diff --git a/mlir/include/mlir/IR/AffineMap.h b/mlir/include/mlir/IR/AffineMap.h
--- a/mlir/include/mlir/IR/AffineMap.h
+++ b/mlir/include/mlir/IR/AffineMap.h
@@ -464,6 +464,18 @@
 /// ```mlir
 ///    affine_map<(d0) -> (0, 0, d0, 0)>
 /// ```
+/// Example 4:
+///
+/// ```mlir
+///    affine_map<(d0, d1, d2) -> (d0, 0)>
+/// ```
+///
+/// returns:
+///
+/// ```mlir
+///    affine_map<(d0, d1) -> (d0, 0, 0)>
+/// ```
+
 AffineMap inverseAndBroadcastProjectedPermuation(AffineMap map);
 
 /// Concatenates a list of `maps` into a single AffineMap, stepping over
diff --git a/mlir/lib/IR/AffineMap.cpp b/mlir/lib/IR/AffineMap.cpp
--- a/mlir/lib/IR/AffineMap.cpp
+++ b/mlir/lib/IR/AffineMap.cpp
@@ -498,17 +498,30 @@
 bool AffineMap::isProjectedPermutation() const {
   if (getNumSymbols() > 0)
     return false;
+
   SmallVector<bool, 8> seen(getNumInputs(), false);
+  unsigned numValidResults = 0;
+  // A projected permutation can have, at most, only one instance of each input
+  // dimension in the result expressions. Zeros are allowed as long as the total
+  // number of result expressions is lower or equal than the number of input
+  // expressions.
   for (auto expr : getResults()) {
     if (auto dim = expr.dyn_cast<AffineDimExpr>()) {
       if (seen[dim.getPosition()])
         return false;
       seen[dim.getPosition()] = true;
-      continue;
+      ++numValidResults;
+    } else if (auto constExpr = expr.dyn_cast<AffineConstantExpr>()) {
+      if (constExpr.getValue() != 0)
+        return false;
+      ++numValidResults;
+    } else {
+      // Neither dim nor zero.
+      return false;
     }
-    return false;
   }
-  return true;
+
+  return numValidResults <= getNumInputs();
 }
 
 bool AffineMap::isPermutation() const {
@@ -702,7 +715,15 @@
   // Start with all the results as 0.
   SmallVector<AffineExpr, 4> exprs(map.getNumInputs(), zero);
   for (unsigned i : llvm::seq(unsigned(0), map.getNumResults())) {
-    // Reverse each dimension existing in the oringal map result.
+    // Skip zeros from input map. 'exprs' is already initialized to zero.
+    if (auto constExpr = map.getResult(i).dyn_cast<AffineConstantExpr>()) {
+      assert(constExpr.getValue() == 0 &&
+             "Unexpected constant in projected permutation");
+      (void)constExpr;
+      continue;
+    }
+
+    // Reverse each dimension existing in the original map result.
     exprs[map.getDimPosition(i)] = getAffineDimExpr(i, context);
   }
   return AffineMap::get(map.getNumResults(), /*symbolCount=*/0, exprs, context);
diff --git a/mlir/test/Dialect/Linalg/vectorization.mlir b/mlir/test/Dialect/Linalg/vectorization.mlir
--- a/mlir/test/Dialect/Linalg/vectorization.mlir
+++ b/mlir/test/Dialect/Linalg/vectorization.mlir
@@ -857,3 +857,61 @@
   return %red : tensor<4xf32>
 }
 
+// -----
+
+// CHECK-DAG: #[[$M5:.*]] = affine_map<(d0, d1) -> (d0, 0)>
+
+// CHECK-LABEL:   func @explicit_broadcast(
+func @explicit_broadcast(%arg0: tensor<4x4xf32>, %arg1: tensor<4x1xf32>) -> tensor<4x4xf32> {
+  // CHECK: vector.transfer_read {{.*}} {in_bounds = [true, true]} : tensor<4x4xf32>, vector<4x4xf32>
+  // CHECK: vector.transfer_read {{.*}} {in_bounds = [true, true], permutation_map = #[[$M5]]} : tensor<4x1xf32>, vector<4x4xf32>
+  // CHECK: subf {{.*}} : vector<4x4xf32>
+  // CHECK: vector.transfer_write {{.*}} {in_bounds = [true, true]} : vector<4x4xf32>, tensor<4x4xf32>
+  %c0 = constant 0.0 : f32
+  %init = linalg.init_tensor [4, 4] : tensor<4x4xf32>
+  %fill = linalg.fill(%c0, %init) : f32, tensor<4x4xf32> -> tensor<4x4xf32>
+  %red = linalg.generic {indexing_maps = [affine_map<(d0, d1) -> (d0, d1)>,
+                                          affine_map<(d0, d1) -> (d0, 0)>,
+                                          affine_map<(d0, d1) -> (d0, d1)>],
+   iterator_types = ["parallel", "parallel"]}
+   ins(%arg0, %arg1 : tensor<4x4xf32>, tensor<4x1xf32>)
+   outs(%fill : tensor<4x4xf32>) {
+    ^bb0(%arg7: f32, %arg8: f32, %arg9: f32):
+      %40 = subf %arg7, %arg8 : f32
+      linalg.yield %40 : f32
+    } -> tensor<4x4xf32>
+  return %red : tensor<4x4xf32>
+}
+
+// -----
+
+// CHECK-DAG: #[[$M6:.*]] = affine_map<(d0, d1) -> (d0, 0)>
+// CHECK-DAG: #[[$M7:.*]] = affine_map<(d0) -> (d0, 0)>
+
+// CHECK-LABEL:   func @fused_broadcast_red_2d
+func @fused_broadcast_red_2d(%arg0: tensor<4x4xf32>, %arg1: tensor<4x1xf32>) -> tensor<4xf32> {
+  // CHECK: vector.transfer_read {{.*}} {in_bounds = [true, true]} : tensor<4x4xf32>, vector<4x4xf32>
+  // CHECK: vector.transfer_read {{.*}} {in_bounds = [true, true], permutation_map = #[[$M6]]} : tensor<4x1xf32>, vector<4x4xf32>
+  // CHECK: vector.transfer_read {{.*}} {in_bounds = [true, true], permutation_map = #[[$M7]]} : tensor<4xf32>, vector<4x4xf32>
+  // CHECK: subf {{.*}} : vector<4x4xf32>
+  // CHECK: math.exp {{.*}} : vector<4x4xf32>
+  // CHECK: addf {{.*}} : vector<4x4xf32>
+  // CHECK: vector.multi_reduction #vector.kind<add>, {{.*}} : vector<4x4xf32> to vector<4xf32>
+  // CHECK: vector.transfer_write {{.*}} {in_bounds = [true]} : vector<4xf32>, tensor<4xf32>
+  %c0 = constant 0.0 : f32
+  %init = linalg.init_tensor [4] : tensor<4xf32>
+  %fill = linalg.fill(%c0, %init) : f32, tensor<4xf32> -> tensor<4xf32>
+  %red = linalg.generic {indexing_maps = [affine_map<(d0, d1) -> (d0, d1)>,
+                                          affine_map<(d0, d1) -> (d0, 0)>,
+                                          affine_map<(d0, d1) -> (d0)>],
+   iterator_types = ["parallel", "reduction"]}
+   ins(%arg0, %arg1 : tensor<4x4xf32>, tensor<4x1xf32>)
+   outs(%fill : tensor<4xf32>) {
+    ^bb0(%arg7: f32, %arg8: f32, %arg9: f32):
+      %40 = subf %arg7, %arg8 : f32
+      %41 = math.exp %40 : f32
+      %42 = addf %41, %arg9 : f32
+      linalg.yield %42 : f32
+    } -> tensor<4xf32>
+  return %red : tensor<4xf32>
+}