diff --git a/e2e_testing/torchscript/xfail_sets.py b/e2e_testing/torchscript/xfail_sets.py
index 0ac56e9cf03c..62aef89911e8 100644
--- a/e2e_testing/torchscript/xfail_sets.py
+++ b/e2e_testing/torchscript/xfail_sets.py
@@ -317,6 +317,8 @@
     "StdDimBiasedModule_basic",
     "StdDimKeepDimFalseModule_basic",
     "StdDimKeepDimTrueModule_basic",
+    "StdDimEmptyDimModule_basic",
+    "StdDimNoneDimModule_basic",
     "StdUnbiasedModule_basic",
     "SubFloatModule_basic",
     "SubIntModule_basic",
diff --git a/include/torch-mlir/Dialect/Torch/IR/GeneratedTorchOps.td b/include/torch-mlir/Dialect/Torch/IR/GeneratedTorchOps.td
index 043e206dc532..ec73d5d33ae4 100644
--- a/include/torch-mlir/Dialect/Torch/IR/GeneratedTorchOps.td
+++ b/include/torch-mlir/Dialect/Torch/IR/GeneratedTorchOps.td
@@ -4049,10 +4049,10 @@ def Torch_AtenStdDimOp : Torch_Op<"aten.std.dim", [
     HasValueSemantics,
     ReadOnly
   ]> {
-  let summary = "Generated op for `aten::std.dim : (Tensor, int[], bool, bool) -> (Tensor)`";
+  let summary = "Generated op for `aten::std.dim : (Tensor, int[]?, bool, bool) -> (Tensor)`";
   let arguments = (ins
     AnyTorchTensorType:$self,
-    AnyTorchListOfTorchIntType:$dim,
+    AnyTorchOptionalListOfTorchIntType:$dim,
     Torch_BoolType:$unbiased,
     Torch_BoolType:$keepdim
   );
@@ -4099,10 +4099,10 @@ def Torch_AtenVarDimOp : Torch_Op<"aten.var.dim", [
     HasValueSemantics,
     ReadOnly
   ]> {
-  let summary = "Generated op for `aten::var.dim : (Tensor, int[], bool, bool) -> (Tensor)`";
+  let summary = "Generated op for `aten::var.dim : (Tensor, int[]?, bool, bool) -> (Tensor)`";
   let arguments = (ins
     AnyTorchTensorType:$self,
-    AnyTorchListOfTorchIntType:$dim,
+    AnyTorchOptionalListOfTorchIntType:$dim,
     Torch_BoolType:$unbiased,
     Torch_BoolType:$keepdim
   );
diff --git a/lib/Dialect/Torch/Transforms/ShapeLibrary.cpp b/lib/Dialect/Torch/Transforms/ShapeLibrary.cpp
index dd2407bcc346..ce315375bca9 100644
--- a/lib/Dialect/Torch/Transforms/ShapeLibrary.cpp
+++ b/lib/Dialect/Torch/Transforms/ShapeLibrary.cpp
@@ -5564,12 +5564,19 @@ module {
     %0 = torch.prim.ListConstruct  : () -> !torch.list<int>
     return %0 : !torch.list<int>
   }
-  func.func @"__torch_mlir_shape_fn.aten.var.dim"(%arg0: !torch.list<int>, %arg1: !torch.list<int>, %arg2: !torch.bool, %arg3: !torch.bool) -> !torch.list<int> {
-    %none = torch.constant.none
+  func.func @"__torch_mlir_shape_fn.aten.var.dim"(%arg0: !torch.list<int>, %arg1: !torch.optional<list<int>>, %arg2: !torch.bool, %arg3: !torch.bool) -> !torch.list<int> {
     %true = torch.constant.bool true
+    %none = torch.constant.none
     %int0 = torch.constant.int 0
-    %0 = torch.aten.len.t %arg1 : !torch.list<int> -> !torch.int
-    %1 = torch.aten.eq.int %0, %int0 : !torch.int, !torch.int -> !torch.bool
+    %0 = torch.aten.__is__ %arg1, %none : !torch.optional<list<int>>, !torch.none -> !torch.bool
+    %1 = torch.prim.If %0 -> (!torch.bool) {
+      torch.prim.If.yield %true : !torch.bool
+    } else {
+      %5 = torch.prim.unchecked_cast %arg1 : !torch.optional<list<int>> -> !torch.list<int>
+      %6 = torch.aten.len.t %5 : !torch.list<int> -> !torch.int
+      %7 = torch.aten.eq.int %6, %int0 : !torch.int, !torch.int -> !torch.bool
+      torch.prim.If.yield %7 : !torch.bool
+    }
     %2 = torch.prim.If %1 -> (!torch.list<int>) {
       %5 = torch.aten.len.t %arg0 : !torch.list<int> -> !torch.int
       %6 = torch.prim.ListConstruct  : () -> !torch.list<int>
@@ -5580,7 +5587,8 @@ module {
       } : (!torch.int, !torch.bool) -> ()
       torch.prim.If.yield %6 : !torch.list<int>
     } else {
-      torch.prim.If.yield %arg1 : !torch.list<int>
+      %5 = torch.prim.unchecked_cast %arg1 : !torch.optional<list<int>> -> !torch.list<int>
+      torch.prim.If.yield %5 : !torch.list<int>
     }
     %3 = torch.derefine %none : !torch.none to !torch.any
     %4 = call @__torch__.torch.jit._shape_functions.mean_dim(%arg0, %2, %arg3, %3) : (!torch.list<int>, !torch.list<int>, !torch.bool, !torch.any) -> !torch.list<int>
@@ -5620,11 +5628,35 @@ module {
     %0 = torch.prim.ListConstruct  : () -> !torch.list<int>
     return %0 : !torch.list<int>
   }
-  func.func @"__torch_mlir_shape_fn.aten.std.dim"(%arg0: !torch.list<int>, %arg1: !torch.list<int>, %arg2: !torch.bool, %arg3: !torch.bool) -> !torch.list<int> {
+  func.func @"__torch_mlir_shape_fn.aten.std.dim"(%arg0: !torch.list<int>, %arg1: !torch.optional<list<int>>, %arg2: !torch.bool, %arg3: !torch.bool) -> !torch.list<int> {
+    %true = torch.constant.bool true
     %none = torch.constant.none
-    %0 = torch.derefine %none : !torch.none to !torch.any
-    %1 = call @__torch__.torch.jit._shape_functions.mean_dim(%arg0, %arg1, %arg3, %0) : (!torch.list<int>, !torch.list<int>, !torch.bool, !torch.any) -> !torch.list<int>
-    return %1 : !torch.list<int>
+    %int0 = torch.constant.int 0
+    %0 = torch.aten.__is__ %arg1, %none : !torch.optional<list<int>>, !torch.none -> !torch.bool
+    %1 = torch.prim.If %0 -> (!torch.bool) {
+      torch.prim.If.yield %true : !torch.bool
+    } else {
+      %5 = torch.prim.unchecked_cast %arg1 : !torch.optional<list<int>> -> !torch.list<int>
+      %6 = torch.aten.len.t %5 : !torch.list<int> -> !torch.int
+      %7 = torch.aten.eq.int %6, %int0 : !torch.int, !torch.int -> !torch.bool
+      torch.prim.If.yield %7 : !torch.bool
+    }
+    %2 = torch.prim.If %1 -> (!torch.list<int>) {
+      %5 = torch.aten.len.t %arg0 : !torch.list<int> -> !torch.int
+      %6 = torch.prim.ListConstruct  : () -> !torch.list<int>
+      torch.prim.Loop %5, %true, init() {
+      ^bb0(%arg4: !torch.int):
+        %7 = torch.aten.append.t %6, %arg4 : !torch.list<int>, !torch.int -> !torch.list<int>
+        torch.prim.Loop.condition %true, iter()
+      } : (!torch.int, !torch.bool) -> ()
+      torch.prim.If.yield %6 : !torch.list<int>
+    } else {
+      %5 = torch.prim.unchecked_cast %arg1 : !torch.optional<list<int>> -> !torch.list<int>
+      torch.prim.If.yield %5 : !torch.list<int>
+    }
+    %3 = torch.derefine %none : !torch.none to !torch.any
+    %4 = call @__torch__.torch.jit._shape_functions.mean_dim(%arg0, %2, %arg3, %3) : (!torch.list<int>, !torch.list<int>, !torch.bool, !torch.any) -> !torch.list<int>
+    return %4 : !torch.list<int>
   }
   func.func @"__torch_mlir_shape_fn.aten.argmax"(%arg0: !torch.list<int>, %arg1: !torch.optional<int>, %arg2: !torch.bool) -> !torch.list<int> {
     %none = torch.constant.none
diff --git a/python/torch_mlir/dialects/torch/importer/jit_ir/build_tools/shape_lib_gen.py b/python/torch_mlir/dialects/torch/importer/jit_ir/build_tools/shape_lib_gen.py
index 58a9de829e36..8036a6c0b39c 100644
--- a/python/torch_mlir/dialects/torch/importer/jit_ir/build_tools/shape_lib_gen.py
+++ b/python/torch_mlir/dialects/torch/importer/jit_ir/build_tools/shape_lib_gen.py
@@ -489,8 +489,8 @@ def aten〇mean(self: List[int], dtype: Optional[int] = None) -> List[int]:
 def aten〇var(self: List[int], unbiased: bool = True) -> List[int]:
     return []
 
-def aten〇var〇dim(self: List[int], dim: List[int], unbiased: bool = True, keepdim: bool = False) -> List[int]:
-    if len(dim)==0:
+def aten〇var〇dim(self: List[int], dim: Optional[List[int]], unbiased: bool = True, keepdim: bool = False) -> List[int]:
+    if dim is None or len(dim)==0:
         dim = list(range(len(self)))
     return upstream_shape_functions.mean_dim(self, dim, keepdim, None)
 
@@ -502,7 +502,9 @@ def aten〇var〇correction(self: List[int], dim: Optional[List[int]], correctio
 def aten〇std(self: List[int], unbiased: bool = True) -> List[int]:
     return []
 
-def aten〇std〇dim(self: List[int], dim: List[int], unbiased: bool = True, keepdim: bool = False) -> List[int]:
+def aten〇std〇dim(self: List[int], dim: Optional[List[int]], unbiased: bool = True, keepdim: bool = False) -> List[int]:
+    if dim is None or len(dim)==0:
+        dim = list(range(len(self)))
     return upstream_shape_functions.mean_dim(self, dim, keepdim, None)
 
 def _reduce_along_dim(self: List[int], dim: int, keepdim: bool):
diff --git a/python/torch_mlir/dialects/torch/importer/jit_ir/build_tools/torch_ods_gen.py b/python/torch_mlir/dialects/torch/importer/jit_ir/build_tools/torch_ods_gen.py
index 2dbaf9a40e56..0f92c14b99f7 100644
--- a/python/torch_mlir/dialects/torch/importer/jit_ir/build_tools/torch_ods_gen.py
+++ b/python/torch_mlir/dialects/torch/importer/jit_ir/build_tools/torch_ods_gen.py
@@ -382,9 +382,9 @@ def emit_with_mutating_variants(key, **kwargs):
     emit("aten::_softmax : (Tensor, int, bool) -> (Tensor)")
     emit("aten::mean : (Tensor, int?) -> (Tensor)")
     emit("aten::std : (Tensor, bool) -> (Tensor)")
-    emit("aten::std.dim : (Tensor, int[], bool, bool) -> (Tensor)")
+    emit("aten::std.dim : (Tensor, int[]?, bool, bool) -> (Tensor)")
     emit("aten::var : (Tensor, bool) -> (Tensor)")
-    emit("aten::var.dim : (Tensor, int[], bool, bool) -> (Tensor)")
+    emit("aten::var.dim : (Tensor, int[]?, bool, bool) -> (Tensor)")
     emit("aten::var.correction : (Tensor, int[]?, int?, bool) -> (Tensor)")
     emit("aten::nll_loss_forward : (Tensor, Tensor, Tensor?, int, int) -> (Tensor, Tensor)")
     emit("aten::nll_loss_backward : (Tensor, Tensor, Tensor, Tensor?, int, int, Tensor) -> (Tensor)")
diff --git a/python/torch_mlir_e2e_test/test_suite/stats.py b/python/torch_mlir_e2e_test/test_suite/stats.py
index 1093a90aa9cf..ebf9573bbdd0 100644
--- a/python/torch_mlir_e2e_test/test_suite/stats.py
+++ b/python/torch_mlir_e2e_test/test_suite/stats.py
@@ -361,6 +361,50 @@ def StdDimBiasedModule_basic(module, tu: TestUtils):
 # ==============================================================================
 
 
+class StdDimEmptyDimModule(torch.nn.Module):
+
+    def __init__(self):
+        super().__init__()
+
+    @export
+    @annotate_args([
+        None,
+        ([-1, -1, -1], torch.float32, True),
+    ])
+    def forward(self, x):
+        return torch.ops.aten.std(x, dim=[], keepdim=False)
+
+
+@register_test_case(module_factory=lambda: StdDimEmptyDimModule())
+def StdDimEmptyDimModule_basic(module, tu: TestUtils):
+    module.forward(tu.rand(3, 4, 5))
+
+
+# ==============================================================================
+
+
+class StdDimNoneDimModule(torch.nn.Module):
+
+    def __init__(self):
+        super().__init__()
+
+    @export
+    @annotate_args([
+        None,
+        ([-1, -1, -1], torch.float32, True),
+    ])
+    def forward(self, x):
+        return torch.ops.aten.std(x, dim=None, keepdim=False)
+
+
+@register_test_case(module_factory=lambda: StdDimNoneDimModule())
+def StdDimNoneDimModule_basic(module, tu: TestUtils):
+    module.forward(tu.rand(3, 4, 5))
+
+
+# ==============================================================================
+
+
 class VarDimModule(torch.nn.Module):
 
     def __init__(self):
@@ -416,7 +460,7 @@ def __init__(self):
         ([-1, -1, -1], torch.float64, True),
     ])
     def forward(self, x):
-        return torch.ops.aten.var(x, dim=0, unbiased=False, keepdim=True)
+        return torch.ops.aten.var(x, dim=(0,1), unbiased=False, keepdim=True)
 
 
 @register_test_case(module_factory=lambda: VarDimBiasedModule())
@@ -438,7 +482,7 @@ def __init__(self):
         ([-1, -1, -1], torch.float64, True),
     ])
     def forward(self, x):
-        return torch.ops.aten.var(x, dim=0, keepdim=True)
+        return torch.ops.aten.var(x, dim=(0,), keepdim=True)
 
 
 @register_test_case(module_factory=lambda: VarDimSingleDimModule())
@@ -537,6 +581,28 @@ def VarDimEmptyDimModule_basic(module, tu: TestUtils):
 # ==============================================================================
 
 
+class VarDimNoneDimModule(torch.nn.Module):
+
+    def __init__(self):
+        super().__init__()
+
+    @export
+    @annotate_args([
+        None,
+        ([-1, -1, -1], torch.float32, True),
+    ])
+    def forward(self, x):
+        return torch.ops.aten.var(x, dim=None, keepdim=False)
+
+
+@register_test_case(module_factory=lambda: VarDimNoneDimModule())
+def VarDimNoneDimModule_basic(module, tu: TestUtils):
+    module.forward(tu.rand(3, 4, 5))
+
+
+# ==============================================================================
+
+
 class VarCorrectionModule(torch.nn.Module):
 
     def __init__(self):