diff --git a/pyproject.toml b/pyproject.toml
index 13b49110..5d4d3918 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -176,6 +176,7 @@ lint.per-file-ignores = {"__init__.py" = [
 ], "noxfile.py" = [
     "T201", # print
 ], "tests*" = [
+    "ANN001",
     "ANN201",
     "D100", # undocumented-public-module
     "D103", # TODO: undocumented-public-function
diff --git a/tests/grf/test_transformations.py b/tests/grf/test_transformations.py
new file mode 100644
index 00000000..e6b8f01f
--- /dev/null
+++ b/tests/grf/test_transformations.py
@@ -0,0 +1,88 @@
+import numpy as np
+import numpy.testing as npt
+
+import glass.grf
+
+
+def test_normal(rng):
+    t = glass.grf.Normal()
+    x = rng.standard_normal(10)
+    npt.assert_array_equal(t(x, 1.0), x)
+
+
+def test_lognormal(rng):
+    for lam in 1.0, rng.uniform():
+        var = rng.uniform()
+        t = glass.grf.Lognormal(lam)
+        x = rng.standard_normal(10)
+        y = lam * np.expm1(x - var / 2)
+        npt.assert_array_equal(t(x, var), y)
+
+
+def test_sqnormal(rng):
+    for lam in 1.0, rng.uniform():
+        var = rng.uniform()
+        a = np.sqrt(1 - var)
+        t = glass.grf.SquaredNormal(a, lam)
+        x = rng.standard_normal(10)
+        y = lam * ((x - a) ** 2 - 1)
+        npt.assert_array_equal(t(x, var), y)
+
+
+def test_normal_normal(rng):
+    t1 = glass.grf.Normal()
+    t2 = glass.grf.Normal()
+    x = rng.random(10)
+    npt.assert_array_equal(glass.grf.corr(t1, t2, x), x)
+    npt.assert_array_equal(glass.grf.icorr(t1, t2, x), x)
+    npt.assert_array_equal(glass.grf.dcorr(t1, t2, x), np.ones_like(x))
+
+
+def test_lognormal_lognormal(rng):
+    lam1 = rng.uniform()
+    t1 = glass.grf.Lognormal(lam1)
+
+    lam2 = rng.uniform()
+    t2 = glass.grf.Lognormal(lam2)
+
+    x = rng.random(10)
+    y = lam1 * lam2 * np.expm1(x)
+    dy = lam1 * lam2 * np.exp(x)
+
+    npt.assert_array_equal(glass.grf.corr(t1, t2, x), y)
+    npt.assert_array_almost_equal_nulp(glass.grf.icorr(t1, t2, y), x)
+    npt.assert_array_equal(glass.grf.dcorr(t1, t2, x), dy)
+
+
+def test_lognormal_normal(rng):
+    lam1 = rng.uniform()
+    t1 = glass.grf.Lognormal(lam1)
+
+    t2 = glass.grf.Normal()
+
+    x = rng.random(10)
+    y = lam1 * x
+    dy = lam1 * np.ones_like(x)
+
+    npt.assert_array_equal(glass.grf.corr(t1, t2, x), y)
+    npt.assert_array_almost_equal_nulp(glass.grf.icorr(t1, t2, y), x)
+    npt.assert_array_equal(glass.grf.dcorr(t1, t2, x), dy)
+
+
+def test_sqnormal_sqnormal(rng):
+    lam1, var1 = rng.uniform(size=2)
+    a1 = np.sqrt(1 - var1)
+    t1 = glass.grf.SquaredNormal(a1, lam1)
+
+    lam2, var2 = rng.uniform(size=2)
+    a2 = np.sqrt(1 - var2)
+    t2 = glass.grf.SquaredNormal(a2, lam2)
+
+    # https://arxiv.org/pdf/2408.16903, (E.7)
+    x = rng.random(10)
+    y = 2 * lam1 * lam2 * x * (x + 2 * a1 * a2)
+    dy = 4 * lam1 * lam2 * (x + a1 * a2)
+
+    npt.assert_array_equal(glass.grf.corr(t1, t2, x), y)
+    npt.assert_array_almost_equal_nulp(glass.grf.icorr(t1, t2, y), x, nulp=2)
+    npt.assert_array_equal(glass.grf.dcorr(t1, t2, x), dy)