diff --git a/tests/test_perceptual_loss_stability.py b/tests/test_perceptual_loss_stability.py
new file mode 100644
index 0000000000..1c8b60203b
--- /dev/null
+++ b/tests/test_perceptual_loss_stability.py
@@ -0,0 +1,65 @@
+# Copyright (c) MONAI Consortium
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#     http://www.apache.org/licenses/LICENSE-2.0
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from __future__ import annotations
+
+import unittest
+
+import torch
+import torch.optim as optim
+from parameterized import parameterized
+
+from monai.losses.perceptual import normalize_tensor
+from monai.utils import set_determinism
+
+
+class TestNormalizeTensorStability(unittest.TestCase):
+    def setUp(self):
+        set_determinism(seed=0)
+        self.addCleanup(set_determinism, None)
+
+    def tearDown(self):
+        set_determinism(None)
+
+    @parameterized.expand([["e-3", 1e-3], ["e-6", 1e-6], ["e-9", 1e-9], ["e-12", 1e-12]])  # Small values
+    def test_normalize_tensor_stability(self, name, scale):
+        """Test that small values don't produce NaNs + are handled gracefully."""
+        # Create tensor
+        x = torch.zeros(2, 3, 10, 10, requires_grad=True)
+
+        optimizer = optim.Adam([x], lr=0.01)
+        x_scaled = x * scale
+        normalized = normalize_tensor(x_scaled)
+
+        # Compute to force backward pass
+        loss = normalized.sum()
+
+        # this is where it failed before
+        loss.backward()
+
+        # Check for NaNs in gradients
+        self.assertFalse(torch.isnan(x.grad).any(), f"NaN gradients detected with scale {scale:.10e}")
+
+    def test_normalize_tensor_zero_input(self):
+        """Test that normalize_tensor handles zero inputs gracefully."""
+        # Create tensor with zeros
+        x = torch.zeros(2, 3, 4, 4, requires_grad=True)
+
+        normalized = normalize_tensor(x)
+        loss = normalized.sum()
+        loss.backward()
+
+        # Check for NaNs in gradients
+        self.assertFalse(torch.isnan(x.grad).any(), "NaN gradients detected with zero input")
+
+
+if __name__ == "__main__":
+    unittest.main()