diff --git a/monai/losses/image_dissimilarity.py b/monai/losses/image_dissimilarity.py
index de10e4b2d4..410ee1e0bc 100644
--- a/monai/losses/image_dissimilarity.py
+++ b/monai/losses/image_dissimilarity.py
@@ -233,9 +233,10 @@ def __init__(
         self.kernel_type = look_up_option(kernel_type, ["gaussian", "b-spline"])
         self.num_bins = num_bins
         self.kernel_type = kernel_type
+        self.bin_centers: torch.Tensor
         if self.kernel_type == "gaussian":
             self.preterm = 1 / (2 * sigma**2)
-            self.bin_centers = bin_centers[None, None, ...]
+            self.register_buffer("bin_centers", bin_centers[None, None, ...], persistent=False)
         self.smooth_nr = float(smooth_nr)
         self.smooth_dr = float(smooth_dr)
 
diff --git a/tests/losses/image_dissimilarity/test_global_mutual_information_loss.py b/tests/losses/image_dissimilarity/test_global_mutual_information_loss.py
index ff7851ed1c..41816a4410 100644
--- a/tests/losses/image_dissimilarity/test_global_mutual_information_loss.py
+++ b/tests/losses/image_dissimilarity/test_global_mutual_information_loss.py
@@ -116,6 +116,15 @@ def transformation(translate_params=(0.0, 0.0, 0.0), rotate_params=(0.0, 0.0, 0.
 
 
 class TestGlobalMutualInformationLossIll(unittest.TestCase):
+    def test_gaussian_bin_centers_registered_buffer(self):
+        loss = GlobalMutualInformationLoss(kernel_type="gaussian", num_bins=16)
+
+        self.assertIn("bin_centers", dict(loss.named_buffers()))
+        self.assertFalse(loss.bin_centers.requires_grad)
+
+        loss = loss.to(dtype=torch.float64)
+        self.assertEqual(loss.bin_centers.dtype, torch.float64)
+
     @parameterized.expand(
         [
             (torch.ones((1, 2), dtype=torch.float), torch.ones((1, 3), dtype=torch.float)),  # mismatched_simple_dims