test_popmin_infinite_distances) {
+    std::vector<size_t> sizes = {1, 2, 3, 4, 5, 7, 9, 11, 16, 27, 32};
+    for (const size_t size : sizes) {
+        for (size_t amount = size; amount > 0; amount /= 2) {
+            test_popmin_identical_distances(
+                    size, amount, std::numeric_limits<float>::infinity());
+        }
+    }
+}