diff --git a/mlir/lib/Transforms/Utils/GreedyPatternRewriteDriver.cpp b/mlir/lib/Transforms/Utils/GreedyPatternRewriteDriver.cpp
--- a/mlir/lib/Transforms/Utils/GreedyPatternRewriteDriver.cpp
+++ b/mlir/lib/Transforms/Utils/GreedyPatternRewriteDriver.cpp
@@ -133,6 +133,16 @@
   };
 #endif
 
+  auto insertKnownConstant = [&](Operation *op) {
+    // Check for existing constants when populating the worklist. This avoids
+    // accidentally reversing the constant order during processing.
+    Attribute constValue;
+    if (matchPattern(op, m_Constant(&constValue)))
+      if (!folder.insertKnownConstant(op, constValue))
+        return true;
+    return false;
+  };
+
   bool changed = false;
   unsigned iteration = 0;
   do {
@@ -142,22 +152,18 @@
     if (!config.useTopDownTraversal) {
       // Add operations to the worklist in postorder.
       for (auto &region : regions) {
-        region.walk([this](Operation *op) {
-          // If we aren't processing top-down, check for existing constants when
-          // populating the worklist. This avoids accidentally reversing the
-          // constant order during processing.
-          Attribute constValue;
-          if (matchPattern(op, m_Constant(&constValue)))
-            if (!folder.insertKnownConstant(op, constValue))
-              return;
-          addToWorklist(op);
+        region.walk([&](Operation *op) {
+          if (!insertKnownConstant(op))
+            addToWorklist(op);
         });
       }
     } else {
       // Add all nested operations to the worklist in preorder.
       for (auto &region : regions)
-        region.walk<WalkOrder::PreOrder>(
-            [this](Operation *op) { worklist.push_back(op); });
+        region.walk<WalkOrder::PreOrder>([&](Operation *op) {
+          if (!insertKnownConstant(op))
+            worklist.push_back(op);
+        });
 
       // Reverse the list so our pop-back loop processes them in-order.
       std::reverse(worklist.begin(), worklist.end());
diff --git a/mlir/test/Dialect/Arithmetic/canonicalize.mlir b/mlir/test/Dialect/Arithmetic/canonicalize.mlir
--- a/mlir/test/Dialect/Arithmetic/canonicalize.mlir
+++ b/mlir/test/Dialect/Arithmetic/canonicalize.mlir
@@ -733,8 +733,8 @@
 // -----
 
 // CHECK-LABEL: test_maxsi
-// CHECK: %[[C0:.+]] = arith.constant 42
-// CHECK: %[[MAX_INT_CST:.+]] = arith.constant 127
+// CHECK-DAG: %[[C0:.+]] = arith.constant 42
+// CHECK-DAG: %[[MAX_INT_CST:.+]] = arith.constant 127
 // CHECK: %[[X:.+]] = arith.maxsi %arg0, %[[C0]]
 // CHECK: return %arg0, %[[MAX_INT_CST]], %arg0, %[[X]]
 func.func @test_maxsi(%arg0 : i8) -> (i8, i8, i8, i8) {
@@ -749,8 +749,8 @@
 }
 
 // CHECK-LABEL: test_maxsi2
-// CHECK: %[[C0:.+]] = arith.constant 42
-// CHECK: %[[MAX_INT_CST:.+]] = arith.constant 127
+// CHECK-DAG: %[[C0:.+]] = arith.constant 42
+// CHECK-DAG: %[[MAX_INT_CST:.+]] = arith.constant 127
 // CHECK: %[[X:.+]] = arith.maxsi %arg0, %[[C0]]
 // CHECK: return %arg0, %[[MAX_INT_CST]], %arg0, %[[X]]
 func.func @test_maxsi2(%arg0 : i8) -> (i8, i8, i8, i8) {
@@ -767,8 +767,8 @@
 // -----
 
 // CHECK-LABEL: test_maxui
-// CHECK: %[[C0:.+]] = arith.constant 42
-// CHECK: %[[MAX_INT_CST:.+]] = arith.constant -1
+// CHECK-DAG: %[[C0:.+]] = arith.constant 42
+// CHECK-DAG: %[[MAX_INT_CST:.+]] = arith.constant -1
 // CHECK: %[[X:.+]] = arith.maxui %arg0, %[[C0]]
 // CHECK: return %arg0, %[[MAX_INT_CST]], %arg0, %[[X]]
 func.func @test_maxui(%arg0 : i8) -> (i8, i8, i8, i8) {
@@ -783,8 +783,8 @@
 }
 
 // CHECK-LABEL: test_maxui
-// CHECK: %[[C0:.+]] = arith.constant 42
-// CHECK: %[[MAX_INT_CST:.+]] = arith.constant -1
+// CHECK-DAG: %[[C0:.+]] = arith.constant 42
+// CHECK-DAG: %[[MAX_INT_CST:.+]] = arith.constant -1
 // CHECK: %[[X:.+]] = arith.maxui %arg0, %[[C0]]
 // CHECK: return %arg0, %[[MAX_INT_CST]], %arg0, %[[X]]
 func.func @test_maxui2(%arg0 : i8) -> (i8, i8, i8, i8) {
@@ -801,8 +801,8 @@
 // -----
 
 // CHECK-LABEL: test_minsi
-// CHECK: %[[C0:.+]] = arith.constant 42
-// CHECK: %[[MIN_INT_CST:.+]] = arith.constant -128
+// CHECK-DAG: %[[C0:.+]] = arith.constant 42
+// CHECK-DAG: %[[MIN_INT_CST:.+]] = arith.constant -128
 // CHECK: %[[X:.+]] = arith.minsi %arg0, %[[C0]]
 // CHECK: return %arg0, %arg0, %[[MIN_INT_CST]], %[[X]]
 func.func @test_minsi(%arg0 : i8) -> (i8, i8, i8, i8) {
@@ -817,8 +817,8 @@
 }
 
 // CHECK-LABEL: test_minsi
-// CHECK: %[[C0:.+]] = arith.constant 42
-// CHECK: %[[MIN_INT_CST:.+]] = arith.constant -128
+// CHECK-DAG: %[[C0:.+]] = arith.constant 42
+// CHECK-DAG: %[[MIN_INT_CST:.+]] = arith.constant -128
 // CHECK: %[[X:.+]] = arith.minsi %arg0, %[[C0]]
 // CHECK: return %arg0, %arg0, %[[MIN_INT_CST]], %[[X]]
 func.func @test_minsi2(%arg0 : i8) -> (i8, i8, i8, i8) {
@@ -835,8 +835,8 @@
 // -----
 
 // CHECK-LABEL: test_minui
-// CHECK: %[[C0:.+]] = arith.constant 42
-// CHECK: %[[MIN_INT_CST:.+]] = arith.constant 0
+// CHECK-DAG: %[[C0:.+]] = arith.constant 42
+// CHECK-DAG: %[[MIN_INT_CST:.+]] = arith.constant 0
 // CHECK: %[[X:.+]] = arith.minui %arg0, %[[C0]]
 // CHECK: return %arg0, %arg0, %[[MIN_INT_CST]], %[[X]]
 func.func @test_minui(%arg0 : i8) -> (i8, i8, i8, i8) {
@@ -851,8 +851,8 @@
 }
 
 // CHECK-LABEL: test_minui
-// CHECK: %[[C0:.+]] = arith.constant 42
-// CHECK: %[[MIN_INT_CST:.+]] = arith.constant 0
+// CHECK-DAG: %[[C0:.+]] = arith.constant 42
+// CHECK-DAG: %[[MIN_INT_CST:.+]] = arith.constant 0
 // CHECK: %[[X:.+]] = arith.minui %arg0, %[[C0]]
 // CHECK: return %arg0, %arg0, %[[MIN_INT_CST]], %[[X]]
 func.func @test_minui2(%arg0 : i8) -> (i8, i8, i8, i8) {
diff --git a/mlir/test/Dialect/SCF/canonicalize.mlir b/mlir/test/Dialect/SCF/canonicalize.mlir
--- a/mlir/test/Dialect/SCF/canonicalize.mlir
+++ b/mlir/test/Dialect/SCF/canonicalize.mlir
@@ -1036,9 +1036,9 @@
   }
   return %0#0, %0#1, %0#2, %0#3, %0#4 : tensor<i32>, tensor<i32>, tensor<i32>, tensor<i32>, tensor<i32>
 }
-// CHECK:    %[[CST42:.*]] = arith.constant dense<42>
-// CHECK:    %[[ONE:.*]] = arith.constant dense<1>
 // CHECK:    %[[ZERO:.*]] = arith.constant dense<0>
+// CHECK:    %[[ONE:.*]] = arith.constant dense<1>
+// CHECK:    %[[CST42:.*]] = arith.constant dense<42>
 // CHECK:    %[[WHILE:.*]]:3 = scf.while (%[[ARG0:.*]] = %[[ZERO]], %[[ARG2:.*]] = %[[ONE]], %[[ARG3:.*]] = %[[ONE]])
 // CHECK:       arith.cmpi slt, %[[ARG0]], %{{.*}}
 // CHECK:       tensor.extract %{{.*}}[]
@@ -1069,9 +1069,9 @@
   }
   return %0#0, %0#1, %0#2, %0#3, %0#4, %0#5 : tensor<i32>, tensor<i32>, tensor<i32>, tensor<i32>, tensor<i32>, tensor<i32>
 }
-// CHECK:    %[[CST42:.*]] = arith.constant dense<42>
-// CHECK:    %[[ONE:.*]] = arith.constant dense<1>
 // CHECK:    %[[ZERO:.*]] = arith.constant dense<0>
+// CHECK:    %[[ONE:.*]] = arith.constant dense<1>
+// CHECK:    %[[CST42:.*]] = arith.constant dense<42>
 // CHECK:    %[[WHILE:.*]]:2 = scf.while (%[[ARG1:.*]] = %[[ONE]], %[[ARG4:.*]] = %[[ZERO]])
 // CHECK:       arith.cmpi slt, %[[ZERO]], %[[CST42]]
 // CHECK:       tensor.extract %{{.*}}[]
diff --git a/mlir/test/Transforms/test-operation-folder.mlir b/mlir/test/Transforms/test-operation-folder.mlir
--- a/mlir/test/Transforms/test-operation-folder.mlir
+++ b/mlir/test/Transforms/test-operation-folder.mlir
@@ -1,4 +1,5 @@
-// RUN: mlir-opt -test-patterns -test-patterns %s | FileCheck %s
+// RUN: mlir-opt -test-patterns='top-down=false' %s | FileCheck %s
+// RUN: mlir-opt -test-patterns='top-down=true' %s | FileCheck %s
 
 func.func @foo() -> i32 {
   %c42 = arith.constant 42 : i32
diff --git a/mlir/test/lib/Dialect/Test/TestPatterns.cpp b/mlir/test/lib/Dialect/Test/TestPatterns.cpp
--- a/mlir/test/lib/Dialect/Test/TestPatterns.cpp
+++ b/mlir/test/lib/Dialect/Test/TestPatterns.cpp
@@ -151,6 +151,9 @@
     : public PassWrapper<TestPatternDriver, OperationPass<func::FuncOp>> {
   MLIR_DEFINE_EXPLICIT_INTERNAL_INLINE_TYPE_ID(TestPatternDriver)
 
+  TestPatternDriver() = default;
+  TestPatternDriver(const TestPatternDriver &other) : PassWrapper(other) {}
+
   StringRef getArgument() const final { return "test-patterns"; }
   StringRef getDescription() const final { return "Run test dialect patterns"; }
   void runOnOperation() override {
@@ -162,8 +165,16 @@
                  FolderInsertBeforePreviouslyFoldedConstantPattern,
                  FolderCommutativeOp2WithConstant>(&getContext());
 
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    GreedyRewriteConfig config;
+    config.useTopDownTraversal = this->useTopDownTraversal;
+    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns),
+                                       config);
   }
+
+  Option<bool> useTopDownTraversal{
+      *this, "top-down",
+      llvm::cl::desc("Seed the worklist in general top-down order"),
+      llvm::cl::init(false)};
 };
 } // namespace