diff --git a/onnxscript/optimizer/_constant_folding.py b/onnxscript/optimizer/_constant_folding.py
index 6aae8efab3..8317d2be63 100644
--- a/onnxscript/optimizer/_constant_folding.py
+++ b/onnxscript/optimizer/_constant_folding.py
@@ -608,6 +608,9 @@ def identity(node: ir.Node, op, state: OptimizerState) -> ReturnValue:
     input = node.inputs[0]
     output = node.outputs[0]
     if input is not None and output is not None:
+        input.shape = _merge_shapes(input.shape, output.shape)
+        if input.type is None:
+            input.type = output.type
         state.set_sym_value(output, input)
     return None