diff --git a/e2e_testing/torchscript/xfail_sets.py b/e2e_testing/torchscript/xfail_sets.py
index 99528fcb2..e44ba8300 100644
--- a/e2e_testing/torchscript/xfail_sets.py
+++ b/e2e_testing/torchscript/xfail_sets.py
@@ -55,6 +55,7 @@ TOSA_PASS_SET = {
     "ReturnTwoTensorF32I64_basic",
     "ElementwisePowModule_basic",
     "BmmModule_basic",
+    "MmDagModule_basic",
     "Matmul_dot",
     "Matmul_3d",
     "RsubModule_basic",
diff --git a/lib/Dialect/Torch/Transforms/RefineTypes.cpp b/lib/Dialect/Torch/Transforms/RefineTypes.cpp
index 091112b2f..7ebdc35cf 100644
--- a/lib/Dialect/Torch/Transforms/RefineTypes.cpp
+++ b/lib/Dialect/Torch/Transforms/RefineTypes.cpp
@@ -823,32 +823,23 @@ ChangeResult TypeAnalyzer::visitAtenMmOp(
   auto &rhs = operands[1]->getValue();
   auto knowledge =
       ValueKnowledge::getNotNonePessimisticValueState(op->getContext());
+
+  auto isRank2 = [](const ValueKnowledge &operand) -> bool {
+    return operand.hasSizes && operand.sizes.size() == 2;
+  };
+
+  // `aten.mm` expects both operands to be rank-2 tensors.
+  if (!isRank2(lhs) || !isRank2(rhs))
+    return getLatticeElement(op->getResult(0)).join(knowledge);
+
+  // If static information is available, check that both tensors are compatible.
+  if (lhs.sizes[1] != kUnknownSize && rhs.sizes[0] != kUnknownSize &&
+      lhs.sizes[1] != rhs.sizes[0])
+    return getLatticeElement(op->getResult(0)).join(knowledge);
+
   knowledge.hasSizes = true;
-  // WARNING: We could be more precise here by calculating the output
-  // shape as "(lhs.shape[0], rhs.shape[1])". However, that is really tricky
-  // at this stage in the compiler because we don't really have many static
-  // guarantees about the input ranks because `aten` ops do dynamic error
-  // checking and safely abort the program. There is nothing preventing us
-  // from (correctly!) statically inferring the shapes of the operands to
-  // shapes that are guaranteed to cause an error at runtime.
-  //
-  // Example: Suppose a user program calls `aten.mm` with two rank-0
-  // operands. The program emits an error when invoked, but when running
-  // this pass, we will (correctly!) infer `lhs.hasSizes && lhs.sizes.size()
-  // == 0 && rhs.hasSizes && rhs.sizes.size() == 0` -- it's not safe to
-  // access `lhs.sizes[0]` / `rhs.sizes[1]`! So when writing this transfer
-  // function, it's not as simple as taking `lhs.sizes[0]` and
-  // `rhs.sizes[1]`, as both of those might read out of bounds of the array.
-  // It would require more complicated logic.
-  //
-  // Just knowing dtypes and ranks is sufficient at this stage
-  // in the compiler. The precise per-dimension size propagation is best
-  // done lower in the stack, such as at the linalg level, where we have
-  // more static guarantees and more structure.
-  knowledge.sizes.resize(2, kUnknownSize);
-  // TODO: Investigate promotion rules if element types mismatch.
-  // This is conservatively correct, assuming that if both element types are
-  // the same, then the result is of that same element type.
+  knowledge.sizes = {lhs.sizes[0], rhs.sizes[1]};
+
   knowledge.dtype =
       getPromotedResultTypeAssumingNonZeroRank(op->getContext(), {&lhs, &rhs});
   return getLatticeElement(op->getResult(0)).join(knowledge);
diff --git a/test/Dialect/Torch/refine-types.mlir b/test/Dialect/Torch/refine-types.mlir
index fedccd54a..84df11b2e 100644
--- a/test/Dialect/Torch/refine-types.mlir
+++ b/test/Dialect/Torch/refine-types.mlir
@@ -41,8 +41,8 @@ builtin.func @f(%arg0: !torch.vtensor<[2,3,?],f32>) -> !torch.vtensor {
 // CHECK-LABEL:   func @f(
 // CHECK-SAME:            %[[LHS:.*]]: !torch.vtensor<[2,?],f32>,
 // CHECK-SAME:            %[[RHS:.*]]: !torch.vtensor<[?,?],f32>) -> !torch.vtensor {
-// CHECK:           %[[MM:.*]] = torch.aten.mm %[[LHS]], %[[RHS]] : !torch.vtensor<[2,?],f32>, !torch.vtensor<[?,?],f32> -> !torch.vtensor<[?,?],f32>
-// CHECK:           %[[SHAPE_ERASED:.*]] = torch.tensor_static_info_cast %[[MM]] : !torch.vtensor<[?,?],f32> to !torch.vtensor
+// CHECK:           %[[MM:.*]] = torch.aten.mm %[[LHS]], %[[RHS]] : !torch.vtensor<[2,?],f32>, !torch.vtensor<[?,?],f32> -> !torch.vtensor<[2,?],f32>
+// CHECK:           %[[SHAPE_ERASED:.*]] = torch.tensor_static_info_cast %[[MM]] : !torch.vtensor<[2,?],f32> to !torch.vtensor
 // CHECK:           return %[[SHAPE_ERASED]] : !torch.vtensor
 builtin.func @f(%arg0: !torch.vtensor<[2,?],f32>, %arg1: !torch.vtensor<[?,?],f32>) -> !torch.vtensor {
   %1 = torch.aten.mm %arg0, %arg1 : !torch.vtensor<[2,?],f32>, !torch.vtensor<[?,?],f32> -> !torch.vtensor
@@ -51,6 +51,44 @@ builtin.func @f(%arg0: !torch.vtensor<[2,?],f32>, %arg1: !torch.vtensor<[?,?],f3
 
 // -----
 
+// CHECK-LABEL:   func @g(
+// CHECK-SAME:            %[[LHS:.*]]: !torch.vtensor<[2,3],f32>,
+// CHECK-SAME:            %[[RHS:.*]]: !torch.vtensor<[3,4],f32>) -> !torch.vtensor {
+// CHECK:           %[[MM:.*]] = torch.aten.mm %[[LHS]], %[[RHS]] : !torch.vtensor<[2,3],f32>, !torch.vtensor<[3,4],f32> -> !torch.vtensor<[2,4],f32>
+// CHECK:           %[[SHAPE_ERASED:.*]] = torch.tensor_static_info_cast %[[MM]] : !torch.vtensor<[2,4],f32> to !torch.vtensor
+// CHECK:           return %[[SHAPE_ERASED]] : !torch.vtensor
+builtin.func @g(%arg0: !torch.vtensor<[2,3],f32>, %arg1: !torch.vtensor<[3,4],f32>) -> !torch.vtensor {
+  %1 = torch.aten.mm %arg0, %arg1 : !torch.vtensor<[2,3],f32>, !torch.vtensor<[3,4],f32> -> !torch.vtensor
+  return %1 : !torch.vtensor
+}
+
+// -----
+
+// CHECK-LABEL:   func @h(
+// CHECK-SAME:            %[[LHS:.*]]: !torch.vtensor<[2,?],f32>,
+// CHECK-SAME:            %[[RHS:.*]]: !torch.vtensor<[3,4],f32>) -> !torch.vtensor {
+// CHECK:           %[[MM:.*]] = torch.aten.mm %[[LHS]], %[[RHS]] : !torch.vtensor<[2,?],f32>, !torch.vtensor<[3,4],f32> -> !torch.vtensor<[2,4],f32>
+// CHECK:           %[[SHAPE_ERASED:.*]] = torch.tensor_static_info_cast %[[MM]] : !torch.vtensor<[2,4],f32> to !torch.vtensor
+// CHECK:           return %[[SHAPE_ERASED]] : !torch.vtensor
+builtin.func @h(%arg0: !torch.vtensor<[2,?],f32>, %arg1: !torch.vtensor<[3,4],f32>) -> !torch.vtensor {
+  %1 = torch.aten.mm %arg0, %arg1 : !torch.vtensor<[2,?],f32>, !torch.vtensor<[3,4],f32> -> !torch.vtensor
+  return %1 : !torch.vtensor
+}
+
+// -----
+
+// CHECK-LABEL:   func @i(
+// CHECK-SAME:            %[[LHS:.*]]: !torch.vtensor<[2,5],f32>,
+// CHECK-SAME:            %[[RHS:.*]]: !torch.vtensor<[3,4],f32>) -> !torch.vtensor {
+// CHECK:           %[[MM:.*]] = torch.aten.mm %[[LHS]], %[[RHS]] : !torch.vtensor<[2,5],f32>, !torch.vtensor<[3,4],f32> -> !torch.vtensor
+// CHECK:           return %[[MM]] : !torch.vtensor
+builtin.func @i(%arg0: !torch.vtensor<[2,5],f32>, %arg1: !torch.vtensor<[3,4],f32>) -> !torch.vtensor {
+  %1 = torch.aten.mm %arg0, %arg1 : !torch.vtensor<[2,5],f32>, !torch.vtensor<[3,4],f32> -> !torch.vtensor
+  return %1 : !torch.vtensor
+}
+
+// -----
+
 // CHECK-LABEL:   func @f(
 // CHECK-SAME:            %[[INPUT:.*]]: !torch.vtensor<[?,3],f32>,
 // CHECK-SAME:            %[[WEIGHT:.*]]: !torch.vtensor<[5,3],f32>,