diff --git a/mlir/lib/Dialect/Linalg/Transforms/Fusion.cpp b/mlir/lib/Dialect/Linalg/Transforms/Fusion.cpp
--- a/mlir/lib/Dialect/Linalg/Transforms/Fusion.cpp
+++ b/mlir/lib/Dialect/Linalg/Transforms/Fusion.cpp
@@ -188,6 +188,27 @@
                                     SmallPtrSet<Operation *, 1>{newIndex});
     }
   }
+  // When the producer has index semantics, we have to transform the indices of
+  // the producer according to the tiling of the consumer, i.e. offset them by
+  // the values computed in `loopRanges`.
+  if (producer.hasIndexSemantics()) {
+    assert(clonedOp->getNumRegions() == 1 &&
+           clonedOp->getRegion(0).getBlocks().size() == 1 &&
+           "expected producer to have one block.");
+    // Shift all indices by the tile offset.
+    Block &block = clonedOp->getRegion(0).front();
+    for (IndexOp indexOp : block.getOps<IndexOp>()) {
+      OpBuilder::InsertionGuard g(builder);
+      builder.setInsertionPointAfter(indexOp);
+      AffineExpr index, offset;
+      bindDims(builder.getContext(), index, offset);
+      AffineApplyOp applyOp = builder.create<AffineApplyOp>(
+          indexOp.getLoc(), index + offset,
+          ValueRange{indexOp.getResult(), loopRanges[indexOp.dim()].offset});
+      indexOp.getResult().replaceAllUsesExcept(
+          applyOp, SmallPtrSet<Operation *, 1>{applyOp});
+    }
+  }
 
   return clonedOp;
 }
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
@@ -232,8 +232,7 @@
          "expected linalg operation to have one block.");
   Block &block = op->getRegion(0).front();
 
-  for (IndexOp indexOp :
-       llvm::make_early_inc_range(block.getOps<linalg::IndexOp>())) {
+  for (IndexOp indexOp : block.getOps<linalg::IndexOp>()) {
     auto rangeIndex = loopIndexToRangeIndex.find(indexOp.dim());
     if (rangeIndex == loopIndexToRangeIndex.end())
       continue;
diff --git a/mlir/test/Dialect/Linalg/fusion-indexed-generic.mlir b/mlir/test/Dialect/Linalg/fusion-indexed-generic.mlir
--- a/mlir/test/Dialect/Linalg/fusion-indexed-generic.mlir
+++ b/mlir/test/Dialect/Linalg/fusion-indexed-generic.mlir
@@ -62,6 +62,70 @@
 
 // -----
 
+#map = affine_map<(d0, d1)[s0, s1, s2] -> (d0 * s1 + s0 + d1 * s2)>
+#id_2d = affine_map<(d0, d1) -> (d0, d1)>
+#pointwise_2d_trait = {
+  indexing_maps = [#id_2d, #id_2d, #id_2d],
+  iterator_types = ["parallel", "parallel"]
+}
+func @fuse_indexed_consumer(%A: memref<?x?xf32>,
+                                    %B: memref<?x?xf32>,
+                                    %C: memref<?x?xf32>,
+                                    %D: memref<?x?xf32>) {
+  linalg.generic #pointwise_2d_trait
+    ins(%A, %B: memref<?x?xf32>, memref<?x?xf32>)
+   outs(%C : memref<?x?xf32>) {
+  ^bb0(%e: f32, %arg5: f32, %arg6: f32):   // no predecessors
+    %2 = addf %e, %arg5 : f32
+    linalg.yield %2 : f32
+  }
+  %c1 = constant 1 : index
+  %c0 = constant 0 : index
+  %c25 = constant 25 : index
+  %c10 = constant 10 : index
+  %0 = memref.dim %C, %c0 : memref<?x?xf32>
+  %1 = memref.dim %C, %c1 : memref<?x?xf32>
+  %2 = memref.dim %D, %c0 : memref<?x?xf32>
+  %3 = memref.dim %D, %c1 : memref<?x?xf32>
+  scf.for %arg2 = %c0 to %0 step %c10 {
+    scf.for %arg3 = %c0 to %1 step %c25 {
+      %4 = memref.subview %C[%arg2, %arg3][%c10, %c25][%c1, %c1] :
+          memref<?x?xf32> to memref<?x?xf32, #map>
+      %5 = memref.subview %D[%arg2, %arg3][%c10, %c25][%c1, %c1] :
+          memref<?x?xf32> to memref<?x?xf32, #map>
+      linalg.generic {
+        indexing_maps = [#id_2d, #id_2d],
+        iterator_types = ["parallel", "parallel"]}
+        ins(%4 : memref<?x?xf32, #map>)
+       outs(%5 : memref<?x?xf32, #map>) {
+      ^bb0(%arg4: f32, %arg5: f32):
+        %idx0 = linalg.index 0 : index
+        %idx1 = linalg.index 1 : index
+        %6 = addi %idx0, %arg2 : index
+        %7 = addi %idx1, %arg3 : index
+        %8 = index_cast %6 : index to i32
+        %9 = sitofp %8 : i32 to f32
+        %10 = index_cast %7 : index to i32
+        %11 = sitofp %10 : i32 to f32
+        %12 = addf %9, %11 : f32
+        linalg.yield %12 : f32
+      }
+    }
+  }
+  return
+}
+// CHECK-LABEL: func @fuse_indexed_consumer
+// CHECK:  scf.for
+// CHECK:    scf.for
+// CHECK-NOT:  scf.for
+// CHECK:      linalg.generic
+// CHECK-NOT:    affine.apply
+// CHECK:        addf
+// CHECK:      linalg.generic
+// CHECK:        index_cast
+
+// -----
+
 #map = affine_map<(d0, d1)[s0, s1, s2] -> (d0 * s1 + s0 + d1 * s2)>
 #id_2d = affine_map<(d0, d1) -> (d0, d1)>
 #pointwise_2d_trait = {
@@ -124,6 +188,56 @@
 
 // -----
 
+#map = affine_map<(d0, d1)[s0, s1, s2] -> (d0 * s1 + s0 + d1 * s2)>
+func @fuse_indexed_producer(%A: memref<?x?xindex>,
+                            %B: memref<?x?xindex>) {
+  %c1 = constant 1 : index
+  %c0 = constant 0 : index
+  %c25 = constant 25 : index
+  %c10 = constant 10 : index
+  linalg.generic {
+    indexing_maps = [affine_map<(i, j) -> (j, i)>],
+    iterator_types = ["parallel", "parallel"]}
+    outs(%A : memref<?x?xindex>) {
+  ^bb0(%a: index):   // no predecessors
+    %idx0 = linalg.index 0 : index
+    %idx1 = linalg.index 1 : index
+    %0 = addi %idx0, %idx1 : index
+    linalg.yield %0 : index
+  }
+  %A_X = memref.dim %A, %c0 : memref<?x?xindex>
+  %A_Y = memref.dim %A, %c1 : memref<?x?xindex>
+  scf.parallel (%arg2, %arg3) = (%c0, %c0) to (%A_X, %A_Y) step (%c10, %c25) {
+    %A_view = memref.subview %A[%arg2, %arg3][%c10, %c25][%c1, %c1] :
+        memref<?x?xindex> to memref<?x?xindex, #map>
+    %B_view = memref.subview %B[%arg2, %arg3][%c10, %c25][%c1, %c1] :
+        memref<?x?xindex> to memref<?x?xindex, #map>
+    linalg.generic {
+      indexing_maps = [affine_map<(i, j) -> (i, j)>,
+                       affine_map<(i, j) -> (i, j)>],
+      iterator_types = ["parallel", "parallel"]}
+      ins(%A_view : memref<?x?xindex, #map>)
+      outs(%B_view : memref<?x?xindex, #map>) {
+    ^bb0(%a: index, %b: index):
+      linalg.yield %a : index
+    }
+  }
+  return
+}
+// CHECK: [[$MAP:#[a-zA-Z0-9_]*]] = affine_map<(d0, d1) -> (d0 + d1)>
+// CHECK-LABEL: func @fuse_indexed_producer
+// CHECK:  scf.parallel ([[I:%.*]], [[J:%.*]]) =
+// CHECK:    linalg.generic
+// CHECK:      [[idx0:%.*]] = linalg.index 0 : index
+// CHECK:      [[i_new:%.*]] = affine.apply [[$MAP]]([[idx0]], [[J]])
+// CHECK:      [[idx1:%.*]] = linalg.index 1 : index
+// CHECK:      [[j_new:%.*]] = affine.apply [[$MAP]]([[idx1]], [[I]])
+// CHECK:      [[sum:%.*]] = addi [[i_new]], [[j_new]] : index
+// CHECK:      linalg.yield [[sum]] : index
+// CHECK:    linalg.generic
+
+// -----
+
 #map = affine_map<(d0, d1)[s0, s1, s2] -> (d0 * s1 + s0 + d1 * s2)>
 #id_2d = affine_map<(d0, d1) -> (d0, d1)>
 #pointwise_2d_trait = {
@@ -192,49 +306,48 @@
 // -----
 
 #map = affine_map<(d0, d1)[s0, s1, s2] -> (d0 * s1 + s0 + d1 * s2)>
-#id_2d = affine_map<(d0, d1) -> (d0, d1)>
-#pointwise_2d_trait = {
-  indexing_maps = [#id_2d],
-  iterator_types = ["parallel", "parallel"]
-}
-func @index_op(%A: memref<?x?xindex>,
-               %B: memref<?x?xindex>) {
-  linalg.generic #pointwise_2d_trait
-   outs(%B : memref<?x?xindex>) {
-  ^bb0(%arg6: index):   // no predecessors
-    %2 = constant 0 : index
-    linalg.yield %2 : index
-  }
+func @fuse_indexed_producer_tiled_second_dim_only(%A: memref<?x?xindex>,
+                                                  %B: memref<?x?xindex>) {
   %c1 = constant 1 : index
   %c0 = constant 0 : index
   %c25 = constant 25 : index
-  %c10 = constant 10 : index
-  %0 = memref.dim %A, %c0 : memref<?x?xindex>
-  %1 = memref.dim %A, %c1 : memref<?x?xindex>
-  %2 = memref.dim %B, %c0 : memref<?x?xindex>
-  %3 = memref.dim %B, %c1 : memref<?x?xindex>
-  scf.for %arg2 = %c0 to %0 step %c10 {
-    scf.for %arg3 = %c0 to %1 step %c25 {
-      %4 = memref.subview %A[%arg2, %arg3][%c10, %c25][%c1, %c1] :
-          memref<?x?xindex> to memref<?x?xindex, #map>
-      %5 = memref.subview %B[%arg2, %arg3][%c10, %c25][%c1, %c1] :
-          memref<?x?xindex> to memref<?x?xindex, #map>
-      linalg.generic {
-        indexing_maps = [#id_2d, #id_2d],
-        iterator_types = ["parallel", "parallel"]}
-        ins(%4 : memref<?x?xindex, #map>)
-       outs(%5 : memref<?x?xindex, #map>) {
-      ^bb0(%arg6: index, %arg7: index):
-        %6 = linalg.index 0 : index
-        linalg.yield %6 : index
-      }
+  linalg.generic {
+    indexing_maps = [affine_map<(i, j) -> (i, j)>],
+    iterator_types = ["parallel", "parallel"]}
+    outs(%A : memref<?x?xindex>) {
+  ^bb0(%a: index):   // no predecessors
+    %idx0 = linalg.index 0 : index
+    %idx1 = linalg.index 1 : index
+    %0 = addi %idx0, %idx1 : index
+    linalg.yield %0 : index
+  }
+  %A_X = memref.dim %A, %c0 : memref<?x?xindex>
+  %A_Y = memref.dim %A, %c1 : memref<?x?xindex>
+  scf.parallel (%arg3) = (%c0) to (%A_Y) step (%c25) {
+    %A_view = memref.subview %A[%c0, %arg3][%A_X, %c25][%c1, %c1] :
+        memref<?x?xindex> to memref<?x?xindex, #map>
+    %B_view = memref.subview %B[%c0, %arg3][%A_X, %c25][%c1, %c1] :
+        memref<?x?xindex> to memref<?x?xindex, #map>
+    linalg.generic {
+      indexing_maps = [affine_map<(i, j) -> (i, j)>,
+                       affine_map<(i, j) -> (i, j)>],
+      iterator_types = ["parallel", "parallel"]}
+      ins(%A_view : memref<?x?xindex, #map>)
+      outs(%B_view : memref<?x?xindex, #map>) {
+    ^bb0(%a: index, %b: index):
+      linalg.yield %a : index
     }
   }
   return
 }
-// CHECK-LABEL: func @index_op
-// CHECK:  linalg.generic
-// CHECK:  scf.for
-// CHECK:    scf.for
-// CHECK-NOT:  scf.for
-// CHECK:      linalg.generic
+// CHECK: [[$MAP:#[a-zA-Z0-9_]*]] = affine_map<(d0, d1) -> (d0 + d1)>
+// CHECK-LABEL: func @fuse_indexed_producer_tiled_second_dim_only
+// CHECK:  scf.parallel ([[J:%.*]]) =
+// CHECK:    linalg.generic
+// CHECK:      [[idx0:%.*]] = linalg.index 0 : index
+// CHECK:      [[idx1:%.*]] = linalg.index 1 : index
+// CHECK:      [[j_new:%.*]] = affine.apply [[$MAP]]([[idx1]], [[J]])
+// CHECK:      [[sum:%.*]] = addi [[idx0]], [[j_new]] : index
+// CHECK:      linalg.yield [[sum]] : index
+// CHECK:    linalg.generic
+
diff --git a/mlir/test/lib/Transforms/TestLinalgFusionTransforms.cpp b/mlir/test/lib/Transforms/TestLinalgFusionTransforms.cpp
--- a/mlir/test/lib/Transforms/TestLinalgFusionTransforms.cpp
+++ b/mlir/test/lib/Transforms/TestLinalgFusionTransforms.cpp
@@ -126,10 +126,6 @@
   // Save original Linalg ops, we only want to make a pass over those.
   SmallVector<LinalgOp, 8> linalgOps;
   f.walk([&](LinalgOp op) {
-    // TODO: remove hasIndexSemantics check once index ops are supported.
-    if (op.hasIndexSemantics())
-      return;
-
     // TODO: support multi-results.
     if (op->getNumResults() <= 1)
       linalgOps.push_back(op);