diff --git a/src/lightning_lite/connector.py b/src/lightning_lite/connector.py
index 7b8d4a9330df8..3e9a7560d6472 100644
--- a/src/lightning_lite/connector.py
+++ b/src/lightning_lite/connector.py
@@ -16,6 +16,7 @@
 from typing import Dict, List, Optional, Union
 
 import torch
+from typing_extensions import Literal
 
 from lightning_lite.accelerators import ACCELERATOR_REGISTRY
 from lightning_lite.accelerators.accelerator import Accelerator
@@ -58,6 +59,7 @@
 
 _PLUGIN = Union[Precision, ClusterEnvironment, CheckpointIO]
 _PLUGIN_INPUT = Union[_PLUGIN, str]
+_PRECISION_INPUT = Literal[16, 32, 64, "bf16"]
 
 
 class _Connector:
@@ -97,7 +99,7 @@ def __init__(
         strategy: Optional[Union[str, Strategy]] = None,
         devices: Optional[Union[List[int], str, int]] = None,
         num_nodes: int = 1,
-        precision: Union[int, str] = 32,
+        precision: _PRECISION_INPUT = 32,
         plugins: Optional[Union[_PLUGIN_INPUT, List[_PLUGIN_INPUT]]] = None,
     ) -> None:
         # 1. Parsing flags
@@ -111,7 +113,7 @@ def __init__(
         # For devices: Assign gpus, ipus, etc. to the accelerator flag and devices flag
         self._strategy_flag: Optional[Union[Strategy, str]] = None
         self._accelerator_flag: Optional[Union[Accelerator, str]] = None
-        self._precision_flag: Optional[Union[int, str]] = None
+        self._precision_flag: Optional[_PRECISION_INPUT] = None
         self._precision_plugin_flag: Optional[Precision] = None
         self._cluster_environment_flag: Optional[Union[ClusterEnvironment, str]] = None
         self._parallel_devices: List[Union[int, torch.device, str]] = []
@@ -154,7 +156,7 @@ def _check_config_and_set_final_flags(
         self,
         strategy: Optional[Union[str, Strategy]],
         accelerator: Optional[Union[str, Accelerator]],
-        precision: Union[int, str],
+        precision: _PRECISION_INPUT,
         plugins: Optional[Union[_PLUGIN_INPUT, List[_PLUGIN_INPUT]]],
     ) -> None:
         """This method checks:
diff --git a/src/lightning_lite/lite.py b/src/lightning_lite/lite.py
index 414c63c841813..04b964e41c5a0 100644
--- a/src/lightning_lite/lite.py
+++ b/src/lightning_lite/lite.py
@@ -27,7 +27,7 @@
 from torch.utils.data import BatchSampler, DataLoader, DistributedSampler
 
 from lightning_lite.accelerators.accelerator import Accelerator
-from lightning_lite.connector import _Connector, _PLUGIN_INPUT
+from lightning_lite.connector import _Connector, _PLUGIN_INPUT, _PRECISION_INPUT
 from lightning_lite.plugins import Precision
 from lightning_lite.strategies import DeepSpeedStrategy, Strategy, XLAStrategy
 from lightning_lite.strategies.strategy import TBroadcast
@@ -74,7 +74,7 @@ def __init__(
         strategy: Optional[Union[str, Strategy]] = None,
         devices: Optional[Union[List[int], str, int]] = None,
         num_nodes: int = 1,
-        precision: Union[int, str] = 32,
+        precision: _PRECISION_INPUT = 32,
         plugins: Optional[Union[_PLUGIN_INPUT, List[_PLUGIN_INPUT]]] = None,
     ) -> None:
         self._connector = _Connector(
diff --git a/src/lightning_lite/plugins/precision/deepspeed.py b/src/lightning_lite/plugins/precision/deepspeed.py
index 3ccf2d3ba09b4..3817bf3aa3f04 100644
--- a/src/lightning_lite/plugins/precision/deepspeed.py
+++ b/src/lightning_lite/plugins/precision/deepspeed.py
@@ -11,12 +11,15 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import Any, Optional, TYPE_CHECKING, Union
+from typing import Any, Optional, TYPE_CHECKING
 
+import torch
 from lightning_utilities.core.imports import RequirementCache
 from torch import Tensor
+from typing_extensions import Literal
 
 from lightning_lite.plugins.precision.precision import Precision
+from lightning_lite.plugins.precision.utils import _convert_fp_tensor
 from lightning_lite.utilities.enums import AMPType, PrecisionType
 from lightning_lite.utilities.imports import _APEX_AVAILABLE
 from lightning_lite.utilities.types import Steppable
@@ -43,7 +46,7 @@ class DeepSpeedPrecision(Precision):
             If unsupported ``precision`` is provided.
     """
 
-    def __init__(self, precision: Union[str, int], amp_type: str, amp_level: Optional[str] = None) -> None:
+    def __init__(self, precision: Literal[16, 32, "bf16"], amp_type: str, amp_level: Optional[str] = None) -> None:
         if amp_type == AMPType.APEX:
             if not _APEX_AVAILABLE:
                 raise ImportError(
@@ -65,6 +68,11 @@ def __init__(self, precision: Union[str, int], amp_type: str, amp_level: Optiona
         self.amp_type = amp_type
         self.amp_level = amp_level
 
+    def convert_input(self, data: Tensor) -> Tensor:
+        precision_to_type = {"bf16": torch.bfloat16, 16: torch.float16, 32: torch.float32}
+        dst_type = precision_to_type[self.precision]
+        return _convert_fp_tensor(data, dst_type)
+
     def backward(self, tensor: Tensor, model: "deepspeed.DeepSpeedEngine", *args: Any, **kwargs: Any) -> None:
         """Performs back-propagation using DeepSpeed's engine."""
         model.backward(tensor, *args, **kwargs)
diff --git a/src/lightning_lite/plugins/precision/double.py b/src/lightning_lite/plugins/precision/double.py
index 9bbb033b742a9..dd0aa73eee5f0 100644
--- a/src/lightning_lite/plugins/precision/double.py
+++ b/src/lightning_lite/plugins/precision/double.py
@@ -15,9 +15,11 @@
 from typing import Generator
 
 import torch
+from torch import Tensor
 from torch.nn import Module
 
 from lightning_lite.plugins.precision.precision import Precision
+from lightning_lite.plugins.precision.utils import _convert_fp_tensor
 
 
 class DoublePrecision(Precision):
@@ -38,3 +40,6 @@ def forward_context(self) -> Generator[None, None, None]:
         torch.set_default_dtype(torch.float64)
         yield
         torch.set_default_dtype(default_dtype)
+
+    def convert_input(self, data: Tensor) -> Tensor:
+        return _convert_fp_tensor(data, torch.double)
diff --git a/src/lightning_lite/plugins/precision/native_amp.py b/src/lightning_lite/plugins/precision/native_amp.py
index 58cdffeb99cbc..34b4fb5591724 100644
--- a/src/lightning_lite/plugins/precision/native_amp.py
+++ b/src/lightning_lite/plugins/precision/native_amp.py
@@ -18,8 +18,10 @@
 from torch import Tensor
 from torch.nn import Module
 from torch.optim import LBFGS
+from typing_extensions import Literal
 
 from lightning_lite.plugins.precision.precision import Precision
+from lightning_lite.plugins.precision.utils import _convert_fp_tensor
 from lightning_lite.utilities.imports import _TORCH_GREATER_EQUAL_1_10
 from lightning_lite.utilities.types import Steppable
 
@@ -39,7 +41,7 @@ class NativeMixedPrecision(Precision):
     """
 
     def __init__(
-        self, precision: Union[str, int], device: str, scaler: Optional[torch.cuda.amp.GradScaler] = None
+        self, precision: Literal[16, "bf16"], device: str, scaler: Optional[torch.cuda.amp.GradScaler] = None
     ) -> None:
         super().__init__()
         if precision == "bf16" and not _TORCH_GREATER_EQUAL_1_10:
@@ -57,6 +59,11 @@ def forward_context(self) -> Generator[None, None, None]:
         with self._autocast_context_manager():
             yield
 
+    def convert_input(self, data: Tensor) -> Tensor:
+        precision_to_type = {"bf16": torch.bfloat16, 16: torch.float16}
+        dst_type = precision_to_type[self.precision]
+        return _convert_fp_tensor(data, dst_type)
+
     def backward(self, tensor: Tensor, model: Optional[Module], *args: Any, **kwargs: Any) -> None:
         if self.scaler is not None:
             tensor = self.scaler.scale(tensor)
diff --git a/src/lightning_lite/plugins/precision/precision.py b/src/lightning_lite/plugins/precision/precision.py
index 07ce77b8897bf..6a3883a022edb 100644
--- a/src/lightning_lite/plugins/precision/precision.py
+++ b/src/lightning_lite/plugins/precision/precision.py
@@ -14,10 +14,12 @@
 import contextlib
 from typing import Any, Dict, Generator, Optional, Union
 
+import torch
 from torch import Tensor
 from torch.nn import Module
 from torch.optim import Optimizer
 
+from lightning_lite.plugins.precision.utils import _convert_fp_tensor
 from lightning_lite.utilities.types import _PARAMETERS, Steppable
 
 
@@ -41,6 +43,13 @@ def forward_context(self) -> Generator[None, None, None]:
         """A contextmanager for managing model forward/training_step/evaluation_step/predict_step."""
         yield
 
+    def convert_input(self, data: Tensor) -> Tensor:
+        """Convert model inputs (forward) to the floating point precision type of this plugin.
+
+        This is a no-op for tensors that are not of floating-point type or already have the desired type.
+        """
+        return _convert_fp_tensor(data, torch.float32)
+
     def pre_backward(self, tensor: Tensor, module: Optional[Module]) -> Any:
         """Runs before precision plugin executes backward.
 
diff --git a/src/lightning_lite/plugins/precision/tpu_bf16.py b/src/lightning_lite/plugins/precision/tpu_bf16.py
index d388a9ae175ac..84824b35e4e0d 100644
--- a/src/lightning_lite/plugins/precision/tpu_bf16.py
+++ b/src/lightning_lite/plugins/precision/tpu_bf16.py
@@ -13,7 +13,11 @@
 # limitations under the License.
 import os
 
+import torch
+from torch import Tensor
+
 from lightning_lite.plugins.precision import TPUPrecision
+from lightning_lite.plugins.precision.utils import _convert_fp_tensor
 
 
 class TPUBf16Precision(TPUPrecision):
@@ -25,5 +29,8 @@ def __init__(self) -> None:
         super().__init__()
         os.environ["XLA_USE_BF16"] = "1"
 
+    def convert_input(self, data: Tensor) -> Tensor:
+        return _convert_fp_tensor(data, torch.bfloat16)
+
     def teardown(self) -> None:
         os.environ.pop("XLA_USE_BF16", None)
diff --git a/src/lightning_lite/plugins/precision/utils.py b/src/lightning_lite/plugins/precision/utils.py
index f607755e5da7d..dc41a5202d817 100644
--- a/src/lightning_lite/plugins/precision/utils.py
+++ b/src/lightning_lite/plugins/precision/utils.py
@@ -15,16 +15,6 @@
 
 import torch
 
-from lightning_lite.utilities.enums import PrecisionType
-
-
-def _fp_to_half(tensor: torch.Tensor, precision: PrecisionType) -> torch.Tensor:
-    if precision == PrecisionType.HALF:
-        return _convert_fp_tensor(tensor, torch.half)
-    if precision == PrecisionType.BFLOAT:
-        return _convert_fp_tensor(tensor, torch.bfloat16)
-    return tensor
-
 
 def _convert_fp_tensor(tensor: torch.Tensor, dst_type: Union[str, torch.dtype]) -> torch.Tensor:
     return tensor.to(dst_type) if torch.is_floating_point(tensor) else tensor
diff --git a/src/lightning_lite/strategies/deepspeed.py b/src/lightning_lite/strategies/deepspeed.py
index facc9f5cbd3ef..da532c5a567fd 100644
--- a/src/lightning_lite/strategies/deepspeed.py
+++ b/src/lightning_lite/strategies/deepspeed.py
@@ -23,16 +23,13 @@
 import torch
 from lightning_utilities.core.imports import RequirementCache
 from lightning_utilities.core.rank_zero import rank_zero_only
-from torch import Tensor
 from torch.nn import Module
 from torch.optim import Optimizer
 
 from lightning_lite.accelerators import Accelerator, CUDAAccelerator
 from lightning_lite.plugins.environments.cluster_environment import ClusterEnvironment
 from lightning_lite.plugins.precision import Precision
-from lightning_lite.plugins.precision.utils import _fp_to_half
 from lightning_lite.strategies.ddp import DDPStrategy
-from lightning_lite.utilities.apply_func import apply_to_collection
 from lightning_lite.utilities.distributed import log
 from lightning_lite.utilities.enums import AMPType, PrecisionType
 from lightning_lite.utilities.rank_zero import rank_zero_info
@@ -366,10 +363,6 @@ def load_module_state_dict(self, module: Module, checkpoint: Mapping[str, Any])
             self.module_to_device(module)
             self._restore_zero_state(module, checkpoint)
 
-    def batch_to_device(self, batch: Any, device: Optional[torch.device] = None) -> Any:
-        batch = apply_to_collection(batch, Tensor, function=_fp_to_half, precision=self.precision_plugin.precision)
-        return super().batch_to_device(batch, device)
-
     @classmethod
     def register_strategies(cls, strategy_registry: Dict) -> None:
         strategy_registry.register("deepspeed", cls, description="Default DeepSpeed Strategy")
diff --git a/src/lightning_lite/wrappers.py b/src/lightning_lite/wrappers.py
index a976edb09a10b..c13f9a450b054 100644
--- a/src/lightning_lite/wrappers.py
+++ b/src/lightning_lite/wrappers.py
@@ -97,23 +97,13 @@ def module(self) -> nn.Module:
     def forward(self, *args: Any, **kwargs: Any) -> Any:
         """Casts all inputs to the right precision and handles autocast for operations in the module forward
         method."""
-        precision = self._precision_plugin.precision
-        precision_to_type = {
-            "bf16": torch.bfloat16,
-            16: torch.float16,
-            32: torch.float32,
-            64: torch.float64,
-        }
-        # TODO: let the precision plugin handle the conversion
-        args, kwargs = apply_to_collection(
-            [args, kwargs], dtype=Tensor, function=_convert_fp_tensor, dst_type=precision_to_type[precision]
-        )
+        args, kwargs = apply_to_collection([args, kwargs], function=self._precision_plugin.convert_input, dtype=Tensor)
 
         with self._precision_plugin.forward_context():
             output = self._forward_module(*args, **kwargs)
 
         output = apply_to_collection(
-            output, dtype=Tensor, function=_convert_fp_tensor, dst_type=torch.get_default_dtype()
+            output, function=_convert_fp_tensor, dtype=Tensor, dst_type=torch.get_default_dtype()
         )
         return output
 
diff --git a/src/pytorch_lightning/lite/lite.py b/src/pytorch_lightning/lite/lite.py
index c34561b702a25..be6f2108249d0 100644
--- a/src/pytorch_lightning/lite/lite.py
+++ b/src/pytorch_lightning/lite/lite.py
@@ -18,6 +18,7 @@
 from lightning_utilities.core.rank_zero import rank_zero_deprecation, rank_zero_warn
 
 from lightning_lite.connector import _PLUGIN_INPUT as _LITE_PLUGIN_INPUT
+from lightning_lite.connector import _PRECISION_INPUT
 from lightning_lite.lite import LightningLite as _NewLightningLite
 from lightning_lite.plugins import CheckpointIO, ClusterEnvironment
 from lightning_lite.plugins import DeepSpeedPrecision as LiteDeepSpeedPrecision
@@ -98,7 +99,7 @@ def __init__(
         strategy: Optional[Union[str, PLStrategy]] = None,
         devices: Optional[Union[List[int], str, int]] = None,
         num_nodes: int = 1,
-        precision: Union[int, str] = 32,
+        precision: _PRECISION_INPUT = 32,
         plugins: Optional[Union[_PL_PLUGIN_INPUT, List[_PL_PLUGIN_INPUT]]] = None,
         gpus: Optional[Union[List[int], str, int]] = None,
         tpu_cores: Optional[Union[List[int], str, int]] = None,
@@ -286,13 +287,17 @@ def _to_lite_precision_plugin(plugin: Optional[PLPrecisionPlugin]) -> LitePrecis
         return LitePrecision()
 
     if type(plugin) is PLNativeMixedPrecisionPlugin:
-        return LiteNativeMixedPrecision(precision=plugin.precision, device=plugin.device, scaler=plugin.scaler)
+        return LiteNativeMixedPrecision(
+            precision=plugin.precision, device=plugin.device, scaler=plugin.scaler  # type: ignore[arg-type]
+        )
 
     if type(plugin) is PLDoublePrecisionPlugin:
         return LiteDoublePrecision()
 
     if type(plugin) is PLDeepSpeedPrecisionPlugin:
-        return LiteDeepSpeedPrecision(precision=plugin.precision, amp_type=plugin.amp_type, amp_level=plugin.amp_level)
+        return LiteDeepSpeedPrecision(
+            precision=plugin.precision, amp_type=plugin.amp_type, amp_level=plugin.amp_level  # type: ignore[arg-type]
+        )
 
     if type(plugin) is PLTPUPrecisionPlugin:
         return LiteTPUPrecision()
diff --git a/src/pytorch_lightning/strategies/deepspeed.py b/src/pytorch_lightning/strategies/deepspeed.py
index a3a6a7998e546..82f0aed9d1366 100644
--- a/src/pytorch_lightning/strategies/deepspeed.py
+++ b/src/pytorch_lightning/strategies/deepspeed.py
@@ -31,7 +31,6 @@
 
 import pytorch_lightning as pl
 from lightning_lite.plugins import ClusterEnvironment
-from lightning_lite.plugins.precision.utils import _fp_to_half
 from lightning_lite.utilities.enums import AMPType, PrecisionType
 from lightning_lite.utilities.optimizer import optimizers_to_device
 from lightning_lite.utilities.seed import reset_seed
@@ -41,6 +40,7 @@
 from pytorch_lightning.overrides.base import _LightningModuleWrapperBase, _LightningPrecisionModuleWrapperBase
 from pytorch_lightning.plugins.precision import PrecisionPlugin
 from pytorch_lightning.strategies.ddp import DDPStrategy
+from pytorch_lightning.strategies.utils import _fp_to_half
 from pytorch_lightning.trainer.states import TrainerFn
 from pytorch_lightning.utilities import GradClipAlgorithmType
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
diff --git a/src/pytorch_lightning/strategies/ipu.py b/src/pytorch_lightning/strategies/ipu.py
index a5daa13dc9de6..66c11b26c90ff 100644
--- a/src/pytorch_lightning/strategies/ipu.py
+++ b/src/pytorch_lightning/strategies/ipu.py
@@ -22,12 +22,12 @@
 
 import pytorch_lightning as pl
 from lightning_lite.plugins import CheckpointIO, ClusterEnvironment
-from lightning_lite.plugins.precision.utils import _fp_to_half
 from lightning_lite.utilities.cloud_io import get_filesystem
 from pytorch_lightning.overrides.base import _LightningModuleWrapperBase
 from pytorch_lightning.plugins.precision import PrecisionPlugin
 from pytorch_lightning.strategies.parallel import ParallelStrategy
 from pytorch_lightning.strategies.strategy import TBroadcast
+from pytorch_lightning.strategies.utils import _fp_to_half
 from pytorch_lightning.trainer.states import RunningStage, TrainerFn
 from pytorch_lightning.utilities import _IPU_AVAILABLE, _POPTORCH_AVAILABLE, rank_zero_warn
 from pytorch_lightning.utilities.data import _get_dataloader_init_args_and_kwargs, _reinstantiate_wrapped_cls
diff --git a/src/pytorch_lightning/strategies/utils.py b/src/pytorch_lightning/strategies/utils.py
index fa360d3770cd7..be602a3929665 100644
--- a/src/pytorch_lightning/strategies/utils.py
+++ b/src/pytorch_lightning/strategies/utils.py
@@ -15,7 +15,11 @@
 import os
 from inspect import getmembers, isclass
 
+import torch
+
+from lightning_lite.plugins.precision.utils import _convert_fp_tensor
 from lightning_lite.strategies import _StrategyRegistry
+from lightning_lite.utilities.enums import PrecisionType
 from lightning_lite.utilities.registry import _is_register_method_overridden
 from pytorch_lightning.strategies.strategy import Strategy
 from pytorch_lightning.utilities.rank_zero import rank_zero_deprecation
@@ -34,3 +38,11 @@ def _call_register_strategies(registry: _StrategyRegistry, base_module: str) ->
     for _, mod in getmembers(module, isclass):
         if issubclass(mod, Strategy) and _is_register_method_overridden(mod, Strategy, "register_strategies"):
             mod.register_strategies(registry)
+
+
+def _fp_to_half(tensor: torch.Tensor, precision: PrecisionType) -> torch.Tensor:
+    if precision == PrecisionType.HALF:
+        return _convert_fp_tensor(tensor, torch.half)
+    if precision == PrecisionType.BFLOAT:
+        return _convert_fp_tensor(tensor, torch.bfloat16)
+    return tensor
diff --git a/tests/tests_lite/plugins/precision/test_native_amp_integration.py b/tests/tests_lite/plugins/precision/test_native_amp_integration.py
index f657236069342..94d8c399679cf 100644
--- a/tests/tests_lite/plugins/precision/test_native_amp_integration.py
+++ b/tests/tests_lite/plugins/precision/test_native_amp_integration.py
@@ -67,6 +67,6 @@ def after_backward(self, model):
     ],
 )
 def test_native_mixed_precision(accelerator, precision, expected_dtype):
-    lite = NativeMixedPrecisionBoringLite(accelerator=accelerator, precision=16)
+    lite = NativeMixedPrecisionBoringLite(accelerator=accelerator, precision=precision)
     lite.expected_dtype = expected_dtype
     lite.run()