diff --git a/onnxscript/function_libs/torch_lib/ops/core.py b/onnxscript/function_libs/torch_lib/ops/core.py
index 4fa43b056..c35898a65 100644
--- a/onnxscript/function_libs/torch_lib/ops/core.py
+++ b/onnxscript/function_libs/torch_lib/ops/core.py
@@ -7827,10 +7827,50 @@ def aten_std(self: TensorType, unbiased: bool = True) -> TensorType:
     raise NotImplementedError()
 
 
-def aten_std_mean(self: TensorType, unbiased: bool = True) -> tuple[TensorType, TensorType]:
+@torch_op("aten::std_mean", trace_only=True)
+def aten_std_mean(self: TReal, unbiased: bool = True) -> Tuple[TReal, TReal]:
     """std_mean(Tensor self, bool unbiased=True) -> (Tensor, Tensor)"""
 
-    raise NotImplementedError()
+    # Assume bool(True) and int(1) are same in ONNX, so pass "unbiased" directly as "correction"
+    # If not this case, should be explicitly set correction value according to unbiased value
+    var, mean = _aten_var_mean_onnx(self, correction=float(unbiased), keepdim=False)
+    return op.Sqrt(var), mean
+
+
+@torch_op("aten::std_mean.dim", trace_only=True)
+def aten_std_mean_dim(
+    self: TReal, dim: Sequence[int], unbiased: bool = True, keepdim: bool = False
+) -> Tuple[TReal, TReal]:
+    """std_mean.dim(Tensor self, int[1]? dim, bool unbiased=True, bool keepdim=False) -> (Tensor, Tensor)"""
+
+    # Although dim is Optional in signature, but we assume it must have value for this overload
+    # Assert(dim is not None)
+    var, mean = _aten_var_mean_dim_onnx(
+        self, dims=dim, correction=float(unbiased), keepdim=keepdim
+    )
+    return op.Sqrt(var), mean
+
+
+@torch_op("aten::std_mean.correction", trace_only=True)
+def aten_std_mean_correction(
+    self: TReal,
+    # FIXME(justinchuby): Make dim Optional[Sequence[int]]
+    dim: Optional[int] = None,
+    correction: Optional[float] = None,
+    keepdim: bool = False,
+) -> Tuple[TReal, TReal]:
+    """std_mean.correction(Tensor self, int[1]? dim=None, *, Scalar? correction=None, bool keepdim=False) -> (Tensor, Tensor)"""
+
+    if correction is None:
+        correction = 1.0
+
+    if dim is None:
+        var, mean = _aten_var_mean_onnx(self, correction=correction, keepdim=keepdim)
+    else:
+        var, mean = _aten_var_mean_dim_onnx(
+            self, dims=dim, correction=correction, keepdim=keepdim
+        )
+    return op.Sqrt(var), mean
 
 
 @torch_op("aten::stft", private=True)
diff --git a/tests/function_libs/torch_lib/ops_test_data.py b/tests/function_libs/torch_lib/ops_test_data.py
index bad3e8eb6..c17b79261 100644
--- a/tests/function_libs/torch_lib/ops_test_data.py
+++ b/tests/function_libs/torch_lib/ops_test_data.py
@@ -1506,6 +1506,33 @@ def _where_input_wrangler(
     ),
     TorchLibOpInfo("stack", core_ops.aten_stack),
     TorchLibOpInfo("stack", core_ops.aten_stack_complex, complex=True),
+    TorchLibOpInfo(
+        "std_mean",
+        core_ops.aten_std_mean,
+    ).xfail(
+        # kwargs is empty
+        matcher=lambda sample: len(sample.kwargs) > 0,
+        reason="this Aten overload only support input[0]=tensor and input[1]=bool as input without any kwargs",
+    ),
+    TorchLibOpInfo(
+        "std_mean_dim",
+        core_ops.aten_std_mean_dim,
+    ).xfail(
+        # kwargs["dim"] must exist, kwargs["correction"] must not exist
+        matcher=lambda sample: not (
+            sample.kwargs.get("dim", None) is not None
+            and sample.kwargs.get("correction", None) is None
+        ),
+        reason="this Aten overload only support with 'dim' argument and without 'correction' argument",
+    ),
+    TorchLibOpInfo(
+        "std_mean_correction",
+        core_ops.aten_std_mean_correction,
+    ).skip(
+        # Don't accept input[1]=bool and 'correction' must be in kwargs
+        matcher=lambda sample: len(sample.args) > 0 or "correction" not in sample.kwargs,
+        reason="this Aten overload only support when correction attribute exists",
+    ),
     TorchLibOpInfo("sub", core_ops.aten_sub),
     TorchLibOpInfo("sub", core_ops.aten_sub_complex, complex=True),
     # TorchLibOpInfo("sym_size", core_ops.aten_sym_size),  # no test case in OPS_DB
@@ -2300,6 +2327,7 @@ def _where_input_wrangler(
 ops_test_common.duplicate_opinfo(OPS_DB, "ops.aten._softmax", ("ops.aten._softmax_half",))
 ops_test_common.duplicate_opinfo(OPS_DB, "round", ("round_decimals",))
 ops_test_common.duplicate_opinfo(OPS_DB, "squeeze", ("squeeze_dim",))
+ops_test_common.duplicate_opinfo(OPS_DB, "std_mean", ("std_mean_dim", "std_mean_correction"))
 ops_test_common.duplicate_opinfo(OPS_DB, "var_mean", ("var_mean_dim", "var_mean_correction"))
 ops_test_common.duplicate_opinfo(OPS_DB, "var", ("var_dim", "var_correction"))
 ops_test_common.duplicate_opinfo(OPS_DB, "view_as_complex", ("view_as_complex_copy",))