diff --git a/test/conftest.py b/test/conftest.py
index 10f0617..9097d4c 100644
--- a/test/conftest.py
+++ b/test/conftest.py
@@ -86,3 +86,17 @@ def kfac_expand_exact_one_datum_case(
     """
     case = request.param
     yield initialize_case(case)
+
+
+@fixture(params=KFAC_EXPAND_EXACT_ONE_DATUM_CASES)
+def kfac_ef_exact_one_datum_case(
+    request,
+) -> Tuple[Module, MSELoss, List[Tensor], Iterable[Tuple[Tensor, Tensor]],]:
+    """Prepare a test case with one datum for which KFAC with empirical gradients equals the EF.
+
+    Yields:
+        A neural network, the mean-squared error function, a list of parameters, and
+        a data set.
+    """
+    case = request.param
+    yield initialize_case(case)
diff --git a/test/test_kfac.py b/test/test_kfac.py
index b384646..3dc04aa 100644
--- a/test/test_kfac.py
+++ b/test/test_kfac.py
@@ -10,6 +10,7 @@
 
 from curvlinops.examples.utils import report_nonclose
 from curvlinops.ggn import GGNLinearOperator
+from curvlinops.gradient_moments import EFLinearOperator
 from curvlinops.kfac import KFACLinearOperator
 
 
@@ -68,3 +69,22 @@ def test_kfac_one_datum(
     rtol = {"sum": 3e-2, "mean": 3e-2}[loss_func.reduction]
 
     report_nonclose(ggn, kfac_mat, rtol=rtol, atol=atol)
+
+
+def test_kfac_ef_one_datum(
+    kfac_ef_exact_one_datum_case: Tuple[
+        Module, MSELoss, List[Parameter], Iterable[Tuple[Tensor, Tensor]]
+    ]
+):
+    model, loss_func, params, data = kfac_ef_exact_one_datum_case
+
+    ef_blocks = []  # list of per-parameter EFs
+    for param in params:
+        ef = EFLinearOperator(model, loss_func, [param], data)
+        ef_blocks.append(ef @ eye(ef.shape[1]))
+    ef = block_diag(*ef_blocks)
+
+    kfac = KFACLinearOperator(model, loss_func, params, data, fisher_type="empirical")
+    kfac_mat = kfac @ eye(kfac.shape[1])
+
+    report_nonclose(ef, kfac_mat)