diff --git a/mlir/lib/Dialect/Shape/IR/Shape.cpp b/mlir/lib/Dialect/Shape/IR/Shape.cpp
--- a/mlir/lib/Dialect/Shape/IR/Shape.cpp
+++ b/mlir/lib/Dialect/Shape/IR/Shape.cpp
@@ -450,34 +450,47 @@
 //===----------------------------------------------------------------------===//
 
 OpFoldResult BroadcastOp::fold(ArrayRef<Attribute> operands) {
-  if (operands.size() == 1)
+  if (shapes().size() == 1)
     return shapes().front();
 
+  // If all but one of the operands are known to be empty shapes, return the
+  // remaining shape.
+  Value onlyPotentiallyNonEmptyShape;
+  Value value;
+  Attribute constOperand;
+  for (auto it : llvm::zip(shapes(), operands)) {
+    std::tie(value, constOperand) = it;
+    if (!constOperand || constOperand.cast<DenseIntElementsAttr>().size() > 0) {
+      if (!onlyPotentiallyNonEmptyShape) {
+        onlyPotentiallyNonEmptyShape = value;
+      } else {
+        onlyPotentiallyNonEmptyShape = nullptr;
+        break;
+      }
+    }
+  }
+  if (onlyPotentiallyNonEmptyShape &&
+      onlyPotentiallyNonEmptyShape.getType().isa<ShapeType>() ==
+          getType().isa<ShapeType>())
+    return onlyPotentiallyNonEmptyShape;
+
   // TODO: Support folding with more than 2 input shapes
   if (shapes().size() > 2)
     return nullptr;
 
-  if (!operands[1])
-    return nullptr;
-
-  auto rhsShape = llvm::to_vector<6>(
-      operands[1].cast<DenseIntElementsAttr>().getValues<int64_t>());
-  if (rhsShape.empty())
-    return shapes()[0];
-
-  if (!operands[0])
+  if (!operands[0] || !operands[1])
     return nullptr;
-
   auto lhsShape = llvm::to_vector<6>(
       operands[0].cast<DenseIntElementsAttr>().getValues<int64_t>());
-  if (lhsShape.empty())
-    return shapes()[1];
-
+  auto rhsShape = llvm::to_vector<6>(
+      operands[1].cast<DenseIntElementsAttr>().getValues<int64_t>());
   SmallVector<int64_t, 6> resultShape;
+
   // If the shapes are not compatible, we can't fold it.
   // TODO: Fold to an "error".
   if (!OpTrait::util::getBroadcastedShape(lhsShape, rhsShape, resultShape))
     return nullptr;
+
   Builder builder(getContext());
   return builder.getIndexTensorAttr(resultShape);
 }
diff --git a/mlir/test/Dialect/Shape/canonicalize.mlir b/mlir/test/Dialect/Shape/canonicalize.mlir
--- a/mlir/test/Dialect/Shape/canonicalize.mlir
+++ b/mlir/test/Dialect/Shape/canonicalize.mlir
@@ -120,6 +120,20 @@
 
 // -----
 
+// All but one operands are known empty shapes.
+// CHECK-LABEL: @all_but_one_empty
+// CHECK-SAME:  (%[[ARG:.*]]: !shape.shape)
+func @all_but_one_empty(%arg0 : !shape.shape) -> !shape.shape {
+  // CHECK: return %[[ARG]]
+  %0 = shape.const_shape [] : !shape.shape
+  %1 = constant dense<[]> : tensor<0xindex>
+  %2 = shape.broadcast %0, %arg0, %1, %0 : !shape.shape, !shape.shape,
+      tensor<0xindex>, !shape.shape -> !shape.shape
+  return %2 : !shape.shape
+}
+
+// -----
+
 // Incompatible shapes. No folding.
 // CHECK-LABEL: func @f
 func @f() -> !shape.shape {