diff --git a/mlir/lib/Dialect/Vector/VectorMultiDimReductionTransforms.cpp b/mlir/lib/Dialect/Vector/VectorMultiDimReductionTransforms.cpp
--- a/mlir/lib/Dialect/Vector/VectorMultiDimReductionTransforms.cpp
+++ b/mlir/lib/Dialect/Vector/VectorMultiDimReductionTransforms.cpp
@@ -41,6 +41,9 @@
     auto src = multiReductionOp.source();
     auto loc = multiReductionOp.getLoc();
     auto srcRank = multiReductionOp.getSourceVectorType().getRank();
+    // If the rank is less than or equal to 1, there is nothing to do.
+    if (srcRank <= 1)
+      return failure();
 
     // Separate reduction and parallel dims
     auto reductionDimsRange =
diff --git a/mlir/test/Dialect/Vector/vector-multi-reduction-outer-lowering.mlir b/mlir/test/Dialect/Vector/vector-multi-reduction-outer-lowering.mlir
--- a/mlir/test/Dialect/Vector/vector-multi-reduction-outer-lowering.mlir
+++ b/mlir/test/Dialect/Vector/vector-multi-reduction-outer-lowering.mlir
@@ -153,3 +153,13 @@
 //       CHECK:   %[[R18:.+]] = arith.addi %[[V19]], %[[R17]] : vector<6xi32>
 //       CHECK:   %[[RESULT_VEC:.+]] = vector.shape_cast %[[R18]] : vector<6xi32> to vector<2x3xi32>
 //       CHECK:   return %[[RESULT_VEC]] : vector<2x3xi32>
+
+// This test is mainly to catch a bug that running
+// `InnerOuterDimReductionConversion` on this function results in an
+// infinite loop. So just check that some value is returned.
+func @vector_reduction_1D(%arg0 : vector<2xf32>) -> f32 {
+  %0 = vector.multi_reduction #vector.kind<maxf>, %arg0 [0] : vector<2xf32> to f32
+  return %0 : f32
+}
+// CHECK-LABEL: func @vector_reduction_1D
+//       CHECK:   return %{{.+}}