diff --git a/mlir/lib/Dialect/Affine/IR/AffineOps.cpp b/mlir/lib/Dialect/Affine/IR/AffineOps.cpp
--- a/mlir/lib/Dialect/Affine/IR/AffineOps.cpp
+++ b/mlir/lib/Dialect/Affine/IR/AffineOps.cpp
@@ -2538,6 +2538,20 @@
   }
 };
 
+template <typename T>
+struct CanonicalizeSingleResultAffineMinMaxOp : public OpRewritePattern<T> {
+  using OpRewritePattern<T>::OpRewritePattern;
+
+  LogicalResult matchAndRewrite(T affineOp,
+                                PatternRewriter &rewriter) const override {
+    if (affineOp.map().getNumResults() != 1)
+      return failure();
+    rewriter.replaceOpWithNewOp<AffineApplyOp>(affineOp, affineOp.map(),
+                                               affineOp.getOperands());
+    return success();
+  }
+};
+
 //===----------------------------------------------------------------------===//
 // AffineMinOp
 //===----------------------------------------------------------------------===//
@@ -2551,7 +2565,8 @@
 
 void AffineMinOp::getCanonicalizationPatterns(RewritePatternSet &patterns,
                                               MLIRContext *context) {
-  patterns.add<DeduplicateAffineMinMaxExpressions<AffineMinOp>,
+  patterns.add<CanonicalizeSingleResultAffineMinMaxOp<AffineMinOp>,
+               DeduplicateAffineMinMaxExpressions<AffineMinOp>,
                MergeAffineMinMaxOp<AffineMinOp>, SimplifyAffineOp<AffineMinOp>>(
       context);
 }
@@ -2569,7 +2584,8 @@
 
 void AffineMaxOp::getCanonicalizationPatterns(RewritePatternSet &patterns,
                                               MLIRContext *context) {
-  patterns.add<DeduplicateAffineMinMaxExpressions<AffineMaxOp>,
+  patterns.add<CanonicalizeSingleResultAffineMinMaxOp<AffineMaxOp>,
+               DeduplicateAffineMinMaxExpressions<AffineMaxOp>,
                MergeAffineMinMaxOp<AffineMaxOp>, SimplifyAffineOp<AffineMaxOp>>(
       context);
 }
diff --git a/mlir/test/Dialect/Affine/canonicalize.mlir b/mlir/test/Dialect/Affine/canonicalize.mlir
--- a/mlir/test/Dialect/Affine/canonicalize.mlir
+++ b/mlir/test/Dialect/Affine/canonicalize.mlir
@@ -870,7 +870,6 @@
   return %1: index
 }
 
-
 // -----
 
 // CHECK-LABEL: func @dont_merge_affine_max_if_not_single_sym
@@ -936,3 +935,21 @@
   return
 }
 
+// -----
+
+// CHECK-DAG: #[[$MAP0:.+]] = affine_map<()[s0] -> (s0 + 16)>
+// CHECK-DAG: #[[$MAP1:.+]] = affine_map<()[s0] -> (s0 * 4)>
+
+// CHECK: func @canonicalize_single_min_max
+// CHECK-SAME: (%[[I0:.+]]: index, %[[I1:.+]]: index)
+func @canonicalize_single_min_max(%i0: index, %i1: index) -> (index, index) {
+  // CHECK-NOT: affine.min
+  // CHECK-NEXT: affine.apply #[[$MAP0]]()[%[[I0]]]
+  %0 = affine.min affine_map<()[s0] -> (s0 + 16)> ()[%i0]
+
+  // CHECK-NOT: affine.max
+  // CHECK-NEXT: affine.apply #[[$MAP1]]()[%[[I1]]]
+  %1 = affine.min affine_map<()[s0] -> (s0 * 4)> ()[%i1]
+
+  return %0, %1: index, index
+}