diff --git a/onnxscript/function_libs/torch_lib/ops/nn.py b/onnxscript/function_libs/torch_lib/ops/nn.py
index a0f7abb449..7be4ef1a89 100644
--- a/onnxscript/function_libs/torch_lib/ops/nn.py
+++ b/onnxscript/function_libs/torch_lib/ops/nn.py
@@ -1700,7 +1700,7 @@ def aten_scaled_dot_product_attention(
 
 
 @torch_op("aten::_scaled_dot_product_flash_attention", private=True)
-def _aten_scaled_dot_product_flash_attention_fillin_empty_outputs(
+def _aten__scaled_dot_product_flash_attention_fillin_empty_outputs(
     query: TFloat,
 ) -> Tuple[FLOAT, INT64, INT64, FLOAT]:
     query_first_three_dims = op.Slice(
@@ -1723,7 +1723,7 @@ def _aten_scaled_dot_product_flash_attention_fillin_empty_outputs(
 
 
 @torch_op("aten::_scaled_dot_product_flash_attention", trace_only=True)
-def aten_scaled_dot_product_flash_attention(
+def aten__scaled_dot_product_flash_attention(
     query: TFloat,
     key: TFloat,
     value: TFloat,
@@ -1751,7 +1751,7 @@ def aten_scaled_dot_product_flash_attention(
         empty_tensor_int,
         empty_int,
         empty_tensor_float,
-    ) = _aten_scaled_dot_product_flash_attention_fillin_empty_outputs(query)
+    ) = _aten__scaled_dot_product_flash_attention_fillin_empty_outputs(query)
 
     return (
         result,
@@ -1766,6 +1766,73 @@ def aten_scaled_dot_product_flash_attention(
     )
 
 
+@torch_op("aten::_scaled_dot_product_efficient_attention", private=True)
+def _aten_scaled_dot_product_efficient_attention_fillin_empty_outputs(
+    query: TFloat,
+    compute_log_sumexp: bool,
+) -> Tuple[FLOAT, INT64]:
+    """_scaled_dot_product_efficient_attention(Tensor query, Tensor key, Tensor value, Tensor? attn_bias, bool compute_log_sumexp, float dropout_p=0.0, bool is_causal=False, *, float? scale=None) -> (Tensor output, Tensor log_sumexp, Tensor philox_seed, Tensor philox_offset)"""
+
+    query = op.Transpose(query, perm=[0, 2, 1, 3])
+    query_shape = op.Shape(query)
+    query_first_dims = query_shape[:1]
+    query_second_dims = query_shape[1:2]
+    num_heads = query_shape[-2:-1]
+
+    if compute_log_sumexp:
+        logsumexp_dim = op.Cast(
+            op.Ceil(op.Cast(query_second_dims, to=FLOAT.dtype) / 32.0) * 32.0, to=INT64.dtype
+        )
+        logsum_exp = op.Expand(
+            0.0, op.Concat(query_first_dims, num_heads, logsumexp_dim, axis=0)
+        )
+    else:
+        logsum_exp = op.Expand(0.0, op.Concat(query_first_dims, num_heads, [0], axis=0))
+
+    # See Note [Seed and Offset]:
+    empty_tensor_int = op.Cast(
+        op.ConstantOfShape(
+            op.Constant(value=onnx.helper.make_tensor("Empty_INTS", INT64.dtype, [0], []))
+        ),
+        to=INT64.dtype,
+    )
+
+    return logsum_exp, empty_tensor_int
+
+
+@torch_op("aten::_scaled_dot_product_efficient_attention", trace_only=True)
+def aten__scaled_dot_product_efficient_attention(
+    query: TFloat,
+    key: TFloat,
+    value: TFloat,
+    attn_bias: Optional[TFloat],  # pylint: disable=unused-argument
+    compute_log_sumexp: bool,
+    dropout_p: float = 0.0,
+    is_causal: bool = False,
+    scale: Optional[float] = None,
+) -> Tuple[TFloat, FLOAT, INT64, INT64]:
+    """_scaled_dot_product_efficient_attention(Tensor query, Tensor key, Tensor value, Tensor? attn_bias, bool compute_log_sumexp, float dropout_p=0.0, bool is_causal=False, *, float? scale=None) -> (Tensor output, Tensor log_sumexp, Tensor philox_seed, Tensor philox_offset)"""
+
+    result = aten_scaled_dot_product_attention(
+        query, key, value, dropout_p=dropout_p, is_causal=is_causal, scale=scale
+    )
+
+    # The followings are not comsumed by the graph.
+    (
+        logsumexp,
+        empty_tensor_int,
+    ) = _aten_scaled_dot_product_efficient_attention_fillin_empty_outputs(
+        query, compute_log_sumexp
+    )
+
+    return (
+        result,
+        logsumexp,
+        empty_tensor_int,
+        empty_tensor_int,
+    )
+
+
 @torch_op("aten::scaled_dot_product_attention", trace_only=True)
 def aten_scaled_dot_product_attention_bool_mask(
     query: TFloat,
diff --git a/onnxscript/tests/function_libs/torch_lib/extra_opinfo.py b/onnxscript/tests/function_libs/torch_lib/extra_opinfo.py
index 2fa8c9a609..64e6a06225 100644
--- a/onnxscript/tests/function_libs/torch_lib/extra_opinfo.py
+++ b/onnxscript/tests/function_libs/torch_lib/extra_opinfo.py
@@ -9,7 +9,11 @@
 
 import torch
 from torch import testing as torch_testing
-from torch.testing._internal import common_dtype, common_methods_invocations
+from torch.testing._internal import (
+    common_device_type,
+    common_dtype,
+    common_methods_invocations,
+)
 from torch.testing._internal.opinfo import core as opinfo_core
 
 S = 5
@@ -1298,7 +1302,7 @@ def sample_inputs__softmax(
         yield opinfo_core.SampleInput(make_arg(shape), args=dim, kwargs=kwargs)
 
 
-def sample_inputs_scaled_dot_product_flash_attention(
+def sample_inputs__scaled_dot_product_flash_attention(
     op_info, device, dtype, requires_grad, **kwargs
 ):
     del op_info
@@ -1342,6 +1346,41 @@ def sample_inputs_scaled_dot_product_flash_attention(
     yield from samples
 
 
+def sample_inputs__scaled_dot_product_efficient_attention(
+    op_info, device, dtype, requires_grad, **kwargs
+):
+    del op_info
+    del kwargs
+
+    make = opinfo_core.partial(
+        opinfo_core.make_tensor, device=device, dtype=dtype, requires_grad=requires_grad
+    )
+    batch, seq_q, seq_kv, num_heads, head_dim = 4, 3, 6, 4, 8
+
+    dim_4_q_shape = (batch, num_heads, seq_q, head_dim)
+    dim_4_kv_shape = (batch, num_heads, seq_kv, head_dim)
+
+    qkv_shapes = [(dim_4_q_shape, dim_4_kv_shape)]
+    samples = []
+    for qkv_shape, is_causal, dropout_p, compute_log_sumexp in opinfo_core.product(
+        qkv_shapes, [True, False], [0.0], [True, False]
+    ):
+        shape_q, shape_kv = qkv_shape
+        samples.append(
+            opinfo_core.SampleInput(
+                make(shape_q),
+                make(shape_kv),
+                make(shape_kv),
+                attn_bias=None,
+                is_causal=is_causal,
+                dropout_p=dropout_p,
+                compute_log_sumexp=compute_log_sumexp,
+            )
+        )
+
+    yield from samples
+
+
 # NOTE: In `_native_batch_norm_legit` tests, it generates two kinds of args:
 # 1. (input, weight, bias, running_mean, running_var, training, momentum, eps)
 # 2. (input, weight, bias, training, momentum, eps)
@@ -1765,11 +1804,26 @@ def sample_inputs_reflection_pad1d(op_info, device, dtype, requires_grad, **kwar
         dtypes=common_dtype.floating_types_and(torch.bfloat16),
         # NOTE: Different from aten::scaled_dot_product_attention, this op doesn't support
         #       dim<=3 input.
-        sample_inputs_func=sample_inputs_scaled_dot_product_flash_attention,
+        sample_inputs_func=sample_inputs__scaled_dot_product_flash_attention,
+        supports_out=False,
+        supports_forward_ad=False,
+        supports_fwgrad_bwgrad=True,
+        check_batched_forward_grad=False,
+    ),
+    opinfo_core.OpInfo(
+        "ops.aten._scaled_dot_product_efficient_attention",
+        aten_name="_scaled_dot_product_efficient_attention",
+        # only support CUDA
+        dtypes=common_dtype.empty_types(),
+        dtypesIfCUDA=common_dtype.floating_types_and(torch.bfloat16),
+        # NOTE: Different from aten::scaled_dot_product_attention, this op doesn't support
+        #       dim<=3 input.
+        sample_inputs_func=sample_inputs__scaled_dot_product_efficient_attention,
         supports_out=False,
         supports_forward_ad=False,
         supports_fwgrad_bwgrad=True,
         check_batched_forward_grad=False,
+        decorators=[common_device_type.onlyCUDA],
     ),
     opinfo_core.OpInfo(
         "ops.aten._native_batch_norm_legit",
diff --git a/onnxscript/tests/function_libs/torch_lib/ops_test.py b/onnxscript/tests/function_libs/torch_lib/ops_test.py
index 0913267be6..9cae237c80 100644
--- a/onnxscript/tests/function_libs/torch_lib/ops_test.py
+++ b/onnxscript/tests/function_libs/torch_lib/ops_test.py
@@ -406,11 +406,11 @@ def test_complex_output_match_opinfo_(
 
 
 common_device_type.instantiate_device_type_tests(
-    TestOutputConsistencyEager, globals(), only_for="cpu"
+    TestOutputConsistencyEager, globals(), only_for=["cpu", "cuda"]
 )
 
 common_device_type.instantiate_device_type_tests(
-    TestOutputConsistencyFullGraph, globals(), only_for="cpu"
+    TestOutputConsistencyFullGraph, globals(), only_for=["cpu", "cuda"]
 )
 
 if __name__ == "__main__":
diff --git a/onnxscript/tests/function_libs/torch_lib/ops_test_data.py b/onnxscript/tests/function_libs/torch_lib/ops_test_data.py
index 15feaa6b02..abf3198723 100644
--- a/onnxscript/tests/function_libs/torch_lib/ops_test_data.py
+++ b/onnxscript/tests/function_libs/torch_lib/ops_test_data.py
@@ -2018,15 +2018,33 @@ def _where_input_wrangler(
     ),
     TorchLibOpInfo(
         "ops.aten._scaled_dot_product_flash_attention",
-        nn_ops.aten_scaled_dot_product_flash_attention,
+        nn_ops.aten__scaled_dot_product_flash_attention,
         trace_only=True,
         tolerance={torch.float32: (3e-4, 1.5e-5)},
         # Output[0] is OK, but other outputs just have the same shape with zero values
         nondeterministic=True,
+        compare_shape_only_for_output=(1, 2, 3, 4, 5, 6, 7, 8),
     ).skip(
         enabled_if=version_utils.torch_older_than("2.1"),
         reason="The operator is not supported in older version.",
     ),
+    TorchLibOpInfo(
+        "ops.aten._scaled_dot_product_efficient_attention",
+        nn_ops.aten__scaled_dot_product_efficient_attention,
+        trace_only=True,
+        tolerance={torch.float32: (3e-4, 1.5e-5)},
+        # Output[0] is OK, but other outputs just have the same shape with zero values
+        nondeterministic=True,
+        compare_shape_only_for_output=(1, 2, 3),
+    )
+    .skip(
+        enabled_if=version_utils.torch_older_than("2.1"),
+        reason="The operator is not supported in older version.",
+    )
+    .skip(
+        enabled_if=not torch.cuda.is_available(),
+        reason="_scaled_dot_product_efficient_attention only supports CUDA",
+    ),
     TorchLibOpInfo(
         "nn.functional.scaled_dot_product_attention_bool_mask",
         nn_ops.aten_scaled_dot_product_attention_bool_mask,