diff --git a/src/moscot/base/problems/problem.py b/src/moscot/base/problems/problem.py
index eb0a340de..63fde8167 100644
--- a/src/moscot/base/problems/problem.py
+++ b/src/moscot/base/problems/problem.py
@@ -635,7 +635,7 @@ def _spatial_norm_callback(
         spatial = TaggedArray._extract_data(adata, attr=attr, key=key)
 
         logger.info(f"Normalizing spatial coordinates of `{term}`.")
-        spatial = (spatial - spatial.mean()) / spatial.std()
+        spatial = (spatial - spatial.mean(axis=0)) / spatial.std()
         return TaggedArray(spatial, tag=Tag.POINT_CLOUD)
 
     @staticmethod
diff --git a/tests/problems/space/test_alignment_problem.py b/tests/problems/space/test_alignment_problem.py
index 0ef586bc0..fe3d9824a 100644
--- a/tests/problems/space/test_alignment_problem.py
+++ b/tests/problems/space/test_alignment_problem.py
@@ -51,8 +51,7 @@ def test_prepare_sequential(
         ap = ap.prepare(batch_key="batch", joint_attr=joint_attr, normalize_spatial=normalize_spatial)
         assert len(ap) == 2
         if normalize_spatial:
-            np.testing.assert_allclose(ap[("1", "2")].x.data_src.std(), ap[("0", "1")].x.data_src.std(), atol=1e-15)
-            np.testing.assert_allclose(ap[("1", "2")].x.data_src.std(), 1.0, atol=1e-15)
+            np.testing.assert_allclose(ap[("1", "2")].x.data_src.std(), ap[("0", "1")].y.data_src.std(), atol=1e-15)
             np.testing.assert_allclose(ap[("1", "2")].x.data_src.mean(), 0, atol=1e-15)
             np.testing.assert_allclose(ap[("0", "1")].x.data_src.mean(), 0, atol=1e-15)
 
@@ -75,7 +74,6 @@ def test_prepare_star(self, adata_space_rotate: AnnData, reference: str):
             assert ref == reference
             assert isinstance(ap[prob_key], ap._base_problem_type)
 
-    @pytest.mark.skip(reason="See https://github.com/theislab/moscot/issues/678")
     @pytest.mark.parametrize(
         ("epsilon", "alpha", "rank", "initializer"),
         [(1, 0.9, -1, None), (1, 0.5, 10, "random"), (1, 0.5, 10, "rank2"), (0.1, 0.1, -1, None)],
@@ -102,8 +100,7 @@ def test_solve_balanced(
         )
         for prob_key in ap:
             assert ap[prob_key].solution.rank == rank
-            if initializer != "random":  # TODO: is this valid?
-                assert ap[prob_key].solution.converged
+            assert ap[prob_key].solution.converged
 
         # TODO(michalk8): use np.testing
         assert np.allclose(*(sol.cost for sol in ap.solutions.values()))
diff --git a/tests/problems/space/test_mapping_problem.py b/tests/problems/space/test_mapping_problem.py
index 485ea52ff..e0a4e99ed 100644
--- a/tests/problems/space/test_mapping_problem.py
+++ b/tests/problems/space/test_mapping_problem.py
@@ -96,7 +96,6 @@ def test_prepare_varnames(self, adata_mapping: AnnData, var_names: Optional[List
             assert prob.x.data_src.shape == (n_obs, x_n_var)
             assert prob.y.data_src.shape == (n_obs, y_n_var)
 
-    @pytest.mark.skip(reason="See https://github.com/theislab/moscot/issues/678")
     @pytest.mark.parametrize(
         ("epsilon", "alpha", "rank", "initializer"),
         [(1e-2, 0.9, -1, None), (2, 0.5, 10, "random"), (2, 0.5, 10, "rank2"), (2, 0.1, -1, None)],
diff --git a/tests/problems/spatio_temporal/test_spatio_temporal_problem.py b/tests/problems/spatio_temporal/test_spatio_temporal_problem.py
index a22d5cd35..b95853863 100644
--- a/tests/problems/spatio_temporal/test_spatio_temporal_problem.py
+++ b/tests/problems/spatio_temporal/test_spatio_temporal_problem.py
@@ -60,7 +60,6 @@ def test_solve_balanced(self, adata_spatio_temporal: AnnData):
             assert isinstance(subsol, BaseSolverOutput)
             assert key in expected_keys
 
-    @pytest.mark.skip(reason="unbalanced does not work yet")
     def test_solve_unbalanced(self, adata_spatio_temporal: AnnData):
         taus = [9e-1, 1e-2]
         problem1 = SpatioTemporalProblem(adata=adata_spatio_temporal)
@@ -76,8 +75,8 @@ def test_solve_unbalanced(self, adata_spatio_temporal: AnnData):
         assert problem2[0, 1].a is not None
         assert problem2[0, 1].b is not None
 
-        problem1 = problem1.solve(epsilon=1, tau_a=taus[0], tau_b=taus[0], max_iterations=10000)
-        problem2 = problem2.solve(epsilon=1, tau_a=taus[1], tau_b=taus[1], max_iterations=10000)
+        problem1 = problem1.solve(epsilon=1, tau_a=taus[0], tau_b=taus[0])
+        problem2 = problem2.solve(epsilon=1, tau_a=taus[1], tau_b=taus[1])
 
         assert problem1[0, 1].solution.a is not None
         assert problem1[0, 1].solution.b is not None
diff --git a/tests/problems/time/test_temporal_problem.py b/tests/problems/time/test_temporal_problem.py
index 43923f285..01a0067c8 100644
--- a/tests/problems/time/test_temporal_problem.py
+++ b/tests/problems/time/test_temporal_problem.py
@@ -78,8 +78,8 @@ def test_solve_unbalanced(self, adata_time: AnnData):
         assert problem2[0, 1].a is not None
         assert problem2[0, 1].b is not None
 
-        problem1 = problem1.solve(epsilon=1, tau_a=taus[0], tau_b=taus[0], max_iterations=10000)
-        problem2 = problem2.solve(epsilon=1, tau_a=taus[1], tau_b=taus[1], max_iterations=10000)
+        problem1 = problem1.solve(epsilon=1, tau_a=taus[0], tau_b=taus[0])
+        problem2 = problem2.solve(epsilon=1, tau_a=taus[1], tau_b=taus[1])
 
         assert problem1[0, 1].solution.a is not None
         assert problem1[0, 1].solution.b is not None