diff --git a/gtsam/hybrid/GaussianMixture.cpp b/gtsam/hybrid/GaussianMixture.cpp
index 9de8aba59..24d166095 100644
--- a/gtsam/hybrid/GaussianMixture.cpp
+++ b/gtsam/hybrid/GaussianMixture.cpp
@@ -170,21 +170,41 @@ KeyVector GaussianMixture::continuousParents() const {
 }
 
 /* ************************************************************************* */
-boost::shared_ptr<GaussianMixtureFactor> GaussianMixture::likelihood(
-    const VectorValues &frontals) const {
-  // Check that values has all frontals
-  for (auto &&kv : frontals) {
-    if (frontals.find(kv.first) == frontals.end()) {
-      throw std::runtime_error("GaussianMixture: frontals missing factor key.");
+boost::shared_ptr<DecisionTreeFactor> GaussianMixture::normalizationConstants()
+    const {
+  DecisionTree<Key, double> constants(
+      conditionals_, [&](const GaussianConditional::shared_ptr &conditional) {
+        return conditional->normalizationConstant();
+      });
+  // If all constants the same, return nullptr:
+  if (constants.nrLeaves() == 1) return nullptr;
+  return boost::make_shared<DecisionTreeFactor>(discreteKeys(), constants);
+}
+
+/* ************************************************************************* */
+bool GaussianMixture::allFrontalsGiven(const VectorValues &given) const {
+  for (auto &&kv : given) {
+    if (given.find(kv.first) == given.end()) {
+      return false;
     }
   }
+  return true;
+}
+
+/* ************************************************************************* */
+boost::shared_ptr<GaussianMixtureFactor> GaussianMixture::likelihood(
+    const VectorValues &given) const {
+  if (!allFrontalsGiven(given)) {
+    throw std::runtime_error(
+        "GaussianMixture::likelihood: given values are missing some frontals.");
+  }
 
   const DiscreteKeys discreteParentKeys = discreteKeys();
   const KeyVector continuousParentKeys = continuousParents();
   const GaussianMixtureFactor::Factors likelihoods(
       conditionals_, [&](const GaussianConditional::shared_ptr &conditional) {
         return GaussianMixtureFactor::FactorAndConstant{
-            conditional->likelihood(frontals),
+            conditional->likelihood(given),
             conditional->logNormalizationConstant()};
       });
   return boost::make_shared<GaussianMixtureFactor>(
@@ -285,8 +305,7 @@ AlgebraicDecisionTree<Key> GaussianMixture::logProbability(
           return 1e50;
         }
       };
-  DecisionTree<Key, double> errorTree(conditionals_, errorFunc);
-  return errorTree;
+  return DecisionTree<Key, double>(conditionals_, errorFunc);
 }
 
 /* *******************************************************************************/
diff --git a/gtsam/hybrid/GaussianMixture.h b/gtsam/hybrid/GaussianMixture.h
index d90e08409..9504f7ffa 100644
--- a/gtsam/hybrid/GaussianMixture.h
+++ b/gtsam/hybrid/GaussianMixture.h
@@ -155,10 +155,16 @@ class GTSAM_EXPORT GaussianMixture
   /// Returns the continuous keys among the parents.
   KeyVector continuousParents() const;
 
-  // Create a likelihood factor for a Gaussian mixture, return a Mixture factor
-  // on the parents.
+  /// Return a discrete factor with possibly varying normalization constants.
+  /// If there is no variation, return nullptr.
+  boost::shared_ptr<DecisionTreeFactor> normalizationConstants() const;
+
+  /**
+   * Create a likelihood factor for a Gaussian mixture, return a Mixture factor
+   * on the parents.
+   */
   boost::shared_ptr<GaussianMixtureFactor> likelihood(
-      const VectorValues &frontals) const;
+      const VectorValues &given) const;
 
   /// Getter for the underlying Conditionals DecisionTree
   const Conditionals &conditionals() const;
@@ -233,6 +239,9 @@ class GTSAM_EXPORT GaussianMixture
   /// @}
 
  private:
+  /// Check whether `given` has values for all frontal keys.
+  bool allFrontalsGiven(const VectorValues &given) const;
+
   /** Serialization function */
   friend class boost::serialization::access;
   template <class Archive>
diff --git a/gtsam/hybrid/tests/testGaussianMixture.cpp b/gtsam/hybrid/tests/testGaussianMixture.cpp
index a2ee2c21f..5bad40728 100644
--- a/gtsam/hybrid/tests/testGaussianMixture.cpp
+++ b/gtsam/hybrid/tests/testGaussianMixture.cpp
@@ -106,13 +106,16 @@ TEST(GaussianMixture, Error) {
        conditional1 = boost::make_shared<GaussianConditional>(X(1), d2, R2,
                                                               X(2), S2, model);
 
-  // Create decision tree
+  // Create Gaussian Mixture.
   DiscreteKey m1(M(1), 2);
   GaussianMixture::Conditionals conditionals(
       {m1},
       vector<GaussianConditional::shared_ptr>{conditional0, conditional1});
   GaussianMixture mixture({X(1)}, {X(2)}, {m1}, conditionals);
 
+  // Check that normalizationConstants returns nullptr, as all constants equal.
+  CHECK(!mixture.normalizationConstants());
+
   VectorValues values;
   values.insert(X(1), Vector2::Ones());
   values.insert(X(2), Vector2::Zero());
@@ -163,6 +166,19 @@ TEST(GaussianMixture, ContinuousParents) {
   EXPECT(continuousParentKeys[0] == X(0));
 }
 
+/* ************************************************************************* */
+/// Check we can create a DecisionTreeFactor with all normalization constants.
+TEST(GaussianMixture, NormalizationConstants) {
+  const GaussianMixture gm = createSimpleGaussianMixture();
+
+  const auto factor = gm.normalizationConstants();
+
+  // Test with 1D Gaussian normalization constants for sigma 0.5 and 3:
+  auto c = [](double sigma) { return 1.0 / (sqrt(2 * M_PI) * sigma); };
+  const DecisionTreeFactor expected({M(0), 2}, {c(0.5), c(3)});
+  EXPECT(assert_equal(expected, *factor));
+}
+
 /* ************************************************************************* */
 /// Check that likelihood returns a mixture factor on the parents.
 TEST(GaussianMixture, Likelihood) {
@@ -186,7 +202,7 @@ TEST(GaussianMixture, Likelihood) {
             conditional->logNormalizationConstant()};
       });
   const GaussianMixtureFactor expected({X(0)}, {mode}, factors);
-  EXPECT(assert_equal(*factor, expected));
+  EXPECT(assert_equal(expected, *factor));
 }
 
 /* ************************************************************************* */