diff --git a/funasr/models/normalize/utterance_mvn.py b/funasr/models/normalize/utterance_mvn.py
index 9128c6d044..8c8353e698 100644
--- a/funasr/models/normalize/utterance_mvn.py
+++ b/funasr/models/normalize/utterance_mvn.py
@@ -81,9 +81,10 @@ def utterance_mvn(
         x -= mean
 
         if norm_vars:
+            x = x.masked_fill(make_pad_mask(ilens, x, 1), 0.0)
             var = x.pow(2).sum(dim=1, keepdim=True) / ilens_
             std = torch.clamp(var.sqrt(), min=eps)
-            x = x / std.sqrt()
+            x = x / std
         return x, ilens
     else:
         if norm_vars:
diff --git a/tests/test_utterance_mvn.py b/tests/test_utterance_mvn.py
new file mode 100644
index 0000000000..f74201cd03
--- /dev/null
+++ b/tests/test_utterance_mvn.py
@@ -0,0 +1,268 @@
+"""Run with: python -m pytest tests/test_utterance_mvn.py -q (CPU and CUDA)."""
+
+from pathlib import Path
+
+import pytest
+import soundfile as sf
+import torch
+from omegaconf import OmegaConf
+
+from funasr import AutoModel
+from funasr.frontends.wav_frontend import WavFrontend
+from funasr.models.normalize.utterance_mvn import UtteranceMVN, utterance_mvn
+from funasr.models.transformer.model import Transformer
+from funasr.tokenizer.char_tokenizer import CharTokenizer
+from funasr.utils.misc import prepare_model_dir
+
+
+@pytest.fixture(params=["cpu", "cuda"])
+def device(request):
+    if request.param == "cuda" and not torch.cuda.is_available():
+        pytest.skip("CUDA is unavailable")
+    return request.param
+
+
+def features(device, dtype=torch.float32):
+    generator = torch.Generator().manual_seed(17)
+    x = torch.randn(2, 17, 3, generator=generator, dtype=dtype) * 2 + 5
+    return x.to(device), torch.tensor([11, 17], device=device)
+
+
+@pytest.mark.parametrize("dtype", [torch.float32, torch.float64, torch.float16, torch.bfloat16])
+@pytest.mark.parametrize(
+    "norm_means,norm_vars", [(True, True), (True, False), (False, True), (False, False)]
+)
+def test_formula_and_switches(device, dtype, norm_means, norm_vars):
+    x, lengths = features(device, dtype)
+    actual, actual_lengths = utterance_mvn(x.clone(), lengths, norm_means, norm_vars)
+    assert actual.dtype == dtype
+    assert actual.device == x.device
+    assert actual_lengths is lengths
+    tolerance = {
+        torch.float64: 1e-12,
+        torch.float32: 2e-6,
+        torch.float16: 0.02,
+        torch.bfloat16: 0.15,
+    }[dtype]
+    for i, length in enumerate(lengths.tolist()):
+        # Independent oracle: unpadded per-utterance torch.std, evaluated in double.
+        valid = x[i, :length].double()
+        mean = valid.mean(0)
+        expected = valid - mean if norm_means else valid
+        if norm_vars:
+            expected = expected / valid.std(0, unbiased=False).clamp_min(1e-20)
+        torch.testing.assert_close(
+            actual[i, :length].double(), expected, rtol=tolerance, atol=tolerance
+        )
+        if norm_means and norm_vars:
+            torch.testing.assert_close(
+                actual[i, :length].double().var(0, unbiased=False),
+                torch.ones(3, device=device, dtype=torch.float64),
+                rtol=tolerance,
+                atol=tolerance,
+            )
+        if norm_means and not norm_vars:
+            # Preserve historical mean-only padding.
+            torch.testing.assert_close(
+                actual[i, length:].double(),
+                -mean.expand(17 - length, -1),
+                rtol=tolerance,
+                atol=tolerance,
+            )
+        else:
+            assert torch.count_nonzero(actual[i, length:]) == 0
+
+
+def test_batch_length_and_order_invariance(device):
+    x, lengths = features(device)
+    layer = UtteranceMVN(norm_vars=True)
+    batch, _ = layer(x.clone(), lengths)
+    single, inferred_lengths = layer(x[:1, :11].clone())
+    reverse, _ = layer(x.flip(0), lengths.flip(0))
+    torch.testing.assert_close(single[0], batch[0, :11], rtol=1e-6, atol=1e-6)
+    torch.testing.assert_close(reverse.flip(0), batch, rtol=0, atol=0)
+    assert inferred_lengths.tolist() == [11]
+
+
+@pytest.mark.parametrize(
+    "norm_means,norm_vars,expected",
+    [
+        (True, False, [-2.0, 2.0, -3.0, -3.0]),
+        (False, True, [0.5, 2.5, 0.0, 0.0]),
+        (False, False, [1.0, 5.0, 0.0, 0.0]),
+    ],
+)
+def test_other_branches_keep_existing_values(device, norm_means, norm_vars, expected):
+    x = torch.tensor([[[1.0], [5.0], [0.0], [0.0]]], device=device)
+    actual, _ = utterance_mvn(x, torch.tensor([2], device=device), norm_means, norm_vars)
+    torch.testing.assert_close(actual.flatten(), x.new_tensor(expected), rtol=0, atol=0)
+
+
+@pytest.mark.parametrize("padding", [0, 2])
+def test_mean_variance_values(device, padding):
+    x = torch.tensor([1.0, 5.0] + [0.0] * padding, device=device).view(1, -1, 1)
+    actual, _ = UtteranceMVN(norm_vars=True)(x, torch.tensor([2], device=device))
+    expected = x.new_tensor([-1.0, 1.0] + [0.0] * padding)
+    torch.testing.assert_close(actual.flatten(), expected, rtol=0, atol=0)
+
+
+@pytest.mark.parametrize("norm_means", [True, False])
+def test_eps_clamps_standard_deviation(device, norm_means):
+    x = torch.tensor([[[1.0], [3.0]]], device=device, dtype=torch.float64)
+    actual, _ = utterance_mvn(x.clone(), norm_means=norm_means, norm_vars=True, eps=4.0)
+    expected = (x - 2.0 if norm_means else x) / 4.0
+    torch.testing.assert_close(actual, expected, rtol=0, atol=0)
+
+
+def test_corrected_gradients(device):
+    x, lengths = features(device, torch.float64)
+    x.requires_grad_()
+    reference = x.detach().clone().requires_grad_()
+    actual, _ = UtteranceMVN(norm_vars=True)(x, lengths)
+    weights = torch.linspace(0.1, 1.3, x.numel(), device=device).reshape_as(x)
+    (actual * weights).sum().backward()
+    loss = 0
+    for i, length in enumerate(lengths.tolist()):
+        valid = reference[i, :length]
+        normalized = (valid - valid.mean(0)) / valid.std(0, unbiased=False)
+        loss = loss + (normalized * weights[i, :length]).sum()
+    loss.backward()
+    assert torch.isfinite(x.grad).all()
+    assert torch.count_nonzero(x.grad[0, :11]) > 0
+    assert torch.count_nonzero(x.grad[0, 11:]) == 0
+    torch.testing.assert_close(x.grad, reference.grad, rtol=1e-9, atol=1e-9)
+
+
+def model_config(normalize_conf):
+    return dict(
+        model="Transformer",
+        input_size=80,
+        vocab_size=9,
+        encoder="TransformerEncoder",
+        encoder_conf=dict(
+            output_size=32,
+            attention_heads=2,
+            linear_units=64,
+            num_blocks=1,
+            input_layer="linear",
+            dropout_rate=0.0,
+            positional_dropout_rate=0.0,
+            attention_dropout_rate=0.0,
+        ),
+        decoder="TransformerDecoder",
+        decoder_conf=dict(
+            attention_heads=2,
+            linear_units=64,
+            num_blocks=1,
+            dropout_rate=0.0,
+            positional_dropout_rate=0.0,
+            self_attention_dropout_rate=0.0,
+            src_attention_dropout_rate=0.0,
+        ),
+        ctc_weight=0.5,
+        normalize="UtteranceMVN",
+        normalize_conf=normalize_conf,
+        frontend="WavFrontend",
+        frontend_conf=dict(fs=16000, dither=0.0),
+        tokenizer="CharTokenizer",
+        tokenizer_conf=dict(
+            token_list=["<blank>", "<s>", "</s>", "你", "好", "语", "音", "识", "<unk>"]
+        ),
+    )
+
+
+def test_saved_config_and_checkpoint_round_trip(tmp_path):
+    normalize_conf = dict(norm_means=True, norm_vars=True)
+    config = model_config(normalize_conf)
+    original = Transformer(**config).eval()
+    # Use the training config writer and the local AutoModel config/weight loader.
+    prepare_model_dir(output_dir=str(tmp_path), **config)
+    torch.save({"state_dict": original.state_dict()}, tmp_path / "model.pt")
+    saved = OmegaConf.load(tmp_path / "config.yaml")
+    assert dict(saved.normalize_conf) == normalize_conf
+    restored = AutoModel(
+        model=str(tmp_path), device="cpu", ncpu=1, disable_update=True, ignore_init_mismatch=False
+    ).model
+    assert restored.normalize.state_dict() == {}
+    for key, value in original.state_dict().items():
+        torch.testing.assert_close(restored.state_dict()[key], value, rtol=0, atol=0)
+    x = torch.randn(2, 17, 80)
+    lengths = torch.tensor([11, 17])
+    with torch.no_grad():
+        expected, _ = original.encode(x.clone(), lengths)
+        actual, _ = restored.encode(x.clone(), lengths)
+    torch.testing.assert_close(actual, expected, rtol=0, atol=0)
+
+
+@pytest.mark.parametrize("norm_vars", [False, True])
+def test_real_audio_transformer_inference(device, norm_vars):
+    """Real loader/frontend/encoder/CTC; small random model, no downloads or training."""
+    audio, fs = sf.read(
+        Path(__file__).resolve().parents[1] / "runtime/funasr_api/asr_example.wav", dtype="float32"
+    )
+    short = audio[: 2 * fs].copy()
+    config = model_config(dict(norm_means=True, norm_vars=norm_vars))
+    with torch.random.fork_rng(devices=[]):
+        torch.manual_seed(2026)
+        model = Transformer(**config).to(device).eval()
+    frontend = WavFrontend(**config["frontend_conf"])
+    tokenizer = CharTokenizer(**config["tokenizer_conf"])
+    captured = {}
+
+    def frontend_hook(module, args, output):
+        captured["frontend_device"] = output[0].device.type
+
+    def raw_hook(module, args):
+        captured["raw"] = args[0].detach().clone()
+
+    def norm_hook(module, args, output):
+        captured["normalized"] = output[0].detach().clone()
+        captured["lengths"] = output[1].detach().clone()
+
+    def encoder_hook(module, args, output):
+        captured["encoded"] = output[0].detach().clone()
+
+    handles = [
+        frontend.register_forward_hook(frontend_hook),
+        model.normalize.register_forward_pre_hook(raw_hook),
+        model.normalize.register_forward_hook(norm_hook),
+        model.encoder.register_forward_hook(encoder_hook),
+    ]
+    outputs = []
+    try:
+        for inputs in [[short], [short, audio], [audio, short]]:
+            with torch.no_grad():
+                results, _ = model.inference(
+                    inputs,
+                    batch_size=2,
+                    frontend=frontend,
+                    tokenizer=tokenizer,
+                    device=device,
+                    fs=fs,
+                )
+            assert len(results) == len(inputs)
+            assert all("text" in result for result in results)
+            outputs.append(dict(captured))
+    finally:
+        for handle in handles:
+            handle.remove()
+    single, batch, reverse = outputs
+    n = int(single["lengths"][0])
+    assert batch["lengths"].tolist() == [198, 553]
+    assert next(model.parameters()).device.type == device
+    assert all(output["frontend_device"] == "cpu" for output in outputs)
+    for name in ["raw", "normalized", "encoded"]:
+        assert batch[name].device.type == device
+        torch.testing.assert_close(single[name][0, :n], batch[name][0, :n], rtol=0, atol=1e-5)
+        torch.testing.assert_close(batch[name][0, :n], reverse[name][1, :n], rtol=0, atol=1e-5)
+    if norm_vars:
+        valid = single["raw"][0, :n].double()
+        expected = (valid - valid.mean(0)) / valid.std(0, unbiased=False)
+        torch.testing.assert_close(batch["normalized"][0, :n].double(), expected, rtol=0, atol=2e-6)
+        torch.testing.assert_close(
+            batch["normalized"][0, :n].var(0, unbiased=False),
+            torch.ones(80, device=device),
+            rtol=0,
+            atol=1e-6,
+        )
+        assert torch.count_nonzero(batch["normalized"][0, n:]) == 0