diff --git a/nifty5/library/gaussian_energy.py b/nifty5/library/gaussian_energy.py
index 24cb752e2419173af27e918a32abfe8da736d05d..f540f3684858ec1834dda61fd4501182cdc5c564 100644
--- a/nifty5/library/gaussian_energy.py
+++ b/nifty5/library/gaussian_energy.py
@@ -61,4 +61,6 @@ class GaussianEnergy(Energy):
     @property
     @memo
     def curvature(self):
-        return SandwichOperator.make(self._inp.gradient)
+        if self._cov is None:
+            return SandwichOperator.make(self._inp.gradient)
+        return SandwichOperator.make(self._inp.gradient, self._cov.inverse)