diff --git a/mlir/lib/Dialect/Tensor/IR/TensorTilingInterfaceImpl.cpp b/mlir/lib/Dialect/Tensor/IR/TensorTilingInterfaceImpl.cpp
--- a/mlir/lib/Dialect/Tensor/IR/TensorTilingInterfaceImpl.cpp
+++ b/mlir/lib/Dialect/Tensor/IR/TensorTilingInterfaceImpl.cpp
@@ -94,14 +94,13 @@
   return loopBounds;
 }
 
-static void applyInversePermToRange(SmallVector<OpFoldResult> &offsets,
-                                    SmallVector<OpFoldResult> &sizes,
-                                    ArrayRef<int64_t> permutation) {
+static void applyPermToRange(SmallVector<OpFoldResult> &offsets,
+                             SmallVector<OpFoldResult> &sizes,
+                             ArrayRef<int64_t> permutation) {
   if (permutation.empty())
     return;
-  SmallVector<int64_t> inversedPerm = invertPermutationVector(permutation);
-  applyPermutationToVector<OpFoldResult>(offsets, inversedPerm);
-  applyPermutationToVector<OpFoldResult>(sizes, inversedPerm);
+  applyPermutationToVector<OpFoldResult>(offsets, permutation);
+  applyPermutationToVector<OpFoldResult>(sizes, permutation);
 }
 
 struct PackOpTiling
@@ -133,7 +132,8 @@
     int64_t inputRank = packOp.getSourceRank();
     SmallVector<OpFoldResult> origOffsets(offsets.begin(), offsets.end());
     SmallVector<OpFoldResult> origSizes(sizes.begin(), sizes.end());
-    applyInversePermToRange(origOffsets, origSizes, packOp.getOuterDimsPerm());
+    applyPermToRange(origOffsets, origSizes,
+                     invertPermutationVector(packOp.getOuterDimsPerm()));
 
     DenseMap<int64_t, OpFoldResult> dimAndTileMapping =
         packOp.getDimAndTileMapping();
@@ -382,8 +382,8 @@
 
     // The tiling is applied on destination dimensions. We have to apply the
     // interchange on source dimensions if outer_dims_perm is set.
-    applyInversePermToRange(sliceSrcIndices, sliceSrcSizes,
-                            unpackOp.getOuterDimsPerm());
+    applyPermToRange(sliceSrcIndices, sliceSrcSizes,
+                     unpackOp.getOuterDimsPerm());
     Attribute zeroAttr = b.getIndexAttr(0);
     sliceSrcIndices.append(numInnerTiles, zeroAttr);
     sliceSrcSizes.append(unpackOp.getMixedTiles());
diff --git a/mlir/test/Dialect/Tensor/tiling.mlir b/mlir/test/Dialect/Tensor/tiling.mlir
--- a/mlir/test/Dialect/Tensor/tiling.mlir
+++ b/mlir/test/Dialect/Tensor/tiling.mlir
@@ -549,6 +549,7 @@
 // CHECK:             %[[RES:.+]] = tensor.insert_slice %[[UNPACK]]
 // CHECK-SAME:          into %{{.+}}[%[[K]], %[[C]]] [%[[OUT_K_SZ]], %[[OUT_C_SZ]]]
 // CHECK:             scf.yield %[[RES]]
+
 func.func @dynamic_perfect_CKkc_to_KC(%source: tensor<?x?x2x2xf32>, %dest: tensor<?x?xf32>) -> tensor<?x?xf32> {
   %0 = tensor.unpack %source outer_dims_perm = [1, 0] inner_dims_pos = [0, 1] inner_tiles = [2, 2] into %dest : tensor<?x?x2x2xf32> -> tensor<?x?xf32>
   return %0 : tensor<?x?xf32>
@@ -559,3 +560,77 @@
     %0 = transform.structured.match ops{["tensor.unpack"]} in %arg1
     %1, %loops:2 = transform.structured.tile_to_scf_for %0 [2, 4]
 }
+
+// -----
+
+// CHECK: #[[MAP:.+]] = affine_map<(d0) -> (d0 floordiv 2)>
+// CHECK: func.func @perfect_NKPQk_to_NPQK(
+// CHECK-SAME:  %[[SOURCE:.+]]: tensor<1x4x6x6x2xf32>,
+// CHECK-SAME:  %{{.+}}: tensor<1x6x6x8xf32>)
+// CHECK-DAG: %[[C0:.*]] = arith.constant 0 : index
+// CHECK-DAG: %[[C1:.*]] = arith.constant 1 : index
+// CHECK-DAG: %[[C6:.*]] = arith.constant 6 : index
+// CHECK-DAG: %[[C8:.*]] = arith.constant 8 : index
+// CHECK-DAG: %[[C4:.*]] = arith.constant 4 : index
+// CHECK: %{{.+}} = scf.for %[[P:.+]] = %[[C0]] to %[[C6]] step %[[C1]]
+// CHECK:   %{{.+}} = scf.for %[[Q:.+]] = %[[C0]] to %[[C6]] step %[[C1]]
+// CHECK:     %{{.+}} = scf.for %[[K:.+]] = %[[C0]] to %[[C8]] step %[[C4]]
+// CHECK:       %[[K_SZ:.+]] = affine.apply #[[MAP]](%[[K]])
+// CHECK:       %[[SLICE_SOURCE:.+]] = tensor.extract_slice %[[SOURCE]][0, %[[K_SZ]], %[[P]], %[[Q]], 0]
+// CHECK:       %[[SLICE_DEST:.+]] = tensor.extract_slice %{{.+}}[0, %[[P]], %[[Q]], %[[K]]]
+// CHECK:       %[[UNPACK:.+]] = tensor.unpack
+// CHECK-SAME:    %[[SLICE_SOURCE]] outer_dims_perm = [0, 3, 1, 2] inner_dims_pos = [3] inner_tiles = [2]
+// CHECK-SAME:    into %[[SLICE_DEST]] 
+// CHECK:       %[[RES:.+]] = tensor.insert_slice %[[UNPACK]] 
+// CHECK-SAME:    into %{{.+}}[0, %[[P]], %[[Q]], %[[K]]]
+// CHECK:       scf.yield %[[RES]]
+
+func.func @perfect_NKPQk_to_NPQK(%source: tensor<1x4x6x6x2xf32>, %dest: tensor<1x6x6x8xf32>) -> tensor<1x6x6x8xf32> {
+  %0 = tensor.unpack %source outer_dims_perm = [0, 3, 1, 2] inner_dims_pos = [3] inner_tiles = [2] into %dest : tensor<1x4x6x6x2xf32> -> tensor<1x6x6x8xf32>
+  return %0 : tensor<1x6x6x8xf32>
+}
+
+transform.sequence failures(propagate) {
+  ^bb0(%arg1: !pdl.operation):
+    %0 = transform.structured.match ops{["tensor.unpack"]} in %arg1
+    %1, %loops:4 = transform.structured.tile_to_scf_for %0 [1, 1, 1, 4]
+}
+
+// -----
+
+// CHECK-DAG: #[[MAP:.+]] = affine_map<(d0) -> (-d0 + 6, 1)>
+// CHECK-DAG: #[[MAP1:.+]] = affine_map<(d0) -> (d0 * 2)>
+// CHECK-DAG: #[[MAP2:.+]] = affine_map<(d0) -> (d0 * -2 + 8, 2)>
+// CHECK: func.func @perfect_NPQK_to_NKPQk
+// CHECK-SAME:  %[[SOURCE:.+]]: tensor<1x6x6x8xf32>,
+// CHECK-SAME:  %{{.+}}: tensor<1x4x6x6x2xf32>)
+// CHECK-DAG: %[[C0:.+]] = arith.constant 0 : index
+// CHECK-DAG: %[[C1:.+]] = arith.constant 1 : index
+// CHECK-DAG: %[[C4:.+]] = arith.constant 4 : index
+// CHECK-DAG: %[[C6:.+]] = arith.constant 6 : index
+// CHECK: %{{.+}} = scf.for %[[ARG2:.+]] = %[[C0]] to %[[C4]] step %[[C1]]
+// CHECK:   %{{.+}} = scf.for %[[ARG4:.+]] = %[[C0]] to %[[C6]] step %[[C1]]
+// CHECK:     %{{.+}} = scf.for %[[ARG6:.+]] = %[[C0]] to %[[C6]] step %[[C1]]
+// CHECK:       %[[MIN_ARG4:.+]] = affine.min #[[MAP]](%[[ARG4]])
+// CHECK:       %[[MIN_ARG6:.+]] = affine.min #[[MAP]](%[[ARG6]])
+// CHECK:       %[[APPLY:.+]] = affine.apply #[[MAP1]](%[[ARG2]])
+// CHECK:       %[[MIN_ARG2:.+]] = affine.min #[[MAP2]](%[[ARG2]])
+// CHECK:       %[[SLICE_SOURCE:.+]] = tensor.extract_slice %[[SOURCE]][0, %[[ARG4]], %[[ARG6]], %[[APPLY]]]
+// CHECK:       %[[SLICE_DEST:.+]] = tensor.extract_slice %{{.+}}[0, %[[ARG2]], %[[ARG4]], %[[ARG6]], 0]
+// CHECK:       %[[PACK:.+]] = tensor.pack
+// CHECK-SAME:    %[[SLICE_SOURCE]] outer_dims_perm = [0, 3, 1, 2] inner_dims_pos = [3] inner_tiles = [2]
+// CHECK-SAME:    into %[[SLICE_DEST]]
+// CHECK:       %[[RES:.+]] = tensor.insert_slice %[[PACK]]
+// CHECK-SAME:    into %{{.+}}[0, %[[ARG2]], %[[ARG4]], %[[ARG6]], 0]
+// CHECK:       scf.yield %[[RES]]
+
+func.func @perfect_NPQK_to_NKPQk(%source: tensor<1x6x6x8xf32>, %dest: tensor<1x4x6x6x2xf32>) -> tensor<1x4x6x6x2xf32> {
+  %0 = tensor.pack %source outer_dims_perm = [0, 3, 1, 2] inner_dims_pos = [3] inner_tiles = [2] into %dest : tensor<1x6x6x8xf32> -> tensor<1x4x6x6x2xf32>
+  return %0 : tensor<1x4x6x6x2xf32>
+}
+
+transform.sequence failures(propagate) {
+  ^bb0(%arg1: !pdl.operation):
+    %0 = transform.structured.match ops{["tensor.pack"]} in %arg1
+    %1, %loops:4 = transform.structured.tile_to_scf_for %0 [1, 1, 1, 1]
+}