diff --git a/proeval/generator/core.py b/proeval/generator/core.py
index 331ff01..5a8009e 100644
--- a/proeval/generator/core.py
+++ b/proeval/generator/core.py
@@ -405,6 +405,8 @@ def get_posterior_embedding(
         return posterior_mean.detach().cpu().numpy(), posterior_cov.detach().cpu().numpy()
     else:
         K_test_diag = torch.ones(phi_test_t.shape[0], device=device)
+        if kernel_type == "linear":
+            K_test_diag = torch.sum(phi_test_t ** 2, dim=1)
         v = torch.cholesky_solve(K_test_train.t(), L)
         posterior_var = K_test_diag - torch.sum(K_test_train * v.t(), dim=1)
         posterior_var = torch.clamp(posterior_var, min=1e-10)
diff --git a/tests/test_bq_sampling.py b/tests/test_bq_sampling.py
index 7783f2c..2aea093 100644
--- a/tests/test_bq_sampling.py
+++ b/tests/test_bq_sampling.py
@@ -48,6 +48,21 @@ def parameters(self):
         yield self._anchor
 
 
+def test_linear_encoder_marginal_variance_matches_covariance():
+    torch = pytest.importorskip("torch")
+    from proeval.generator.core import get_posterior_embedding
+
+    phi = np.array([[0.0, 0.0], [0.2, -0.2], [1.0, -1.0]], dtype=np.float32)
+    args = (
+        phi[[2]], np.array([1.0]), phi, 0.3, [2],
+        np.full(3, 0.5), _DummyLinearEncoder(torch),
+    )
+    _, variance = get_posterior_embedding(*args)
+    _, covariance = get_posterior_embedding(*args, full_cov=True)
+
+    np.testing.assert_allclose(variance, np.diag(covariance), atol=1e-6)
+
+
 def _run_active(kind, budget, n_init=0):
     features, labels, prior_mean, prior_cov = _synthetic_case()
     np.random.seed(7)