diff --git a/mlir/lib/Conversion/SCFToGPU/SCFToGPU.cpp b/mlir/lib/Conversion/SCFToGPU/SCFToGPU.cpp
--- a/mlir/lib/Conversion/SCFToGPU/SCFToGPU.cpp
+++ b/mlir/lib/Conversion/SCFToGPU/SCFToGPU.cpp
@@ -328,6 +328,13 @@
     }
   }
 
+  if (auto minOp = upperBound.getDefiningOp<arith::MinSIOp>()) {
+    for (Value operand : {minOp.getLhs(), minOp.getRhs()}) {
+      if (auto staticBound = deriveStaticUpperBound(operand, rewriter))
+        return staticBound;
+    }
+  }
+
   if (auto multiplyOp = upperBound.getDefiningOp<arith::MulIOp>()) {
     if (auto lhs = dyn_cast_or_null<arith::ConstantIndexOp>(
             deriveStaticUpperBound(multiplyOp.getOperand(0), rewriter)
@@ -336,8 +343,8 @@
               deriveStaticUpperBound(multiplyOp.getOperand(1), rewriter)
                   .getDefiningOp())) {
         // Assumptions about the upper bound of minimum computations no longer
-        // work if multiplied by a negative value, so abort in this case.
-        if (lhs.value() < 0 || rhs.value() < 0)
+        // work if multiplied by mixed signs, so abort in this case.
+        if (lhs.value() < 0 != rhs.value() < 0)
           return {};
 
         return rewriter.create<arith::ConstantIndexOp>(
diff --git a/mlir/test/Conversion/SCFToGPU/parallel_loop.mlir b/mlir/test/Conversion/SCFToGPU/parallel_loop.mlir
--- a/mlir/test/Conversion/SCFToGPU/parallel_loop.mlir
+++ b/mlir/test/Conversion/SCFToGPU/parallel_loop.mlir
@@ -215,7 +215,8 @@
       %3 = affine.min #map1(%arg3)[%2]
       %squared_min = arith.muli %3, %3 : index
       %4 = memref.dim %arg0, %c1 : memref<?x?xf32, #map0>
-      %5 = affine.min #map2(%arg4)[%4]
+      %d = arith.subi %4, %arg4 : index
+      %5 = arith.minsi %c3, %d : index
       %6 = memref.subview %arg0[%arg3, %arg4][%squared_min, %5][%c1, %c1] : memref<?x?xf32, #map0> to memref<?x?xf32, #map3>
       %7 = memref.dim %arg1, %c0 : memref<?x?xf32, #map0>
       %8 = affine.min #map1(%arg3)[%7]
@@ -241,12 +242,12 @@
   }
 }
 
-// CHECK:       #[[$MAP0:.*]] = affine_map<(d0, d1)[s0, s1] -> (d0 * s1 + s0 + d1)>
-// CHECK:       #[[$MAP1:.*]] = affine_map<(d0)[s0, s1] -> ((d0 - s0) ceildiv s1)>
-// CHECK:       #[[$MAP2:.*]] = affine_map<(d0)[s0, s1] -> (d0 * s0 + s1)>
-// CHECK:       #[[$MAP3:.*]] = affine_map<(d0)[s0] -> (2, -d0 + s0)>
-// CHECK:       #[[$MAP4:.*]] = affine_map<(d0)[s0] -> (3, -d0 + s0)>
-// CHECK:       #[[$MAP5:.*]] = affine_map<(d0, d1)[s0, s1, s2] -> (d0 * s1 + s0 + d1 * s2)>
+// CHECK-DAG:       #[[$MAP0:.*]] = affine_map<(d0, d1)[s0, s1] -> (d0 * s1 + s0 + d1)>
+// CHECK-DAG:       #[[$MAP1:.*]] = affine_map<(d0)[s0, s1] -> ((d0 - s0) ceildiv s1)>
+// CHECK-DAG:       #[[$MAP2:.*]] = affine_map<(d0)[s0, s1] -> (d0 * s0 + s1)>
+// CHECK-DAG:       #[[$MAP3:.*]] = affine_map<(d0)[s0] -> (2, -d0 + s0)>
+// CHECK-DAG:       #[[$MAP4:.*]] = affine_map<(d0)[s0] -> (3, -d0 + s0)>
+// CHECK-DAG:       #[[$MAP5:.*]] = affine_map<(d0, d1)[s0, s1, s2] -> (d0 * s1 + s0 + d1 * s2)>
 
 // CHECK:       module {
 // CHECK-LABEL:   func @sum(
@@ -262,8 +263,7 @@
 // CHECK:           [[VAL_11:%.*]] = affine.apply #[[$MAP1]]([[VAL_8]]){{\[}}%[[C0]], %[[C3]]]
 // CHECK:           [[VAL_12:%.*]] = arith.constant 4 : index
 // CHECK:           [[VAL_13:%.*]] = affine.apply #[[$MAP1]]([[VAL_12]]){{\[}}%[[C0]], %[[C1]]]
-// CHECK:           [[VAL_14:%.*]] = arith.constant 3 : index
-// CHECK:           [[VAL_15:%.*]] = affine.apply #[[$MAP1]]([[VAL_14]]){{\[}}%[[C0]], %[[C1]]]
+// CHECK:           [[VAL_15:%.*]] = affine.apply #[[$MAP1]](%[[C3]]){{\[}}%[[C0]], %[[C1]]]
 // CHECK:           gpu.launch blocks([[VAL_16:%.*]], [[VAL_17:%.*]], [[VAL_18:%.*]]) in ([[VAL_19:%.*]] = [[VAL_10]], [[VAL_20:%.*]] = [[VAL_11]], [[VAL_21:%.*]] = [[VAL_9]]) threads([[VAL_22:%.*]], [[VAL_23:%.*]], [[VAL_24:%.*]]) in ([[VAL_25:%.*]] = [[VAL_13]], [[VAL_26:%.*]] = [[VAL_15]], [[VAL_27:%.*]] = [[VAL_9]]) {
 // CHECK:             [[VAL_28:%.*]] = affine.apply #[[$MAP2]]([[VAL_16]]){{\[}}%[[C2]], %[[C0]]]
 // CHECK:             [[VAL_29:%.*]] = affine.apply #[[$MAP2]]([[VAL_17]]){{\[}}%[[C3]], %[[C0]]]
@@ -271,7 +271,8 @@
 // CHECK:             [[VAL_31:%.*]] = affine.min #[[$MAP3]]([[VAL_28]]){{\[}}[[VAL_30]]]
 // CHECK:             [[VAL_31_SQUARED:%.*]] = arith.muli [[VAL_31]], [[VAL_31]] : index
 // CHECK:             [[VAL_32:%.*]] = memref.dim [[VAL_0]], %[[C1]] : memref<?x?xf32, #[[$MAP0]]>
-// CHECK:             [[VAL_33:%.*]] = affine.min #[[$MAP4]]([[VAL_29]]){{\[}}[[VAL_32]]]
+// CHECK:             [[VAL_D:%.*]] = arith.subi [[VAL_32]], [[VAL_29]] : index
+// CHECK:             [[VAL_33:%.*]] = arith.minsi %[[C3]], [[VAL_D]] : index
 // CHECK:             [[VAL_34:%.*]] = memref.subview [[VAL_0]]{{\[}}[[VAL_28]], [[VAL_29]]] {{\[}}[[VAL_31_SQUARED]], [[VAL_33]]] {{\[}}%[[C1]], %[[C1]]] : memref<?x?xf32, #[[$MAP0]]> to memref<?x?xf32, #[[$MAP5]]>
 // CHECK:             [[VAL_35:%.*]] = memref.dim [[VAL_1]], %[[C0]] : memref<?x?xf32, #[[$MAP0]]>
 // CHECK:             [[VAL_36:%.*]] = affine.min #[[$MAP3]]([[VAL_28]]){{\[}}[[VAL_35]]]