diff --git a/pyproject.toml b/pyproject.toml
index 761c7be04cc0e..8db782df357d8 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -53,7 +53,6 @@ module = [
     "pytorch_lightning.callbacks.quantization",
     "pytorch_lightning.core.datamodule",
     "pytorch_lightning.core.module",
-    "pytorch_lightning.core.saving",
     "pytorch_lightning.demos.boring_classes",
     "pytorch_lightning.demos.mnist_datamodule",
     "pytorch_lightning.profilers.base",
diff --git a/src/pytorch_lightning/core/saving.py b/src/pytorch_lightning/core/saving.py
index da81e4c212560..ffdc0988a1a6e 100644
--- a/src/pytorch_lightning/core/saving.py
+++ b/src/pytorch_lightning/core/saving.py
@@ -20,10 +20,9 @@
 from argparse import Namespace
 from copy import deepcopy
 from enum import Enum
-from typing import Any, Callable, Dict, IO, MutableMapping, Optional, Union
+from typing import Any, Callable, cast, Dict, IO, MutableMapping, Optional, Type, Union
 from warnings import warn
 
-import torch
 import yaml
 
 import pytorch_lightning as pl
@@ -34,7 +33,7 @@
 from pytorch_lightning.utilities.migration import pl_legacy_patch
 from pytorch_lightning.utilities.parsing import parse_class_init_keys
 from pytorch_lightning.utilities.rank_zero import rank_zero_warn
-from pytorch_lightning.utilities.types import _PATH
+from pytorch_lightning.utilities.types import _MAP_LOCATION_TYPE, _PATH
 
 log = logging.getLogger(__name__)
 PRIMITIVE_TYPES = (bool, int, float, str)
@@ -58,11 +57,11 @@ class ModelIO:
     def load_from_checkpoint(
         cls,
         checkpoint_path: Union[str, IO],
-        map_location: Optional[Union[Dict[str, str], str, torch.device, int, Callable]] = None,
+        map_location: _MAP_LOCATION_TYPE = None,
         hparams_file: Optional[str] = None,
         strict: bool = True,
-        **kwargs,
-    ):
+        **kwargs: Any,
+    ) -> Union["pl.LightningModule", "pl.LightningDataModule"]:
         r"""
         Primary way of loading a model from a checkpoint. When Lightning saves a checkpoint
         it stores the arguments passed to ``__init__``  in the checkpoint under ``"hyper_parameters"``.
@@ -171,15 +170,15 @@ def on_hpc_load(self, checkpoint: Dict[str, Any]) -> None:
 
 
 def _load_from_checkpoint(
-    cls: Union["pl.LightningModule", "pl.LightningDataModule"],
+    cls: Union[Type["ModelIO"], Type["pl.LightningModule"], Type["pl.LightningDataModule"]],
     checkpoint_path: Union[str, IO],
-    map_location: Optional[Union[Dict[str, str], str, torch.device, int, Callable]] = None,
+    map_location: _MAP_LOCATION_TYPE = None,
     hparams_file: Optional[str] = None,
-    strict: Optional[bool] = None,
+    strict: bool = True,
     **kwargs: Any,
-) -> Any:
+) -> Union["pl.LightningModule", "pl.LightningDataModule"]:
     if map_location is None:
-        map_location = lambda storage, loc: storage
+        map_location = cast(_MAP_LOCATION_TYPE, lambda storage, loc: storage)
     with pl_legacy_patch():
         checkpoint = pl_load(checkpoint_path, map_location=map_location)
 
@@ -202,15 +201,18 @@ def _load_from_checkpoint(
 
     if issubclass(cls, pl.LightningDataModule):
         return _load_state(cls, checkpoint, **kwargs)
-    return _load_state(cls, checkpoint, strict=strict, **kwargs)
+    # allow cls to be evaluated as subclassed LightningModule or,
+    # as LightningModule for internal tests
+    if issubclass(cls, pl.LightningModule):
+        return _load_state(cls, checkpoint, strict=strict, **kwargs)
 
 
 def _load_state(
-    cls: Union["pl.LightningModule", "pl.LightningDataModule"],
+    cls: Union[Type["pl.LightningModule"], Type["pl.LightningDataModule"]],
     checkpoint: Dict[str, Any],
-    strict: Optional[bool] = None,
+    strict: bool = True,
     **cls_kwargs_new: Any,
-) -> Any:
+) -> Union["pl.LightningModule", "pl.LightningDataModule"]:
     cls_spec = inspect.getfullargspec(cls.__init__)
     cls_init_args_name = inspect.signature(cls.__init__).parameters.keys()
 
@@ -228,8 +230,7 @@ def _load_state(
                 cls_kwargs_loaded.update(checkpoint.get(_old_hparam_key, {}))
 
         # 2. Try to restore model hparams from checkpoint using the new key
-        _new_hparam_key = cls.CHECKPOINT_HYPER_PARAMS_KEY
-        cls_kwargs_loaded.update(checkpoint.get(_new_hparam_key))
+        cls_kwargs_loaded.update(checkpoint.get(cls.CHECKPOINT_HYPER_PARAMS_KEY, {}))
 
         # 3. Ensure that `cls_kwargs_old` has the right type, back compatibility between dict and Namespace
         cls_kwargs_loaded = _convert_loaded_hparams(cls_kwargs_loaded, checkpoint.get(cls.CHECKPOINT_HYPER_PARAMS_TYPE))
@@ -271,7 +272,9 @@ def _load_state(
     return obj
 
 
-def _convert_loaded_hparams(model_args: dict, hparams_type: Optional[Union[Callable, str]] = None) -> object:
+def _convert_loaded_hparams(
+    model_args: Dict[str, Any], hparams_type: Optional[Union[Callable, str]] = None
+) -> Dict[str, Any]:
     """Convert hparams according given type in callable or string (past) format."""
     # if not hparams type define
     if not hparams_type:
diff --git a/src/pytorch_lightning/utilities/cloud_io.py b/src/pytorch_lightning/utilities/cloud_io.py
index ee3358be59541..99629bcda8980 100644
--- a/src/pytorch_lightning/utilities/cloud_io.py
+++ b/src/pytorch_lightning/utilities/cloud_io.py
@@ -15,19 +15,19 @@
 
 import io
 from pathlib import Path
-from typing import Any, Callable, Dict, IO, Optional, Union
+from typing import Any, Dict, IO, Union
 
 import fsspec
 import torch
 from fsspec.core import url_to_fs
 from fsspec.implementations.local import AbstractFileSystem
 
-from pytorch_lightning.utilities.types import _DEVICE, _PATH
+from pytorch_lightning.utilities.types import _MAP_LOCATION_TYPE, _PATH
 
 
 def load(
     path_or_url: Union[IO, _PATH],
-    map_location: Optional[Union[_DEVICE, Callable[[_DEVICE], _DEVICE], Dict[_DEVICE, _DEVICE]]] = None,
+    map_location: _MAP_LOCATION_TYPE = None,
 ) -> Any:
     """Loads a checkpoint.
 
diff --git a/src/pytorch_lightning/utilities/parsing.py b/src/pytorch_lightning/utilities/parsing.py
index 9f5fe2d6b6841..81877f1dffba7 100644
--- a/src/pytorch_lightning/utilities/parsing.py
+++ b/src/pytorch_lightning/utilities/parsing.py
@@ -108,7 +108,9 @@ def clean_namespace(hparams: Union[Dict[str, Any], Namespace]) -> None:
         del hparams_dict[k]
 
 
-def parse_class_init_keys(cls: Type["pl.LightningModule"]) -> Tuple[str, Optional[str], Optional[str]]:
+def parse_class_init_keys(
+    cls: Union[Type["pl.LightningModule"], Type["pl.LightningDataModule"]]
+) -> Tuple[str, Optional[str], Optional[str]]:
     """Parse key words for standard ``self``, ``*args`` and ``**kwargs``.
 
     Examples:
diff --git a/src/pytorch_lightning/utilities/types.py b/src/pytorch_lightning/utilities/types.py
index f6c14d366805f..18e2db6feb6c6 100644
--- a/src/pytorch_lightning/utilities/types.py
+++ b/src/pytorch_lightning/utilities/types.py
@@ -19,7 +19,7 @@
 from contextlib import contextmanager
 from dataclasses import dataclass
 from pathlib import Path
-from typing import Any, Dict, Generator, Iterator, List, Mapping, Optional, Sequence, Type, Union
+from typing import Any, Callable, Dict, Generator, Iterator, List, Mapping, Optional, Sequence, Type, Union
 
 import torch
 from torch import Tensor
@@ -49,6 +49,7 @@
 ]
 EVAL_DATALOADERS = Union[DataLoader, Sequence[DataLoader]]
 _DEVICE = Union[torch.device, str, int]
+_MAP_LOCATION_TYPE = Optional[Union[_DEVICE, Callable[[_DEVICE], _DEVICE], Dict[_DEVICE, _DEVICE]]]
 
 
 @runtime_checkable