diff --git a/mlir/lib/Dialect/Affine/Utils/Utils.cpp b/mlir/lib/Dialect/Affine/Utils/Utils.cpp
--- a/mlir/lib/Dialect/Affine/Utils/Utils.cpp
+++ b/mlir/lib/Dialect/Affine/Utils/Utils.cpp
@@ -564,31 +564,37 @@
   OpBuilder opBuilder(op);
   int64_t origLoopStep = op.getStep();
 
-  // Calculate upperBound for normalized loop.
-  SmallVector<Value, 4> ubOperands;
   AffineBound lb = op.getLowerBound();
+  AffineMap originalLbMap = lb.getMap();
+  SmallVector<Value, 4> origLbOperands;
+  llvm::append_range(origLbOperands, lb.getOperands());
+
   AffineBound ub = op.getUpperBound();
+  AffineMap originalUbMap = ub.getMap();
+  SmallVector<Value, 4> origUbOperands;
+  llvm::append_range(origUbOperands, ub.getOperands());
+
+  // Calculate upperBound for normalized loop.
+  SmallVector<Value, 4> ubOperands;
   ubOperands.reserve(ub.getNumOperands() + lb.getNumOperands());
-  AffineMap origLbMap = lb.getMap();
-  AffineMap origUbMap = ub.getMap();
 
   // Add dimension operands from upper/lower bound.
-  for (unsigned j = 0, e = origUbMap.getNumDims(); j < e; ++j)
+  for (unsigned j = 0, e = originalUbMap.getNumDims(); j < e; ++j)
     ubOperands.push_back(ub.getOperand(j));
-  for (unsigned j = 0, e = origLbMap.getNumDims(); j < e; ++j)
+  for (unsigned j = 0, e = originalLbMap.getNumDims(); j < e; ++j)
     ubOperands.push_back(lb.getOperand(j));
 
   // Add symbol operands from upper/lower bound.
-  for (unsigned j = 0, e = origUbMap.getNumSymbols(); j < e; ++j)
-    ubOperands.push_back(ub.getOperand(origUbMap.getNumDims() + j));
-  for (unsigned j = 0, e = origLbMap.getNumSymbols(); j < e; ++j)
-    ubOperands.push_back(lb.getOperand(origLbMap.getNumDims() + j));
+  for (unsigned j = 0, e = originalUbMap.getNumSymbols(); j < e; ++j)
+    ubOperands.push_back(ub.getOperand(originalUbMap.getNumDims() + j));
+  for (unsigned j = 0, e = originalLbMap.getNumSymbols(); j < e; ++j)
+    ubOperands.push_back(lb.getOperand(originalLbMap.getNumDims() + j));
 
   // Add original result expressions from lower/upper bound map.
-  SmallVector<AffineExpr, 1> origLbExprs(origLbMap.getResults().begin(),
-                                         origLbMap.getResults().end());
-  SmallVector<AffineExpr, 2> origUbExprs(origUbMap.getResults().begin(),
-                                         origUbMap.getResults().end());
+  SmallVector<AffineExpr, 1> origLbExprs(originalLbMap.getResults().begin(),
+                                         originalLbMap.getResults().end());
+  SmallVector<AffineExpr, 2> origUbExprs(originalUbMap.getResults().begin(),
+                                         originalUbMap.getResults().end());
   SmallVector<AffineExpr, 4> newUbExprs;
 
   // The original upperBound can have more than one result. For the new
@@ -607,15 +613,15 @@
   }
 
   // Construct newUbMap.
-  AffineMap newUbMap =
-      AffineMap::get(origLbMap.getNumDims() + origUbMap.getNumDims(),
-                     origLbMap.getNumSymbols() + origUbMap.getNumSymbols(),
-                     newUbExprs, opBuilder.getContext());
+  AffineMap newUbMap = AffineMap::get(
+      originalLbMap.getNumDims() + originalUbMap.getNumDims(),
+      originalLbMap.getNumSymbols() + originalUbMap.getNumSymbols(), newUbExprs,
+      opBuilder.getContext());
   canonicalizeMapAndOperands(&newUbMap, &ubOperands);
 
   SmallVector<Value, 4> lbOperands(lb.getOperands().begin(),
                                    lb.getOperands().begin() +
-                                       lb.getMap().getNumDims());
+                                       originalLbMap.getNumDims());
 
   // Normalize the loop.
   op.setUpperBound(ubOperands, newUbMap);
@@ -628,13 +634,14 @@
   // Add an extra dim operand for loopIV.
   lbOperands.push_back(op.getInductionVar());
   // Add symbol operands from lower bound.
-  for (unsigned j = 0, e = origLbMap.getNumSymbols(); j < e; ++j)
-    lbOperands.push_back(lb.getOperand(origLbMap.getNumDims() + j));
-
-  AffineExpr origIVExpr = opBuilder.getAffineDimExpr(lb.getMap().getNumDims());
-  AffineExpr newIVExpr = origIVExpr * origLoopStep + origLbMap.getResult(0);
-  AffineMap ivMap = AffineMap::get(origLbMap.getNumDims() + 1,
-                                   origLbMap.getNumSymbols(), newIVExpr);
+  for (unsigned j = 0, e = originalLbMap.getNumSymbols(); j < e; ++j)
+    lbOperands.push_back(origLbOperands[originalLbMap.getNumDims() + j]);
+
+  AffineExpr origIVExpr =
+      opBuilder.getAffineDimExpr(originalLbMap.getNumDims());
+  AffineExpr newIVExpr = origIVExpr * origLoopStep + originalLbMap.getResult(0);
+  AffineMap ivMap = AffineMap::get(originalLbMap.getNumDims() + 1,
+                                   originalLbMap.getNumSymbols(), newIVExpr);
   canonicalizeMapAndOperands(&ivMap, &lbOperands);
   Operation *newIV = opBuilder.create<AffineApplyOp>(loc, ivMap, lbOperands);
   op.getInductionVar().replaceAllUsesExcept(newIV->getResult(0), newIV);
diff --git a/mlir/test/Dialect/Affine/affine-loop-normalize.mlir b/mlir/test/Dialect/Affine/affine-loop-normalize.mlir
--- a/mlir/test/Dialect/Affine/affine-loop-normalize.mlir
+++ b/mlir/test/Dialect/Affine/affine-loop-normalize.mlir
@@ -213,3 +213,82 @@
   }
   return
 }
+
+// -----
+
+// CHECK-LABEL: func @constant_lower_bound
+func.func @constant_lower_bound() {
+  %c0 = arith.constant 0 : index
+  %c1 = arith.constant 1 : index
+  scf.for %j = %c0 to %c1 step %c1 {
+    // CHECK: affine.for %[[ARG0:.*]] =
+    affine.for %i = %c0 to %c1 {
+      // CHECK-NEXT: %{{.*}} = affine.apply #map{{.*}}(%[[ARG0]])
+    }
+  }
+  return
+}
+
+// -----
+
+// CHECK-DAG: [[$UB_MAP:#map[0-9]*]] = affine_map<()[s0] -> (s0 ceildiv 4)>
+// CHECK-DAG: [[$IV_MAP:#map[0-9]*]] = affine_map<(d0) -> (d0 * 4)>
+
+// CHECK-LABEL: func @upper_bound_by_symbol
+func.func @upper_bound_by_symbol(%arg0: index, %arg1: index) {
+  // CHECK: affine.for %[[ARG0:.*]] = 0 to [[$UB_MAP]]()[%arg{{.*}}] {
+  affine.for %i = 0 to affine_map<()[s0, s1] -> (s0)>()[%arg0, %arg1] step 4 {
+    // CHECK-NEXT: %[[IV:.*]] = affine.apply [[$IV_MAP]](%[[ARG0]])
+    // CHECK-NEXT: "test.foo"(%[[IV]]) : (index) -> ()
+    "test.foo"(%i) : (index) -> ()
+  }
+  return
+}
+
+// -----
+
+// CHECK-DAG: [[$UB_MAP:#map[0-9]*]] = affine_map<()[s0] -> ((-s0 + 10) ceildiv 4)>
+// CHECK-DAG: [[$IV_MAP:#map[0-9]*]] = affine_map<(d0)[s0] -> (d0 * 4 + s0)>
+
+// CHECK-LABEL: func @lower_bound_by_symbol
+func.func @lower_bound_by_symbol(%arg0: index, %arg1: index) {
+  // CHECK: affine.for %[[ARG0:.*]] = 0 to [[$UB_MAP]]()[%arg{{.*}}] {
+  affine.for %i = affine_map<()[s0, s1] -> (s0)>()[%arg0, %arg1] to 10 step 4 {
+    // CHECK-NEXT: %[[IV:.*]] = affine.apply [[$IV_MAP]](%[[ARG0]])[%arg{{.*}}]
+    // CHECK-NEXT: "test.foo"(%[[IV]]) : (index) -> ()
+    "test.foo"(%i) : (index) -> ()
+  }
+  return
+}
+
+// -----
+
+// CHECK-DAG: [[$UB_MAP:#map[0-9]*]] = affine_map<()[s0] -> (s0 ceildiv 4)>
+// CHECK-DAG: [[$IV_MAP:#map[0-9]*]] = affine_map<(d0) -> (d0 * 4)>
+
+// CHECK-LABEL: func @upper_bound_by_dim
+func.func @upper_bound_by_dim(%arg0: index, %arg1: index) {
+  // CHECK: affine.for %[[ARG0:.*]] = 0 to [[$UB_MAP]]()[%arg{{.*}}] {
+  affine.for %i = 0 to affine_map<(d0, d1) -> (d0)>(%arg0, %arg1) step 4 {
+    // CHECK-NEXT: %[[IV:.*]] = affine.apply [[$IV_MAP]](%[[ARG0]])
+    // CHECK-NEXT: "test.foo"(%[[IV]]) : (index) -> ()
+    "test.foo"(%i) : (index) -> ()
+  }
+  return
+}
+
+// -----
+
+// CHECK-DAG: [[$UB_MAP:#map[0-9]*]] = affine_map<()[s0] -> ((-s0 + 10) ceildiv 4)>
+// CHECK-DAG: [[$IV_MAP:#map[0-9]*]] = affine_map<(d0)[s0] -> (d0 * 4 + s0)>
+
+// CHECK-LABEL: func @upper_bound_by_dim
+func.func @upper_bound_by_dim(%arg0: index, %arg1: index) {
+  // CHECK: affine.for %[[ARG0:.*]] = 0 to [[$UB_MAP]]()[%arg{{.*}}] {
+  affine.for %i = affine_map<(d0, d1) -> (d0)>(%arg0, %arg1) to 10 step 4 {
+    // CHECK-NEXT: %[[IV:.*]] = affine.apply [[$IV_MAP]](%[[ARG0]])[%arg{{.*}}]
+    // CHECK-NEXT: "test.foo"(%[[IV]]) : (index) -> ()
+    "test.foo"(%i) : (index) -> ()
+  }
+  return
+}