diff --git a/pyproject.toml b/pyproject.toml
index 989e63122f640..5838495239725 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -58,8 +58,6 @@ module = [
     "pytorch_lightning.core.saving",
     "pytorch_lightning.demos.boring_classes",
     "pytorch_lightning.demos.mnist_datamodule",
-    "pytorch_lightning.loggers.comet",
-    "pytorch_lightning.loggers.mlflow",
     "pytorch_lightning.loggers.neptune",
     "pytorch_lightning.loggers.tensorboard",
     "pytorch_lightning.loggers.wandb",
diff --git a/src/pytorch_lightning/loggers/comet.py b/src/pytorch_lightning/loggers/comet.py
index 2b853f59259ff..dc9a2d3364408 100644
--- a/src/pytorch_lightning/loggers/comet.py
+++ b/src/pytorch_lightning/loggers/comet.py
@@ -141,7 +141,7 @@ def __init__(
         prefix: str = "",
         agg_key_funcs: Optional[Mapping[str, Callable[[Sequence[float]], float]]] = None,
         agg_default_func: Optional[Callable[[Sequence[float]], float]] = None,
-        **kwargs,
+        **kwargs: Any,
     ):
         if comet_ml is None:
             raise ModuleNotFoundError(
@@ -149,6 +149,8 @@ def __init__(
             )
         super().__init__(agg_key_funcs=agg_key_funcs, agg_default_func=agg_default_func)
         self._experiment = None
+        self._save_dir: Optional[str]
+        self.rest_api_key: Optional[str]
 
         # Determine online or offline mode based on which arguments were passed to CometLogger
         api_key = api_key or comet_ml.config.get_api_key(None, comet_ml.config.get_config())
@@ -170,12 +172,12 @@ def __init__(
 
         log.info(f"CometLogger will be initialized in {self.mode} mode")
 
-        self._project_name = project_name
-        self._experiment_key = experiment_key
-        self._experiment_name = experiment_name
-        self._prefix = prefix
-        self._kwargs = kwargs
-        self._future_experiment_key = None
+        self._project_name: Optional[str] = project_name
+        self._experiment_key: Optional[str] = experiment_key
+        self._experiment_name: Optional[str] = experiment_name
+        self._prefix: str = prefix
+        self._kwargs: Any = kwargs
+        self._future_experiment_key: Optional[str] = None
 
         if rest_api_key is not None:
             # Comet.ml rest API, used to determine version number
@@ -187,7 +189,7 @@ def __init__(
 
         self._kwargs = kwargs
 
-    @property
+    @property  # type: ignore[misc]
     @rank_zero_experiment
     def experiment(self) -> Union[CometExperiment, CometExistingExperiment, CometOfflineExperiment]:
         r"""
@@ -246,13 +248,13 @@ def log_metrics(self, metrics: Dict[str, Union[Tensor, float]], step: Optional[i
         metrics_without_epoch = metrics.copy()
         for key, val in metrics_without_epoch.items():
             if is_tensor(val):
-                metrics_without_epoch[key] = val.cpu().detach()
+                metrics_without_epoch[key] = val.cpu().detach()  # type: ignore[union-attr]
 
         epoch = metrics_without_epoch.pop("epoch", None)
         metrics_without_epoch = _add_prefix(metrics_without_epoch, self._prefix, self.LOGGER_JOIN_CHAR)
         self.experiment.log_metrics(metrics_without_epoch, step=step, epoch=epoch)
 
-    def reset_experiment(self):
+    def reset_experiment(self) -> None:
         self._experiment = None
 
     @rank_zero_only
@@ -326,7 +328,7 @@ def version(self) -> str:
 
         return self._future_experiment_key
 
-    def __getstate__(self):
+    def __getstate__(self):  # type: ignore[no-untyped-def]
         state = self.__dict__.copy()
 
         # Save the experiment id in case an experiment object already exists,
@@ -340,6 +342,6 @@ def __getstate__(self):
         state["_experiment"] = None
         return state
 
-    def log_graph(self, model: "pl.LightningModule", input_array=None) -> None:
+    def log_graph(self, model: "pl.LightningModule", input_array: Optional[Tensor] = None) -> None:
         if self._experiment is not None:
             self._experiment.set_model_graph(model)
diff --git a/src/pytorch_lightning/loggers/csv_logs.py b/src/pytorch_lightning/loggers/csv_logs.py
index 72d21ae2c4974..45d5fffb51e33 100644
--- a/src/pytorch_lightning/loggers/csv_logs.py
+++ b/src/pytorch_lightning/loggers/csv_logs.py
@@ -195,7 +195,7 @@ def log_hyperparams(self, params: Union[Dict[str, Any], Namespace]) -> None:
         self.experiment.log_hparams(params)
 
     @rank_zero_only
-    def log_metrics(self, metrics: Dict[str, float], step: Optional[int] = None) -> None:
+    def log_metrics(self, metrics: Dict[str, Union[Tensor, float]], step: Optional[int] = None) -> None:
         metrics = _add_prefix(metrics, self._prefix, self.LOGGER_JOIN_CHAR)
         self.experiment.log_metrics(metrics, step)
         if step is not None and (step + 1) % self._flush_logs_every_n_steps == 0:
diff --git a/src/pytorch_lightning/utilities/logger.py b/src/pytorch_lightning/utilities/logger.py
index 07ecf4c3c0ca0..7e404482bea24 100644
--- a/src/pytorch_lightning/utilities/logger.py
+++ b/src/pytorch_lightning/utilities/logger.py
@@ -132,7 +132,9 @@ def _sanitize_params(params: Dict[str, Any]) -> Dict[str, Any]:
     return params
 
 
-def _add_prefix(metrics: Dict[str, float], prefix: str, separator: str) -> Dict[str, float]:
+def _add_prefix(
+    metrics: Dict[str, Union[Tensor, float]], prefix: str, separator: str
+) -> Dict[str, Union[Tensor, float]]:
     """Insert prefix before each key in a dict, separated by the separator.
 
     Args: