diff --git a/monai/losses/image_dissimilarity.py b/monai/losses/image_dissimilarity.py
index 37c78fae60..d9a3050223 100644
--- a/monai/losses/image_dissimilarity.py
+++ b/monai/losses/image_dissimilarity.py
@@ -233,10 +233,14 @@ def __init__(
         self.kernel_type = look_up_option(kernel_type, ["gaussian", "b-spline"])
         self.num_bins = num_bins
         self.kernel_type = kernel_type
+        # declared as buffers so they move with the module (e.g. ``.to(device)``); only populated for the
+        # gaussian kernel, hence the ``Tensor`` annotation reflects the type at the use sites in that path.
+        self.preterm: torch.Tensor | None
         self.bin_centers: torch.Tensor | None
+        self.register_buffer("preterm", None, persistent=False)
         self.register_buffer("bin_centers", None, persistent=False)
         if self.kernel_type == "gaussian":
-            self.preterm = 1 / (2 * sigma**2)
+            self.register_buffer("preterm", 1 / (2 * sigma**2), persistent=False)
             self.register_buffer("bin_centers", bin_centers[None, None, ...], persistent=False)
         self.smooth_nr = float(smooth_nr)
         self.smooth_dr = float(smooth_dr)
@@ -316,8 +320,8 @@ def parzen_windowing_gaussian(self, img: torch.Tensor) -> tuple[torch.Tensor, to
         """
         img = torch.clamp(img, 0, 1)
         img = img.reshape(img.shape[0], -1, 1)  # (batch, num_sample, 1)
-        if self.bin_centers is None:
-            raise ValueError("bin_centers must be defined for gaussian parzen windowing.")
+        if self.bin_centers is None or self.preterm is None:
+            raise ValueError("bin_centers and preterm must be defined for gaussian parzen windowing.")
         weight = torch.exp(
             -self.preterm.to(img) * (img - self.bin_centers.to(img)) ** 2
         )  # (batch, num_sample, num_bin)
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 a16499ac11..19a60f7219 100644
--- a/tests/losses/image_dissimilarity/test_global_mutual_information_loss.py
+++ b/tests/losses/image_dissimilarity/test_global_mutual_information_loss.py
@@ -164,5 +164,51 @@ def test_ill_opts(self, num_bins, reduction, expected_exception, expected_messag
             GlobalMutualInformationLoss(num_bins=num_bins, reduction=reduction)(pred, target)
 
 
+class TestGlobalMutualInformationLossBuffers(unittest.TestCase):
+    def test_gaussian_kernel_registers_buffers(self):
+        """Verify gaussian kernel registers preterm and bin_centers as non-trainable, non-persistent buffers."""
+        loss = GlobalMutualInformationLoss(kernel_type="gaussian")
+        self.assertIn("preterm", loss._buffers)
+        self.assertIn("bin_centers", loss._buffers)
+        self.assertFalse(loss.preterm.requires_grad)
+        self.assertFalse(loss.bin_centers.requires_grad)
+        self.assertEqual(loss.bin_centers.ndim, 3)
+        state = loss.state_dict()
+        self.assertNotIn("preterm", state)
+        self.assertNotIn("bin_centers", state)
+
+    def test_bspline_kernel_has_no_gaussian_buffers(self):
+        """Verify b-spline kernel does not populate gaussian-specific buffers."""
+        loss = GlobalMutualInformationLoss(kernel_type="b-spline")
+        self.assertIsNone(loss.preterm)
+        self.assertIsNone(loss.bin_centers)
+        state = loss.state_dict()
+        self.assertNotIn("preterm", state)
+        self.assertNotIn("bin_centers", state)
+
+    def test_gaussian_kernel_forward_correct(self):
+        """Verify gaussian kernel forward pass returns a scalar loss tensor."""
+        pred = torch.rand(2, 1, 8, 8, dtype=torch.float32)
+        target = torch.rand(2, 1, 8, 8, dtype=torch.float32)
+        loss = GlobalMutualInformationLoss(kernel_type="gaussian")
+        result = loss(pred, target)
+        self.assertEqual(result.shape, torch.Size([]))
+
+    def test_gaussian_buffers_move_with_module(self):
+        """Verify preterm and bin_centers buffers move to the target device with the module."""
+        loss = GlobalMutualInformationLoss(kernel_type="gaussian")
+        self.assertEqual(loss.preterm.device.type, "cpu")
+        self.assertEqual(loss.bin_centers.device.type, "cpu")
+        if not torch.cuda.is_available():
+            self.skipTest("CUDA not available")
+        loss = loss.cuda()
+        self.assertEqual(loss.preterm.device.type, "cuda")
+        self.assertEqual(loss.bin_centers.device.type, "cuda")
+        pred = torch.rand(2, 1, 8, 8, device="cuda")
+        target = torch.rand(2, 1, 8, 8, device="cuda")
+        result = loss(pred, target)
+        self.assertEqual(result.device.type, "cuda")
+
+
 if __name__ == "__main__":
     unittest.main()