diff --git a/tests/solvers/quadratic/gw_test.py b/tests/solvers/quadratic/gw_test.py
index e8d7c7ca4..fb3825ce1 100644
--- a/tests/solvers/quadratic/gw_test.py
+++ b/tests/solvers/quadratic/gw_test.py
@@ -407,3 +407,77 @@ def test_relative_epsilon(
     else:
       assert 0.215 < out.reg_gw_cost < 0.22
       assert 0.19 < out.primal_cost < 0.20
+
+  @pytest.mark.parametrize(("tau_a", "tau_b", "eps", "ti"),
+                           [(0.99, 0.95, 0.0, True), (0.9, 0.8, 1e-3, False),
+                            (1.0, 0.999, 0.0, True), (0.5, 1.0, 1e-2, False)])
+  def test_gwlr_unbalanced(
+      self, tau_a: float, tau_b: float, eps: float, ti: bool
+  ):
+    geom_x = pointcloud.PointCloud(self.x)
+    geom_y = pointcloud.PointCloud(self.y)
+    a = self.a.at[:2].set(0.0)
+    b = self.b.at[15:20].set(0.0)
+    prob = quadratic_problem.QuadraticProblem(
+        geom_x,
+        geom_y,
+        a=a,
+        b=b,
+        tau_a=tau_a,
+        tau_b=tau_b,
+    )
+    solver = jax.jit(
+        gromov_wasserstein_lr.LRGromovWasserstein(
+            rank=4, epsilon=eps, kwargs_dys={"translation_invariant": ti}
+        )
+    )
+
+    res = solver(prob)
+
+    np.testing.assert_array_equal(jnp.isfinite(res.errors), True)
+    np.testing.assert_array_equal(jnp.isfinite(res.costs), True)
+
+  @pytest.mark.parametrize(("rank", "eps"), [(5, 0.0), (10, 1e-3), (15, 1e-2)])
+  def test_gwlr_unbalanced_matches_balanced(
+      self, rank: int, eps: float, enable_x64: bool
+  ):
+    del enable_x64
+
+    geom_x = pointcloud.PointCloud(self.x)
+    geom_y = pointcloud.PointCloud(self.y)
+    prob = quadratic_problem.QuadraticProblem(
+        geom_x,
+        geom_y,
+        a=self.a,
+        b=self.b,
+        tau_a=1.0,
+        tau_b=1.0,
+    )
+    prob_unbal = quadratic_problem.QuadraticProblem(
+        geom_x,
+        geom_y,
+        a=self.a,
+        b=self.b,
+        tau_a=0.9999,
+        tau_b=0.9999,
+    )
+    solver = jax.jit(
+        gromov_wasserstein_lr.LRGromovWasserstein(
+            rank=rank,
+            epsilon=eps,
+            initializer="random",
+            min_iterations=50,
+            max_iterations=50
+        )
+    )
+
+    res = solver(prob)
+    res_unbal = solver(prob_unbal)
+
+    np.testing.assert_allclose(res.transport_mass, 1.0, rtol=1e-4, atol=1e-4)
+    np.testing.assert_allclose(
+        res.transport_mass, res_unbal.transport_mass, rtol=1e-4, atol=1e-4
+    )
+    np.testing.assert_allclose(
+        res.primal_cost, res_unbal.primal_cost, rtol=1e-3, atol=1e-3
+    )