diff --git a/onnxscript/function_libs/tools/torch_lib/deduce_type_constraints_test.py b/onnxscript/function_libs/tools/torch_lib/deduce_type_constraints_test.py
index a2882d283..4e01d37ac 100644
--- a/onnxscript/function_libs/tools/torch_lib/deduce_type_constraints_test.py
+++ b/onnxscript/function_libs/tools/torch_lib/deduce_type_constraints_test.py
@@ -30,7 +30,6 @@ class TestDeduceTypeConstraints(unittest.TestCase):
         "_aten_embedding_bag_onnx",
         "_aten_embedding_bag_1d_padding_idx_onnx",
     )
-    _SKIP_FUNCTIONS_WITH_NESTED_FUNCTION = ("aten_all",)
 
     @parameterized.parameterized.expand(
         ((op,) for op in torch_lib_onnx_functions_from_registry()),
@@ -41,11 +40,13 @@ def test_deduce_type_constraints_does_not_crash_for_onnx_function(
     ):
         if onnx_function.name in self._SKIP_FUNCTIONS_WITH_LOOP_OR_SCAN:
             self.skipTest("Unimplemented: function contains loop or scan node.")
-        if onnx_function.name in self._SKIP_FUNCTIONS_WITH_NESTED_FUNCTION:
-            self.skipTest("Unimplemented: function contains nested function.")
-        signature_type_constraint = deduce_type_constraints.deduce_type_constraints(
-            onnx_function
-        )
+        try:
+            signature_type_constraint = deduce_type_constraints.deduce_type_constraints(
+                onnx_function
+            )
+        except NotImplementedError as e:
+            if "Nested function" in str(e):
+                self.skipTest("Unimplemented: function contains nested function.")
         logger.info(
             "Original signature: %s%s",
             onnx_function.name,
diff --git a/onnxscript/function_libs/torch_lib/ops/core.py b/onnxscript/function_libs/torch_lib/ops/core.py
index 6d770254e..775e149da 100644
--- a/onnxscript/function_libs/torch_lib/ops/core.py
+++ b/onnxscript/function_libs/torch_lib/ops/core.py
@@ -222,8 +222,8 @@ def aten_addcmul(
 
 @torch_op("aten::addmm")
 def aten_addmm(
-    self: TReal, mat1: TReal, mat2: TReal, beta: float = 1.0, alpha: float = 1.0
-) -> TReal:
+    self: TInt, mat1: TInt, mat2: TInt, beta: float = 1.0, alpha: float = 1.0
+) -> TInt:
     """addmm(Tensor self, Tensor mat1, Tensor mat2, *, Scalar beta=1, Scalar alpha=1) -> Tensor"""
 
     mat1_mat2 = op.MatMul(mat1, mat2)
@@ -232,6 +232,29 @@ def aten_addmm(
     return op.Add(scaled_self, scaled_mat1_mat2)
 
 
+@torch_op("aten::addmm")
+def aten_addmm_gemm(
+    self: TFloat, mat1: TFloat, mat2: TFloat, beta: float = 1.0, alpha: float = 1.0
+) -> TFloat:
+    """addmm(Tensor self, Tensor mat1, Tensor mat2, *, Scalar beta=1, Scalar alpha=1) -> Tensor"""
+
+    # A special case when rank of mat1 and mat2 are 2, we can use Gemm instead of MatMul
+    # We expect the if branches to be folded away by optimization passes
+    # TODO(#1110): Handle Gemm with a graph rewriting pass instead of hard coding the branching logic here
+    use_gemm = op.And(
+        op.Equal(Rank(mat1), op.Constant(value_int=2)),
+        op.Equal(Rank(mat2), op.Constant(value_int=2)),
+    )
+    if use_gemm:
+        result = op.Gemm(mat1, mat2, self, alpha=alpha, beta=beta)
+    else:
+        mat1_mat2 = op.MatMul(mat1, mat2)
+        scaled_mat1_mat2 = op.Mul(mat1_mat2, alpha)
+        scaled_self = op.Mul(self, beta)
+        result = op.Add(scaled_self, scaled_mat1_mat2)
+    return result
+
+
 @torch_op("aten::addmv")
 def aten_addmv(
     self: TReal, mat: TReal, vec: TReal, beta: float = 1.0, alpha: float = 1.0
@@ -5235,7 +5258,6 @@ def aten_mm(
 ) -> TRealUnlessInt16OrInt8:
     """mm(Tensor self, Tensor mat2) -> Tensor"""
 
-    # TODO(justinchuby): Specify type conversion for uint8/int8/int16
     return op.MatMul(self, mat2)
 
 
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 7c6a64b49..7304aa8ba 100644
--- a/onnxscript/tests/function_libs/torch_lib/ops_test_data.py
+++ b/onnxscript/tests/function_libs/torch_lib/ops_test_data.py
@@ -489,6 +489,14 @@ def _where_input_wrangler(
     TorchLibOpInfo("addcdiv", core_ops.aten_addcdiv),
     TorchLibOpInfo("addcmul", core_ops.aten_addcmul, tolerance={torch.float16: (4e-3, 3e-3)}),
     TorchLibOpInfo("addmm", core_ops.aten_addmm),
+    TorchLibOpInfo("addmm_gemm", core_ops.aten_addmm_gemm).xfail(
+        "decomposed",
+        reason=(
+            "The float attributes alpha/beta come in as int in the test cases, which breaks"
+            "eager mode. We don't need to care about this as long as the full graph tests pass"
+        ),
+        test_class_name="TestOutputConsistencyEager",
+    ),
     TorchLibOpInfo("addmv", core_ops.aten_addmv),
     TorchLibOpInfo(
         "addr",
@@ -1968,6 +1976,7 @@ def _where_input_wrangler(
     TorchLibOpInfo("zeros_like", core_ops.aten_zeros_like, trace_only=True),
 )
 
+ops_test_common.duplicate_opinfo(OPS_DB, "addmm", ("addmm_gemm",))
 ops_test_common.duplicate_opinfo(OPS_DB, "all", ("all_dim",))
 ops_test_common.duplicate_opinfo(OPS_DB, "any", ("any_dim",))
 ops_test_common.duplicate_opinfo(OPS_DB, "arange", ("arange_start", "arange_start_step"))