diff --git a/deepmd/pt/entrypoints/main.py b/deepmd/pt/entrypoints/main.py
index adaec0968a..77091c3cf7 100644
--- a/deepmd/pt/entrypoints/main.py
+++ b/deepmd/pt/entrypoints/main.py
@@ -123,13 +123,12 @@ def prepare_trainer_input_single(
         if rank != 0:
             stat_file_path_single = None
         elif stat_file_path_single is not None:
-            if Path(stat_file_path_single).is_dir():
-                raise ValueError(
-                    f"stat_file should be a file, not a directory: {stat_file_path_single}"
-                )
-            if not Path(stat_file_path_single).is_file():
-                with h5py.File(stat_file_path_single, "w") as f:
-                    pass
+            if not Path(stat_file_path_single).exists():
+                if stat_file_path_single.endswith((".h5", ".hdf5")):
+                    with h5py.File(stat_file_path_single, "w") as f:
+                        pass
+                else:
+                    Path(stat_file_path_single).mkdir()
             stat_file_path_single = DPPath(stat_file_path_single, "a")
 
         # validation and training data
diff --git a/deepmd/utils/argcheck.py b/deepmd/utils/argcheck.py
index 2a98bee6fe..07add486c1 100644
--- a/deepmd/utils/argcheck.py
+++ b/deepmd/utils/argcheck.py
@@ -2179,7 +2179,9 @@ def training_args():  # ! modified by Ziyao: data configuration isolated.
     doc_stat_file = (
         "The file path for saving the data statistics results. "
         "If set, the results will be saved and directly loaded during the next training session, "
-        "avoiding the need to recalculate the statistics"
+        "avoiding the need to recalculate the statistics. "
+        "If the file extension is .h5 or .hdf5, an HDF5 file is used to store the statistics; "
+        "otherwise, a directory containing NumPy binary files are used."
     )
     doc_opt_type = "The type of optimizer to use."
     doc_kf_blocksize = "The blocksize for the Kalman filter."
diff --git a/deepmd/utils/env_mat_stat.py b/deepmd/utils/env_mat_stat.py
index 217c46844b..bbb43fd703 100644
--- a/deepmd/utils/env_mat_stat.py
+++ b/deepmd/utils/env_mat_stat.py
@@ -132,7 +132,7 @@ def save_stats(self, path: DPPath) -> None:
 
         Parameters
         ----------
-        path : DPH5Path
+        path : DPPath
             The path to save the statistics of the environment matrix.
         """
         if len(self.stats) == 0:
@@ -146,7 +146,7 @@ def load_stats(self, path: DPPath) -> None:
 
         Parameters
         ----------
-        path : DPH5Path
+        path : DPPath
             The path to load the statistics of the environment matrix.
         """
         if len(self.stats) > 0:
@@ -166,7 +166,7 @@ def load_or_compute_stats(
 
         Parameters
         ----------
-        path : DPH5Path
+        path : DPPath
             The path to load the statistics of the environment matrix.
         data : List[Dict[str, np.ndarray]]
             The environment matrix.
diff --git a/examples/water/dpa2/input_torch.json b/examples/water/dpa2/input_torch.json
index 108e75df62..e94086b898 100644
--- a/examples/water/dpa2/input_torch.json
+++ b/examples/water/dpa2/input_torch.json
@@ -69,7 +69,7 @@
     "_comment": " that's all"
   },
   "training": {
-    "stat_file": "./dpa2",
+    "stat_file": "./dpa2.hdf5",
     "training_data": {
       "systems": [
         "../data/data_0",
diff --git a/examples/water/se_atten/input_torch.json b/examples/water/se_atten/input_torch.json
index 7e9cf06f35..4160feda17 100644
--- a/examples/water/se_atten/input_torch.json
+++ b/examples/water/se_atten/input_torch.json
@@ -61,7 +61,7 @@
     "_comment": " that's all"
   },
   "training": {
-    "stat_file": "./dpa1",
+    "stat_file": "./dpa1.hdf5",
     "training_data": {
       "systems": [
         "../data/data_0",
diff --git a/examples/water/se_e2_a/input_torch.json b/examples/water/se_e2_a/input_torch.json
index fe424afed3..3fc889212c 100644
--- a/examples/water/se_e2_a/input_torch.json
+++ b/examples/water/se_e2_a/input_torch.json
@@ -52,7 +52,7 @@
     "_comment": " that's all"
   },
   "training": {
-    "stat_file": "./se_e2_a",
+    "stat_file": "./se_e2_a.hdf5",
     "training_data": {
       "systems": [
         "../data/data_0",
diff --git a/source/tests/pt/model/test_saveload_dpa1.py b/source/tests/pt/model/test_saveload_dpa1.py
index 712b44485e..3da06938b5 100644
--- a/source/tests/pt/model/test_saveload_dpa1.py
+++ b/source/tests/pt/model/test_saveload_dpa1.py
@@ -101,7 +101,7 @@ def create_wrapper(self, read: bool):
         model_config = copy.deepcopy(self.config["model"])
         model_config["resuming"] = read
         model_config["stat_file_dir"] = "stat_files"
-        model_config["stat_file"] = "stat.npz"
+        model_config["stat_file"] = "stat.hdf5"
         model_config["stat_file_path"] = os.path.join(
             model_config["stat_file_dir"], model_config["stat_file"]
         )
diff --git a/source/tests/pt/model/water/multitask.json b/source/tests/pt/model/water/multitask.json
index 2f706e4cd9..c59618145d 100644
--- a/source/tests/pt/model/water/multitask.json
+++ b/source/tests/pt/model/water/multitask.json
@@ -95,7 +95,7 @@
     },
     "data_dict": {
       "model_1": {
-        "stat_file": "./stat_files/model_1",
+        "stat_file": "./stat_files/model_1.hdf5",
         "training_data": {
           "systems": [
             "pt/water/data/data_0"
@@ -112,7 +112,7 @@
         }
       },
       "model_2": {
-        "stat_file": "./stat_files/model_2",
+        "stat_file": "./stat_files/model_2.hdf5",
         "training_data": {
           "systems": [
             "pt/water/data/data_0"