diff --git a/mlir/lib/Dialect/Linalg/Transforms/HoistPadding.cpp b/mlir/lib/Dialect/Linalg/Transforms/HoistPadding.cpp
--- a/mlir/lib/Dialect/Linalg/Transforms/HoistPadding.cpp
+++ b/mlir/lib/Dialect/Linalg/Transforms/HoistPadding.cpp
@@ -255,23 +255,44 @@
   SetVector<Value> toProjectOut;
   for (scf::ForOp loop : loops) {
     auto ub = loop.upperBound();
-    if (isDefinedOutsideOrConstant(outerLimit, ub))
-      continue;
 
-    // Compute a backward slice up to, but not including, `outerLimit`.
-    SetVector<Operation *> backwardSlice;
-    getBackwardSlice(ub, &backwardSlice, [&](Operation *op) {
-      return outerLimit->isProperAncestor(op);
+    // Compute the index computation slice for the upper bound `ub`.
+    SetVector<Value> indexEdges;
+    indexEdges.insert(ub);
+    SetVector<Operation *> indexSlice;
+    getBackwardSlice(ub, &indexSlice, [&](Operation *op) {
+      // Continue only along the index operands of the ForOp.
+      if (auto forOp = dyn_cast<scf::ForOp>(op)) {
+        if (!outerLimit->isAncestor(op))
+          return false;
+        if (!indexEdges.contains(forOp.getInductionVar()))
+          return false;
+        indexEdges.insert(forOp.lowerBound());
+        indexEdges.insert(forOp.upperBound());
+        indexEdges.insert(forOp.step());
+        return true;
+      }
+      // All supported index operations have one result.
+      assert(op->getNumResults() == 1 &&
+             "expect operations to have one result");
+      if (!indexEdges.contains(op->getResult(0)))
+        return false;
+      for (Value value : op->getOperands())
+        indexEdges.insert(value);
+      return true;
     });
-    backwardSlice.insert(ub.getDefiningOp());
+    indexSlice.insert(ub.getDefiningOp());
 
     // Iterate over all ops in the slice and compose them in the constraints.
-    for (Operation *op : llvm::reverse(backwardSlice)) {
-      if (!isa<scf::ForOp, AffineApplyOp, AffineMinOp>(op))
-        return failure();
-      if (isa<scf::ForOp>(op))
+    for (Operation *op : llvm::reverse(indexSlice)) {
+      // All ForOps have previously been added to the constraints and ConstantOp
+      // and DimOp are terminals of the index computation.
+      if (isa<scf::ForOp, arith::ConstantOp, tensor::DimOp>(op))
         continue;
-      // Ensure there is a
+      // Check all index computation operations are supported.
+      if (!isa<AffineApplyOp, AffineMinOp>(op))
+        return failure();
+      // Ensure there is an id.
       auto ensureIdFailed = [&](Value v) {
         if (constraints.containsId(v)) {
           unsigned pos;
@@ -289,6 +310,8 @@
 
       // All supported ops have 1 result.
       // TODO: extend when needed.
+      assert(op->getNumResults() == 1 &&
+             "expect operations to have one result");
       toProjectOut.insert(op->getResult(0));
 
       // Compose supported ops.
diff --git a/mlir/test/Dialect/Linalg/hoist-padding.mlir b/mlir/test/Dialect/Linalg/hoist-padding.mlir
--- a/mlir/test/Dialect/Linalg/hoist-padding.mlir
+++ b/mlir/test/Dialect/Linalg/hoist-padding.mlir
@@ -168,18 +168,16 @@
   //      CHECK: scf.for %[[I:[0-9a-z]+]] =
   //
   //      CHECK:   %[[MR8:.*]] = affine.min #[[$MIN_REST8]](%[[I]])
-  //      CHECK:   %[[D0:.*]] = affine.apply #[[$DIV4]](%[[MR8]])
   // Init tensor and pack.
-  //      CHECK:   %[[INIT_PACKED_A:.*]] = linalg.init_tensor [%[[D0]], 2, 2] : tensor<?x2x2xf32>
-  //      CHECK:   %[[CAST_INIT_PACKED_A:.*]] = tensor.cast %[[INIT_PACKED_A]] : tensor<?x2x2xf32> to tensor<?x?x2xf32>
+  //      CHECK:   %[[INIT_PACKED_A:.*]] = linalg.init_tensor [2, 2, 2] : tensor<2x2x2xf32>
+  //      CHECK:   %[[CAST_INIT_PACKED_A:.*]] = tensor.cast %[[INIT_PACKED_A]] : tensor<2x2x2xf32> to tensor<?x?x2xf32>
   //      CHECK:   %[[PACKED_A:.*]] = scf.for %[[II:[0-9a-z]+]] = {{.*}} iter_args(%{{.*}} = %[[CAST_INIT_PACKED_A]]) -> (tensor<?x?x2xf32>) {
   //      CHECK:     scf.for %[[III:[0-9a-z]+]] =
   //      CHECK:       tensor.insert_slice %{{.*}} into %{{.*}}[%{{.*}}, %{{.*}}, 0] [1, 1, 2] [1, 1, 1] : tensor<2xf32> into tensor<?x?x2xf32>
   //
-  //      CHECK:   %[[D0_2:.*]] = affine.apply #[[$DIV4]](%[[MR8]])
   // Init tensor and pack.
-  //      CHECK:   %[[INIT_PACKED_B:.*]] = linalg.init_tensor [%[[D0_2]], 2, 2] : tensor<?x2x2xf32>
-  //      CHECK:   %[[CAST_INIT_PACKED_B:.*]] = tensor.cast %[[INIT_PACKED_B]] : tensor<?x2x2xf32> to tensor<?x?x2xf32>
+  //      CHECK:   %[[INIT_PACKED_B:.*]] = linalg.init_tensor [2, 2, 2] : tensor<2x2x2xf32>
+  //      CHECK:   %[[CAST_INIT_PACKED_B:.*]] = tensor.cast %[[INIT_PACKED_B]] : tensor<2x2x2xf32> to tensor<?x?x2xf32>
   //      CHECK:   %[[PACKED_B:.*]] = scf.for %[[II_2:[0-9a-z]+]] = {{.*}} iter_args(%{{.*}} = %[[CAST_INIT_PACKED_B]]) -> (tensor<?x?x2xf32>) {
   //      CHECK:     scf.for %[[III_2:[0-9a-z]+]] =
   //      CHECK:       tensor.insert_slice %{{.*}} into %{{.*}}[%{{.*}}, %{{.*}}, 0] [1, 1, 2] [1, 1, 1] : tensor<2xf32> into tensor<?x?x2xf32>
diff --git a/mlir/test/Dialect/Linalg/pad-and-hoist.mlir b/mlir/test/Dialect/Linalg/pad-and-hoist.mlir
--- a/mlir/test/Dialect/Linalg/pad-and-hoist.mlir
+++ b/mlir/test/Dialect/Linalg/pad-and-hoist.mlir
@@ -236,7 +236,7 @@
       %4 = tensor.extract_slice %arg6[%arg3, %arg5] [%2, %3] [1, 1] : tensor<24x25xf32> to tensor<?x?xf32>
 
       // Packing the second input operand.
-      //    CHECK-DOUBLE:  = linalg.init_tensor [%{{.*}}, 12, 6]
+      //    CHECK-DOUBLE:  = linalg.init_tensor [3, 12, 6]
       //    CHECK-DOUBLE:  %[[PT1:.*]] = scf.for %[[PIV1:[0-9a-z]+]] =
       //      CHECK-DOUBLE:   %[[PIDX1:.*]] = affine.apply #[[DIV6]](%[[PIV1]])
       //      CHECK-DOUBLE:   %[[T3:.*]] = tensor.extract_slice %[[ARG1]]