diff --git a/mlir/lib/Dialect/Linalg/Transforms/LinalgStrategyPasses.cpp b/mlir/lib/Dialect/Linalg/Transforms/LinalgStrategyPasses.cpp
--- a/mlir/lib/Dialect/Linalg/Transforms/LinalgStrategyPasses.cpp
+++ b/mlir/lib/Dialect/Linalg/Transforms/LinalgStrategyPasses.cpp
@@ -25,9 +25,11 @@
 #include "mlir/Dialect/Vector/VectorTransforms.h"
 #include "mlir/IR/AffineExpr.h"
 #include "mlir/IR/AffineMap.h"
+#include "mlir/Pass/PassManager.h"
 #include "mlir/Support/LLVM.h"
 #include "mlir/Transforms/GreedyPatternRewriteDriver.h"
 #include "mlir/Transforms/LoopUtils.h"
+#include "mlir/Transforms/Passes.h"
 #include "mlir/Transforms/Utils.h"
 
 using namespace mlir;
@@ -335,6 +337,12 @@
 
     if (options.hoistRedundantVectorTransfersOnTensor)
       hoistRedundantVectorTransfersOnTensor(funcOp);
+
+    // Run CSE to cleanup after canonicalization.
+    OpPassManager dynamicPM("builtin.func");
+    dynamicPM.addPass(createCSEPass());
+    if (failed(runPipeline(dynamicPM, funcOp)))
+      return signalPassFailure();
   }
 
   LinalgEnablingOptions options;
diff --git a/mlir/test/Dialect/Linalg/codegen-strategy.mlir b/mlir/test/Dialect/Linalg/codegen-strategy.mlir
--- a/mlir/test/Dialect/Linalg/codegen-strategy.mlir
+++ b/mlir/test/Dialect/Linalg/codegen-strategy.mlir
@@ -40,14 +40,19 @@
 
 // -----
 
+//     CHECK-PAD-DAG: #[[MAP0:[0-9a-z]+]] = affine_map<(d0) -> (16, -d0 + 72)>
+
 //         CHECK-PAD: func @matmul(
 func @matmul(%arg0: tensor<72x72xf32>, %arg1: tensor<72x72xf32>, %arg2: tensor<72x72xf32>) -> tensor<72x72xf32> {
 
   // Check the padding of the input operands has been hoisted out of the tile loop nest.
   //      CHECK-PAD-COUNT=2: linalg.pad_tensor %{{.*}} nofold
-  //      CHECK-PAD-COUNT=3: scf.for
+  //              CHECK-PAD: scf.for
+  // Check CSE eliminates the duplicate min operations introduced by tiling.
+  //              CHECK-PAD: affine.min #[[MAP0]]
+  //          CHECK-PAD-NOT: affine.min #[[MAP0]]
+  //      CHECK-PAD-COUNT=2: scf.for
   //              CHECK-PAD: linalg.matmul
   %0 = linalg.matmul ins(%arg0, %arg1: tensor<72x72xf32>, tensor<72x72xf32>) outs(%arg2: tensor<72x72xf32>) -> tensor<72x72xf32>
   return %0 : tensor<72x72xf32>
 }
-