diff --git a/monai/losses/cldice.py b/monai/losses/cldice.py
index 406cc3825f..64f2cbfb09 100644
--- a/monai/losses/cldice.py
+++ b/monai/losses/cldice.py
@@ -142,7 +142,7 @@ def forward(self, y_true: torch.Tensor, y_pred: torch.Tensor) -> torch.Tensor:
         tsens = (torch.sum(torch.multiply(skel_true, y_pred)[:, 1:, ...]) + self.smooth) / (
             torch.sum(skel_true[:, 1:, ...]) + self.smooth
         )
-        cl_dice: torch.Tensor = 1.0 - 2.0 * (tprec * tsens) / (tprec + tsens)
+        cl_dice: torch.Tensor = 1.0 - 2.0 * (tprec * tsens) / (tprec + tsens + 1e-7)
         return cl_dice
 
 
@@ -179,6 +179,6 @@ def forward(self, y_true: torch.Tensor, y_pred: torch.Tensor) -> torch.Tensor:
         tsens = (torch.sum(torch.multiply(skel_true, y_pred)[:, 1:, ...]) + self.smooth) / (
             torch.sum(skel_true[:, 1:, ...]) + self.smooth
         )
-        cl_dice = 1.0 - 2.0 * (tprec * tsens) / (tprec + tsens)
+        cl_dice = 1.0 - 2.0 * (tprec * tsens) / (tprec + tsens + 1e-7)
         total_loss: torch.Tensor = (1.0 - self.alpha) * dice + self.alpha * cl_dice
         return total_loss
diff --git a/tests/losses/test_cldice_loss.py b/tests/losses/test_cldice_loss.py
index 14d3575e3b..33430d7480 100644
--- a/tests/losses/test_cldice_loss.py
+++ b/tests/losses/test_cldice_loss.py
@@ -46,6 +46,31 @@ def test_with_cuda(self):
         np.testing.assert_allclose(output.detach().cpu().numpy(), 0.0, atol=1e-4, rtol=1e-4)
         np.testing.assert_allclose(output_dice.detach().cpu().numpy(), 0.0, atol=1e-4, rtol=1e-4)
 
+    def test_zero_input_no_nan(self):
+        """Test that zero-valued inputs do not produce NaN loss (division by zero guard)."""
+        loss = SoftclDiceLoss(smooth=0.0)
+        loss_dice = SoftDiceclDiceLoss(smooth=0.0)
+        y_pred = torch.zeros((2, 3, 8, 8))
+        y_true = torch.zeros((2, 3, 8, 8))
+        result = loss(y_true, y_pred)
+        result_dice = loss_dice(y_true, y_pred)
+        self.assertFalse(torch.isnan(result).any(), "SoftclDiceLoss produced NaN for zero inputs with smooth=0")
+        self.assertFalse(torch.isnan(result_dice).any(), "SoftDiceclDiceLoss produced NaN for zero inputs with smooth=0")
+
+    def test_no_overlap_no_nan(self):
+        """Test that non-overlapping pred/target do not produce NaN loss."""
+        loss = SoftclDiceLoss(smooth=0.0)
+        loss_dice = SoftDiceclDiceLoss(smooth=0.0)
+        # Create non-overlapping predictions and ground truth
+        y_pred = torch.zeros((2, 3, 16, 16))
+        y_true = torch.zeros((2, 3, 16, 16))
+        y_pred[:, 1:, :8, :] = 1.0  # prediction in left half
+        y_true[:, 1:, 8:, :] = 1.0  # ground truth in right half
+        result = loss(y_true, y_pred)
+        result_dice = loss_dice(y_true, y_pred)
+        self.assertFalse(torch.isnan(result).any(), "SoftclDiceLoss produced NaN for non-overlapping inputs")
+        self.assertFalse(torch.isnan(result_dice).any(), "SoftDiceclDiceLoss produced NaN for non-overlapping inputs")
+
 
 if __name__ == "__main__":
     unittest.main()