diff --git a/src/Builder/FrontendDialectTransformer.cpp b/src/Builder/FrontendDialectTransformer.cpp
index 91d25a6..02990c4 100644
--- a/src/Builder/FrontendDialectTransformer.cpp
+++ b/src/Builder/FrontendDialectTransformer.cpp
@@ -248,15 +248,31 @@ private:
     bool variadicIn = expectedNumOperands == -1;
     bool variadicOut = expectedNumResults == -1;
 
+    // In ONNX, there are two ways to leave an optional input or output
+    // unspecified: the first, available only for trailing inputs and outputs,
+    // is to simply not provide that input; the second method is to use an empty
+    // string in place of an input or output name.
+    //
+    // Here, we import optional inputs and outputs as NoneType.
+
+    // Trailing optional inputs.
     if (!variadicIn)
       for (auto i = inputs.size(); i < expectedNumOperands; i++)
         inputs.emplace_back(none_);
 
     std::vector<mlir::Type> outputTypes;
     for (auto item : node.output()) {
-      outputTypes.push_back(
-          mlir::UnrankedTensorType::get(builder_.getF32Type()));
+      // Optional outputs using empty string.
+      if (item.empty())
+        outputTypes.emplace_back(builder_.getNoneType());
+      else
+        outputTypes.push_back(
+            mlir::UnrankedTensorType::get(builder_.getF32Type()));
     }
+    // Trailing optional outputs.
+    if (!variadicOut)
+      for (int i = node.output().size(); i < expectedNumResults; ++i)
+        outputTypes.emplace_back(builder_.getNoneType());
 
     auto attributes = ImportNodeAttributes(node);
 
diff --git a/src/Transform/ONNX/ShapeInferencePass.cpp b/src/Transform/ONNX/ShapeInferencePass.cpp
index ab05931..1bf9855 100644
--- a/src/Transform/ONNX/ShapeInferencePass.cpp
+++ b/src/Transform/ONNX/ShapeInferencePass.cpp
@@ -126,7 +126,8 @@ public:
         op->getName().getStringRef() != "onnx.Unsqueeze")
       return false;
     return llvm::any_of(op->getResultTypes(), [](Type result_type) {
-      return !result_type.isa<RankedTensorType>();
+      return !result_type.isa<NoneType>() &&
+             !result_type.isa<RankedTensorType>();
     });
   }
 };