diff --git a/mmengine/optim/optimizer/builder.py b/mmengine/optim/optimizer/builder.py
index 8557f4d34c..013fa2f3af 100644
--- a/mmengine/optim/optimizer/builder.py
+++ b/mmengine/optim/optimizer/builder.py
@@ -25,7 +25,11 @@ def register_torch_optimizers() -> List[str]:
         _optim = getattr(torch.optim, module_name)
         if inspect.isclass(_optim) and issubclass(_optim,
                                                   torch.optim.Optimizer):
-            OPTIMIZERS.register_module(module=_optim)
+            if module_name == 'Adafactor':
+                OPTIMIZERS.register_module(
+                    name='torch_Adafactor', module=_optim)
+            else:
+                OPTIMIZERS.register_module(module=_optim)
             torch_optimizers.append(module_name)
     return torch_optimizers
 
diff --git a/mmengine/registry/build_functions.py b/mmengine/registry/build_functions.py
index 9d195162bc..4fee07569a 100644
--- a/mmengine/registry/build_functions.py
+++ b/mmengine/registry/build_functions.py
@@ -3,8 +3,10 @@
 import logging
 from typing import TYPE_CHECKING, Any, Optional, Union
 
+import torch
+
 from mmengine.config import Config, ConfigDict
-from mmengine.utils import ManagerMixin
+from mmengine.utils import ManagerMixin, digit_version
 from .registry import Registry
 
 if TYPE_CHECKING:
@@ -232,6 +234,18 @@ def build_model_from_cfg(
         return build_from_cfg(cfg, registry, default_args)
 
 
+def build_optimizer_from_cfg(
+        cfg: Union[dict, ConfigDict, Config],
+        registry: Registry,
+        default_args: Optional[Union[dict, ConfigDict, Config]] = None) -> Any:
+    if 'Adafactor' == cfg['type'] and digit_version(
+            torch.__version__) >= digit_version('2.5.0'):
+        from ..logging import print_log
+        print_log(
+            'the torch version of Adafactor is registered as torch_Adafactor')
+    return build_from_cfg(cfg, registry, default_args)
+
+
 def build_scheduler_from_cfg(
     cfg: Union[dict, ConfigDict, Config],
     registry: Registry,
diff --git a/mmengine/registry/root.py b/mmengine/registry/root.py
index 2663dffcd9..eb9a225a91 100644
--- a/mmengine/registry/root.py
+++ b/mmengine/registry/root.py
@@ -6,8 +6,8 @@
 https://mmengine.readthedocs.io/en/latest/advanced_tutorials/registry.html.
 """
 
-from .build_functions import (build_model_from_cfg, build_runner_from_cfg,
-                              build_scheduler_from_cfg)
+from .build_functions import (build_model_from_cfg, build_optimizer_from_cfg,
+                              build_runner_from_cfg, build_scheduler_from_cfg)
 from .registry import Registry
 
 # manage all kinds of runners like `EpochBasedRunner` and `IterBasedRunner`
@@ -35,7 +35,7 @@
 WEIGHT_INITIALIZERS = Registry('weight initializer')
 
 # mangage all kinds of optimizers like `SGD` and `Adam`
-OPTIMIZERS = Registry('optimizer')
+OPTIMIZERS = Registry('optimizer', build_func=build_optimizer_from_cfg)
 # manage optimizer wrapper
 OPTIM_WRAPPERS = Registry('optim_wrapper')
 # manage constructors that customize the optimization hyperparameters.