diff --git a/src/pyrecest/filters/gaussian_hypothesis_mixture.py b/src/pyrecest/filters/gaussian_hypothesis_mixture.py
index 7bd1ff478..e9ba1b1c2 100644
--- a/src/pyrecest/filters/gaussian_hypothesis_mixture.py
+++ b/src/pyrecest/filters/gaussian_hypothesis_mixture.py
@@ -59,6 +59,8 @@ def normalize_log_weights(log_weights: list[float] | np.ndarray) -> np.ndarray:
     values = np.asarray(log_weights, dtype=float).reshape(-1)
     if values.size == 0:
         raise ValueError("log_weights must not be empty")
+    if np.any(np.isnan(values)):
+        raise ValueError("log_weights must not contain NaN values")
 
     positive_infinite = np.isposinf(values)
     if np.any(positive_infinite):
diff --git a/tests/filters/test_gaussian_hypothesis_mixture.py b/tests/filters/test_gaussian_hypothesis_mixture.py
index 6af41b986..592865bb4 100644
--- a/tests/filters/test_gaussian_hypothesis_mixture.py
+++ b/tests/filters/test_gaussian_hypothesis_mixture.py
@@ -24,6 +24,22 @@ def test_multiple_positive_infinite_log_weights_share_mass(self):
 
         self.assertTrue(np.allclose(weights, np.array([0.5, 0.0, 0.5])))
 
+    def test_nan_log_weights_are_rejected(self):
+        with self.assertRaisesRegex(ValueError, "NaN"):
+            normalize_log_weights(np.array([0.0, np.nan]))
+
+        with self.assertRaisesRegex(ValueError, "NaN"):
+            moment_match_gaussian_hypotheses(
+                [
+                    WeightedGaussianHypothesis(
+                        np.array([0.0]), np.array([[1.0]]), log_weight=0.0
+                    ),
+                    WeightedGaussianHypothesis(
+                        np.array([1.0]), np.array([[1.0]]), log_weight=np.nan
+                    ),
+                ]
+            )
+
     def test_moment_matching_respects_dominant_infinite_weight(self):
         mean, covariance, weights = moment_match_gaussian_hypotheses(
             [