diff --git a/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp b/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
--- a/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
+++ b/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
@@ -361,11 +361,10 @@
       if (!cst || cst.getValue() != 0)
         return op.emitOpError("expected indexing_map #")
                << idx << " to be 0 to match 0-D view: " << view;
-    }
-
-    if (m.getNumResults() != view.getRank())
+    } else if (m.getNumResults() != view.getRank()) {
       return op.emitOpError("expected indexing_map #")
              << idx << " results to match view rank: " << view;
+    }
   }
 
   auto concatMap = concatAffineMaps(indexingMaps);
diff --git a/mlir/lib/Dialect/Linalg/Transforms/LinalgToLoops.cpp b/mlir/lib/Dialect/Linalg/Transforms/LinalgToLoops.cpp
--- a/mlir/lib/Dialect/Linalg/Transforms/LinalgToLoops.cpp
+++ b/mlir/lib/Dialect/Linalg/Transforms/LinalgToLoops.cpp
@@ -238,9 +238,14 @@
 
     // 1.a. Emit std_load from input views.
     for (unsigned i = 0; i < nInputs; ++i) {
-      ValueHandleArray indexing(makeCanonicalAffineApplies(
-          b, loc, genericOp.getInputIndexingMap(i), allIvs));
-      indexedValues[i] = std_load(genericOp.getInput(i), indexing);
+      Value input = genericOp.getInput(i);
+      if (!input.getType().cast<ShapedType>().getRank()) {
+        indexedValues[i] = std_load(input);
+      } else {
+        ValueHandleArray indexing(makeCanonicalAffineApplies(
+            b, loc, genericOp.getInputIndexingMap(i), allIvs));
+        indexedValues[i] = std_load(input, indexing);
+      }
     }
 
     // 1.b. Emit std_load from output views.
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
@@ -351,12 +351,12 @@
 AffineMap mlir::concatAffineMaps(ArrayRef<AffineMap> maps) {
   unsigned numResults = 0;
   for (auto m : maps)
-    numResults += m ? m.getNumResults() : 0;
+    numResults += (m && !m.isSingleConstant()) ? m.getNumResults() : 0;
   unsigned numDims = 0;
   SmallVector<AffineExpr, 8> results;
   results.reserve(numResults);
   for (auto m : maps) {
-    if (!m)
+    if (!m || m.isSingleConstant())
       continue;
     assert(m.getNumSymbols() == 0 && "expected map without symbols");
     results.append(m.getResults().begin(), m.getResults().end());
diff --git a/mlir/test/Dialect/Linalg/loops.mlir b/mlir/test/Dialect/Linalg/loops.mlir
--- a/mlir/test/Dialect/Linalg/loops.mlir
+++ b/mlir/test/Dialect/Linalg/loops.mlir
@@ -356,3 +356,36 @@
 // CHECK:       %[[result_2:.*]] = addf %[[c]], %[[ijk_float]] : f32
 // CHECK:       store %[[result_1]], %{{.*}}[%[[i]], %[[j]], %[[k]]]
 // CHECK:       store %[[result_2]], %{{.*}}[%[[i]], %[[k]], %[[j]]]
+
+// -----
+
+
+#broadcast_access = [
+  affine_map<(i, j) -> (0)>,
+  affine_map<(i,j) -> (i,j)>
+]
+
+#trait_broadcast = {
+  args_in = 1,
+  args_out = 1,
+  indexing_maps = #broadcast_access,
+  iterator_types = ["parallel", "parallel"],
+  library_call = "some_broadcast_external_fn"
+}
+
+func @generic_op_zero_rank(%arg0 : memref<f32>, %arg1:  memref<3x4xf32>)
+{
+  linalg.generic #trait_broadcast %arg0, %arg1 {
+    ^bb(%a: f32, %b : f32) :
+      linalg.yield %a : f32
+  } : memref<f32>, memref<3x4xf32>
+  return
+}
+
+// CHECK-LABEL: @generic_op_zero_rank
+// CHECK-SAME: %[[ARG0:[a-zA-Z0-9_]*]]: memref<f32>
+// CHECK-SAME: %[[ARG1:[a-zA-Z0-9_]*]]: memref<3x4xf32>
+// CHECK: loop.for %[[i:.*]] = {{.*}}
+// CHECK:   loop.for %[[j:.*]] = {{.*}}
+// CHECK:     %[[a:.*]] = load %[[ARG0]][]
+// CHECK:     store %[[a]], %[[ARG1]][%[[i]], %[[j]]]
diff --git a/mlir/test/Dialect/Linalg/roundtrip.mlir b/mlir/test/Dialect/Linalg/roundtrip.mlir
--- a/mlir/test/Dialect/Linalg/roundtrip.mlir
+++ b/mlir/test/Dialect/Linalg/roundtrip.mlir
@@ -345,6 +345,30 @@
 
 // -----
 
+#broadcast_access = [
+  affine_map<(i, j) -> (0)>,
+  affine_map<(i,j) -> (i,j)>
+]
+
+#trait_broadcast = {
+  args_in = 1,
+  args_out = 1,
+  indexing_maps = #broadcast_access,
+  iterator_types = ["parallel", "parallel"],
+  library_call = "some_broadcast_external_fn"
+}
+
+func @generic_op_zero_rank(%arg0 : tensor<f32>) ->  (tensor<3x4xf32>)
+{
+  %0 = linalg.generic #trait_broadcast %arg0 {
+    ^bb(%a: f32) :
+      linalg.yield %a : f32
+  } : tensor<f32> -> tensor<3x4xf32>
+  return %0 : tensor<3x4xf32>
+}
+
+// -----
+
 // CHECK-DAG: #[[strided2D:.*]] = affine_map<(d0, d1)[s0, s1] -> (d0 * s1 + s0 + d1)>
 // CHECK-DAG: #[[strided3D:.*]] = affine_map<(d0, d1, d2)[s0, s1, s2] -> (d0 * s1 + s0 + d1 * s2 + d2)>