diff --git a/tf_slim/metrics/metric_ops.py b/tf_slim/metrics/metric_ops.py
index 3febbfa..cdd844c 100644
--- a/tf_slim/metrics/metric_ops.py
+++ b/tf_slim/metrics/metric_ops.py
@@ -3242,7 +3242,7 @@ def streaming_covariance(predictions,
     delta_comoment = (
         batch_comoment + (prev_mean_prediction - batch_mean_prediction) *
         (prev_mean_label - batch_mean_label) *
-        (prev_count * batch_count / update_count))
+        (math_ops.div_no_nan(prev_count * batch_count, update_count)))
     update_comoment = state_ops.assign_add(comoment, delta_comoment)
 
     covariance = array_ops.where(
diff --git a/tf_slim/metrics/metric_ops_test.py b/tf_slim/metrics/metric_ops_test.py
index 9920fa2..3d63758 100644
--- a/tf_slim/metrics/metric_ops_test.py
+++ b/tf_slim/metrics/metric_ops_test.py
@@ -5947,12 +5947,13 @@ def testMultiUpdateWithErrorAndWeights(self):
     with self.cached_session() as sess:
       np.random.seed(123)
       n = 100
+      stride = 10
       predictions = np.random.randn(n)
       labels = 0.5 * predictions + np.random.randn(n)
-      weights = np.tile(np.arange(n // 10), n // 10)
+      weights = np.tile(np.arange(n // stride), n // stride)
       np.random.shuffle(weights)
+      weights[0:stride] = 0.0
 
-      stride = 10
       predictions_t = array_ops.placeholder(dtypes_lib.float32, [stride])
       labels_t = array_ops.placeholder(dtypes_lib.float32, [stride])
       weights_t = array_ops.placeholder(dtypes_lib.float32, [stride])
@@ -5974,14 +5975,20 @@ def testMultiUpdateWithErrorAndWeights(self):
         if not np.isnan(prev_expected_cov):
           self.assertAlmostEqual(prev_expected_cov,
                                  sess.run(cov, feed_dict=feed_dict), 5)
-        expected_cov = np.cov(
-            predictions[:stride * (i + 1)],
-            labels[:stride * (i + 1)],
-            fweights=weights[:stride * (i + 1)])[0, 1]
-        self.assertAlmostEqual(expected_cov,
-                               sess.run(update_op, feed_dict=feed_dict), 5)
-        self.assertAlmostEqual(expected_cov, sess.run(cov, feed_dict=feed_dict),
-                               5)
+        if np.sum(weights[:stride * (i + 1)]) != 0.0:
+          expected_cov = np.cov(
+              predictions[:stride * (i + 1)],
+              labels[:stride * (i + 1)],
+              fweights=weights[:stride * (i + 1)])[0, 1]
+        else:
+          expected_cov = NAN
+        sess.run(update_op, feed_dict=feed_dict)
+        self.assertEqual(
+            np.isnan(expected_cov),
+            np.isnan(sess.run(cov, feed_dict=feed_dict)))
+        if not np.isnan(expected_cov):
+          self.assertAlmostEqual(expected_cov,
+                                 sess.run(cov, feed_dict=feed_dict), 5)
         prev_expected_cov = expected_cov