diff --git a/pydantic/_internal/_core_utils.py b/pydantic/_internal/_core_utils.py
index 45e39dc7d9..ebf12ec0fa 100644
--- a/pydantic/_internal/_core_utils.py
+++ b/pydantic/_internal/_core_utils.py
@@ -169,17 +169,10 @@ def _is_schema_valid(s: core_schema.CoreSchema, recurse: Recurse) -> core_schema
             metadata = s['metadata']
             if HAS_INVALID_SCHEMAS_METADATA_KEY in metadata:
                 invalid = metadata[HAS_INVALID_SCHEMAS_METADATA_KEY]
-                if invalid is True:
-                    invalid = True
                 return s
         return recurse(s, _is_schema_valid)
 
     walk_core_schema(schema, _is_schema_valid)
-    if 'metadata' in schema:
-        metadata = schema['metadata']
-        metadata[HAS_INVALID_SCHEMAS_METADATA_KEY] = invalid
-    else:
-        schema['metadata'] = {HAS_INVALID_SCHEMAS_METADATA_KEY: invalid}
     return invalid
 
 
@@ -444,7 +437,8 @@ def collect_refs(s: core_schema.CoreSchema, recurse: Recurse) -> core_schema.Cor
             for definition in s['definitions']:
                 ref = get_ref(definition)
                 assert ref is not None
-                definitions[ref] = definition
+                if ref not in definitions:
+                    definitions[ref] = definition
                 recurse(definition, collect_refs)
             return recurse(s['schema'], collect_refs)
         else:
diff --git a/pydantic/_internal/_generate_schema.py b/pydantic/_internal/_generate_schema.py
index 6fa6bc407f..a8be03b2e8 100644
--- a/pydantic/_internal/_generate_schema.py
+++ b/pydantic/_internal/_generate_schema.py
@@ -50,7 +50,6 @@
     build_metadata_dict,
 )
 from ._core_utils import (
-    HAS_INVALID_SCHEMAS_METADATA_KEY,
     NEEDS_APPLY_DISCRIMINATED_UNION_METADATA_KEY,
     CoreSchemaOrField,
     define_expected_missing_refs,
@@ -535,10 +534,6 @@ def _model_schema(self, cls: type[BaseModel]) -> core_schema.CoreSchema:
                     new_inner_schema = define_expected_missing_refs(inner_schema, recursively_defined_type_refs())
                     if new_inner_schema is not None:
                         inner_schema = new_inner_schema
-                        self._has_invalid_schema = True
-                        metadata[HAS_INVALID_SCHEMAS_METADATA_KEY] = True
-                    else:
-                        metadata[HAS_INVALID_SCHEMAS_METADATA_KEY] = False
                     inner_schema = apply_model_validators(inner_schema, model_validators, 'inner')
 
                     model_schema = core_schema.model_schema(
@@ -659,11 +654,9 @@ def _post_process_generated_schema(self, schema: core_schema.CoreSchema) -> core
         if 'metadata' in schema:
             metadata = schema['metadata']
             metadata[NEEDS_APPLY_DISCRIMINATED_UNION_METADATA_KEY] = self._needs_apply_discriminated_union
-            metadata[HAS_INVALID_SCHEMAS_METADATA_KEY] = self._has_invalid_schema
         else:
             schema['metadata'] = {
                 NEEDS_APPLY_DISCRIMINATED_UNION_METADATA_KEY: self._needs_apply_discriminated_union,
-                HAS_INVALID_SCHEMAS_METADATA_KEY: self._has_invalid_schema,
             }
         return schema
 
diff --git a/pydantic/_internal/_model_construction.py b/pydantic/_internal/_model_construction.py
index 969b9ea2e4..15dbb3ee1c 100644
--- a/pydantic/_internal/_model_construction.py
+++ b/pydantic/_internal/_model_construction.py
@@ -488,12 +488,12 @@ def complete_model_class(
     core_config = config_wrapper.core_config(cls)
 
     schema = gen_schema.collect_definitions(schema)
+
+    schema = apply_discriminators(simplify_schema_references(schema))
     if collect_invalid_schemas(schema):
         set_model_mocks(cls, cls_name)
         return False
 
-    schema = apply_discriminators(simplify_schema_references(schema))
-
     # debug(schema)
     cls.__pydantic_core_schema__ = schema = validate_core_schema(schema)
     cls.__pydantic_validator__ = create_schema_validator(schema, core_config, config_wrapper.plugin_settings)
diff --git a/tests/test_model_signature.py b/tests/test_model_signature.py
index 727901922a..e37ac4b093 100644
--- a/tests/test_model_signature.py
+++ b/tests/test_model_signature.py
@@ -32,7 +32,6 @@ class Model(BaseModel):
     assert _equals(str(sig), '(*, a: float, b: int = 10) -> None')
 
 
-@pytest.mark.xfail(reason='https://github.com/pydantic/pydantic/pull/7523#discussion_r1331765978')
 def test_generic_model_signature():
     T = TypeVar('T')