diff --git a/cosmos/airflow/graph.py b/cosmos/airflow/graph.py
index 9ea919118..6c2307596 100644
--- a/cosmos/airflow/graph.py
+++ b/cosmos/airflow/graph.py
@@ -342,6 +342,7 @@ def generate_task_or_group(
         normalize_task_id=normalize_task_id,
         test_behavior=test_behavior,
         on_warning_callback=on_warning_callback,
+        detached_from_parent=detached_from_parent,
     )
 
     # In most cases, we'll  map one DBT node to one Airflow task
diff --git a/tests/test_converter.py b/tests/test_converter.py
index 1868cc4de..f1fc6f7b3 100644
--- a/tests/test_converter.py
+++ b/tests/test_converter.py
@@ -7,7 +7,7 @@
 from airflow.models import DAG
 
 from cosmos.config import ExecutionConfig, ProfileConfig, ProjectConfig, RenderConfig
-from cosmos.constants import DbtResourceType, ExecutionMode, InvocationMode, LoadMode
+from cosmos.constants import DbtResourceType, ExecutionMode, InvocationMode, LoadMode, TestBehavior
 from cosmos.converter import DbtToAirflowConverter, validate_arguments, validate_initial_user_config
 from cosmos.dbt.graph import DbtGraph, DbtNode
 from cosmos.exceptions import CosmosValueError
@@ -205,6 +205,56 @@ def test_converter_creates_dag_with_test_with_multiple_parents():
     assert args[1:] == ["test", "--select", "custom_test_combined_model_combined_model_.c6e4587380"]
 
 
+@pytest.mark.integration
+def test_converter_creates_dag_with_test_with_multiple_parents_and_build():
+    """
+    Validate topology of a project that uses the MULTIPLE_PARENTS_TEST_DBT_PROJECT project
+    """
+    project_config = ProjectConfig(dbt_project_path=MULTIPLE_PARENTS_TEST_DBT_PROJECT)
+    execution_config = ExecutionConfig(execution_mode=ExecutionMode.LOCAL)
+    profile_config = ProfileConfig(
+        profile_name="default",
+        target_name="dev",
+        profile_mapping=PostgresUserPasswordProfileMapping(
+            conn_id="example_conn",
+            profile_args={"schema": "public"},
+            disable_event_tracking=True,
+        ),
+    )
+    with DAG("sample_dag", start_date=datetime(2024, 4, 16)) as dag:
+        converter = DbtToAirflowConverter(
+            dag=dag,
+            project_config=project_config,
+            profile_config=profile_config,
+            execution_config=execution_config,
+            render_config=RenderConfig(test_behavior=TestBehavior.BUILD),
+        )
+    tasks = converter.tasks_map
+
+    assert len(converter.tasks_map) == 4
+
+    # We exclude the test that depends on combined_model and model_a from their commands
+    args = tasks["model.my_dbt_project.combined_model"].build_cmd({})[0]
+    assert args[1:] == [
+        "build",
+        "--exclude",
+        "custom_test_combined_model_combined_model_",
+        "--models",
+        "combined_model",
+    ]
+
+    args = tasks["model.my_dbt_project.model_a"].build_cmd({})[0]
+    assert args[1:] == ["build", "--exclude", "custom_test_combined_model_combined_model_", "--models", "model_a"]
+
+    # The test for model_b should not be changed, since it is not a parent of this test
+    args = tasks["model.my_dbt_project.model_b"].build_cmd({})[0]
+    assert args[1:] == ["build", "--models", "model_b"]
+
+    # We should have a task dedicated to run the test with multiple parents
+    args = tasks["test.my_dbt_project.custom_test_combined_model_combined_model_.c6e4587380"].build_cmd({})[0]
+    assert args[1:] == ["test", "--select", "custom_test_combined_model_combined_model_.c6e4587380"]
+
+
 @pytest.mark.parametrize(
     "execution_mode,operator_args",
     [