diff --git a/tests/test_networks/conftest.py b/tests/test_networks/conftest.py
index 84c011812..01ea5ad70 100644
--- a/tests/test_networks/conftest.py
+++ b/tests/test_networks/conftest.py
@@ -85,6 +85,7 @@ def typical_point_inference_network_subnet():
         "spline_coupling_flow",
         "flow_matching",
         "free_form_flow",
+        "consistency_model",
     ],
     scope="function",
 )
@@ -106,7 +107,8 @@ def inference_network_subnet(request):
 
 
 @pytest.fixture(
-    params=["affine_coupling_flow", "spline_coupling_flow", "flow_matching", "free_form_flow"], scope="function"
+    params=["affine_coupling_flow", "spline_coupling_flow", "flow_matching", "free_form_flow", "consistency_model"],
+    scope="function",
 )
 def generative_inference_network(request):
     return request.getfixturevalue(request.param)
diff --git a/tests/test_networks/test_inference_networks.py b/tests/test_networks/test_inference_networks.py
index 880a4d082..7766b29f9 100644
--- a/tests/test_networks/test_inference_networks.py
+++ b/tests/test_networks/test_inference_networks.py
@@ -36,13 +36,21 @@ def test_variable_batch_size(inference_network, random_samples, random_condition
         else:
             new_conditions = keras.ops.zeros((bs,) + keras.ops.shape(random_conditions)[1:])
 
-        inference_network(new_input, conditions=new_conditions)
+        try:
+            inference_network(new_input, conditions=new_conditions)
+        except NotImplementedError:
+            # network is not invertible
+            pass
         inference_network(new_input, conditions=new_conditions, inverse=True)
 
 
 @pytest.mark.parametrize("density", [True, False])
 def test_output_structure(density, generative_inference_network, random_samples, random_conditions):
-    output = generative_inference_network(random_samples, conditions=random_conditions, density=density)
+    try:
+        output = generative_inference_network(random_samples, conditions=random_conditions, density=density)
+    except NotImplementedError:
+        # network not invertible
+        return
 
     if density:
         assert isinstance(output, tuple)
@@ -57,9 +65,13 @@ def test_output_structure(density, generative_inference_network, random_samples,
 
 
 def test_output_shape(generative_inference_network, random_samples, random_conditions):
-    forward_output, forward_log_density = generative_inference_network(
-        random_samples, conditions=random_conditions, density=True
-    )
+    try:
+        forward_output, forward_log_density = generative_inference_network(
+            random_samples, conditions=random_conditions, density=True
+        )
+    except NotImplementedError:
+        # network is not invertible, not forward function available
+        return
 
     assert keras.ops.shape(forward_output) == keras.ops.shape(random_samples)
     assert keras.ops.shape(forward_log_density) == (keras.ops.shape(random_samples)[0],)
@@ -74,9 +86,13 @@ def test_output_shape(generative_inference_network, random_samples, random_condi
 
 def test_cycle_consistency(generative_inference_network, random_samples, random_conditions):
     # cycle-consistency means the forward and inverse methods are inverses of each other
-    forward_output, forward_log_density = generative_inference_network(
-        random_samples, conditions=random_conditions, density=True
-    )
+    try:
+        forward_output, forward_log_density = generative_inference_network(
+            random_samples, conditions=random_conditions, density=True
+        )
+    except NotImplementedError:
+        # network is not invertible, cycle consistency cannot be tested.
+        return
     inverse_output, inverse_log_density = generative_inference_network(
         forward_output, conditions=random_conditions, density=True, inverse=True
     )
@@ -88,7 +104,11 @@ def test_cycle_consistency(generative_inference_network, random_samples, random_
 def test_density_numerically(generative_inference_network, random_samples, random_conditions):
     from bayesflow.utils import jacobian
 
-    output, log_density = generative_inference_network(random_samples, conditions=random_conditions, density=True)
+    try:
+        output, log_density = generative_inference_network(random_samples, conditions=random_conditions, density=True)
+    except NotImplementedError:
+        # network does not support density estimation
+        return
 
     def f(x):
         return generative_inference_network(x, conditions=random_conditions)