diff --git a/mlir/include/mlir/Dialect/Linalg/Utils/Utils.h b/mlir/include/mlir/Dialect/Linalg/Utils/Utils.h
--- a/mlir/include/mlir/Dialect/Linalg/Utils/Utils.h
+++ b/mlir/include/mlir/Dialect/Linalg/Utils/Utils.h
@@ -29,16 +29,20 @@
 // General utilities
 //===----------------------------------------------------------------------===//
 
+/// Check if `permutation` is a permutation of the range
+/// `[0, permutation.size())`.
+bool isPermutation(ArrayRef<int64_t> permutation, MLIRContext *context);
+
 /// Apply the permutation defined by `permutation` to `inVec`.
 /// Element `i` in `inVec` is mapped to location `j = permutation[i]`.
 /// E.g.: for an input vector `inVec = ['a', 'b', 'c']` and a permutation vector
 /// `permutation = [2, 0, 1]`, this function leaves `inVec = ['c', 'a', 'b']`.
 template <typename T, unsigned N>
 void applyPermutationToVector(SmallVector<T, N> &inVec,
-                              ArrayRef<unsigned> permutation) {
+                              ArrayRef<int64_t> permutation) {
   SmallVector<T, N> auxVec(inVec.size());
-  for (unsigned i = 0; i < permutation.size(); ++i)
-    auxVec[i] = inVec[permutation[i]];
+  for (auto en : enumerate(permutation))
+    auxVec[en.index()] = inVec[en.value()];
   inVec = auxVec;
 }
 
diff --git a/mlir/lib/Dialect/Linalg/Transforms/FusionOnTensors.cpp b/mlir/lib/Dialect/Linalg/Transforms/FusionOnTensors.cpp
--- a/mlir/lib/Dialect/Linalg/Transforms/FusionOnTensors.cpp
+++ b/mlir/lib/Dialect/Linalg/Transforms/FusionOnTensors.cpp
@@ -363,6 +363,8 @@
                                            ArrayRef<int64_t> tileInterchange) {
   assert(tileSizes.size() == tileInterchange.size() &&
          "expect the number of tile sizes and interchange dims to match");
+  assert(isPermutation(tileInterchange, b.getContext()) &&
+         "expect tile interchange is a permutation");
 
   // Create an empty tile loop nest.
   TileLoopNest tileLoopNest(consumerOp);
@@ -371,9 +373,7 @@
   // inner reduction dimensions.
   SmallVector<StringAttr> iterTypes =
       llvm::to_vector<6>(consumerOp.iterator_types().getAsRange<StringAttr>());
-  applyPermutationToVector(
-      iterTypes,
-      SmallVector<unsigned>(tileInterchange.begin(), tileInterchange.end()));
+  applyPermutationToVector(iterTypes, tileInterchange);
   auto *it = find_if(iterTypes, [&](StringAttr iterType) {
     return !isParallelIterator(iterType);
   });
@@ -455,14 +455,10 @@
                                    tileInterchange.begin() +
                                        rootOp.getNumLoops());
 
-    // As a tiling can only tile a loop dimension once, `rootInterchange` has to
-    // be a permutation of the `rootOp` loop dimensions.
-    SmallVector<AffineExpr> rootInterchangeExprs;
-    transform(rootInterchange, std::back_inserter(rootInterchangeExprs),
-              [&](int64_t dim) { return b.getAffineDimExpr(dim); });
-    AffineMap rootInterchangeMap = AffineMap::get(
-        rootOp.getNumLoops(), 0, rootInterchangeExprs, funcOp.getContext());
-    if (!rootInterchangeMap.isPermutation())
+    // Check `rootInterchange` is a permutation of the `rootOp` loop dimensions.
+    // It has to be a permutation since the tiling cannot tile the same loop
+    // dimension multiple times.
+    if (!isPermutation(rootInterchange, funcOp.getContext()))
       return notifyFailure(
           "expect the tile interchange permutes the root loops");
 
diff --git a/mlir/lib/Dialect/Linalg/Transforms/Interchange.cpp b/mlir/lib/Dialect/Linalg/Transforms/Interchange.cpp
--- a/mlir/lib/Dialect/Linalg/Transforms/Interchange.cpp
+++ b/mlir/lib/Dialect/Linalg/Transforms/Interchange.cpp
@@ -69,7 +69,9 @@
   ArrayRef<Attribute> itTypes = genericOp.iterator_types().getValue();
   SmallVector<Attribute, 4> itTypesVector;
   llvm::append_range(itTypesVector, itTypes);
-  applyPermutationToVector(itTypesVector, interchangeVector);
+  SmallVector<int64_t> permutation(interchangeVector.begin(),
+                                   interchangeVector.end());
+  applyPermutationToVector(itTypesVector, permutation);
   genericOp->setAttr(getIteratorTypesAttrName(),
                      ArrayAttr::get(context, itTypesVector));
 
diff --git a/mlir/lib/Dialect/Linalg/Transforms/Tiling.cpp b/mlir/lib/Dialect/Linalg/Transforms/Tiling.cpp
--- a/mlir/lib/Dialect/Linalg/Transforms/Tiling.cpp
+++ b/mlir/lib/Dialect/Linalg/Transforms/Tiling.cpp
@@ -205,9 +205,10 @@
     // `inversePermutation` must succeed.
     invPermutationMap = inversePermutation(
         AffineMap::getPermutationMap(interchangeVector, b.getContext()));
-    assert(invPermutationMap);
-    applyPermutationToVector(loopRanges, interchangeVector);
-    applyPermutationToVector(iteratorTypes, interchangeVector);
+    SmallVector<int64_t> permutation(interchangeVector.begin(),
+                                     interchangeVector.end());
+    applyPermutationToVector(loopRanges, permutation);
+    applyPermutationToVector(iteratorTypes, permutation);
   }
 
   // 2. Create the tiled loops.
diff --git a/mlir/lib/Dialect/Linalg/Utils/Utils.cpp b/mlir/lib/Dialect/Linalg/Utils/Utils.cpp
--- a/mlir/lib/Dialect/Linalg/Utils/Utils.cpp
+++ b/mlir/lib/Dialect/Linalg/Utils/Utils.cpp
@@ -138,6 +138,15 @@
 namespace mlir {
 namespace linalg {
 
+bool isPermutation(ArrayRef<int64_t> permutation, MLIRContext *context) {
+  SmallVector<AffineExpr> permutationExprs;
+  transform(permutation, std::back_inserter(permutationExprs),
+            [&](int64_t dim) { return getAffineDimExpr(dim, context); });
+  AffineMap permutationMap =
+      AffineMap::get(permutation.size(), 0, permutationExprs, context);
+  return permutationMap.isPermutation();
+}
+
 /// Helper function that creates a memref::DimOp or tensor::DimOp depending on
 /// the type of `source`.
 Value createOrFoldDimOp(OpBuilder &b, Location loc, Value source, int64_t dim) {