diff --git a/src/onnx/onnx_parser.cpp b/src/onnx/onnx_parser.cpp
index a091d4f7086..5545be47069 100644
--- a/src/onnx/onnx_parser.cpp
+++ b/src/onnx/onnx_parser.cpp
@@ -620,6 +620,9 @@ static void log_node_parse_exception(const onnx::NodeProto& node,
 std::vector<instruction_ref>
 onnx_parser::parse_graph(module* mod, const onnx::GraphProto& graph, bool inlining)
 {
+    // Save/restore parent_input_nodes so sibling subgraphs can't see each other's inputs.
+    auto saved_parent_inputs = parent_input_nodes;
+
     std::vector<size_t> node_indices(graph.node_size());
 
     if(check_sorted(graph, parent_input_nodes))
@@ -741,6 +744,7 @@ onnx_parser::parse_graph(module* mod, const onnx::GraphProto& graph, bool inlini
         erase_if(instructions, [&](auto&& p) { return mod->has_instruction(p.second); });
     }
 
+    parent_input_nodes = std::move(saved_parent_inputs);
     return output_ins;
 }
 
diff --git a/src/replace_allocate.cpp b/src/replace_allocate.cpp
index a8573f94ea0..737aeac9378 100644
--- a/src/replace_allocate.cpp
+++ b/src/replace_allocate.cpp
@@ -115,17 +115,24 @@ get_output_debug_symbols(const module& mod)
     return mod_output_debug_symbols;
 }
 
-void insert_copy(module& m, const allocation_model& model)
+void insert_copy(module& m, const allocation_model& model, bool is_root)
 {
     auto returns = m.get_returns();
     std::unordered_set<instruction_ref> returns_set(returns.begin(), returns.end());
     for(auto ins : returns_set)
     {
+        if(is_root and (ins->name() == "@param" or ins->name() == "@literal"))
+            continue;
         if(ins->get_shape().any_of_dynamic())
             continue;
         auto aliases = instruction::get_output_alias(ins);
         if(std::any_of(aliases.begin(), aliases.end(), [&](instruction_ref alias) {
-               return alias->get_shape() == ins->get_shape();
+               if(alias->get_shape() != ins->get_shape())
+                   return false;
+               if(alias->name() == "allocate" or alias->name() == model.name())
+                   return true;
+               return alias->name() == "@param" and alias != ins and
+                      not ins->get_operator().is_context_free();
            }))
             continue;
         auto insert_ins = std::next(ins);
@@ -176,7 +183,7 @@ void replace_allocate::apply(module_pass_manager& mpm) const
         insert_submod_allocations(ins, m, model);
     }
     if(not root_offload_copy and model.needs_out_params())
-        insert_copy(m, model);
+        insert_copy(m, model, is_root);
     auto mod_output_names         = create_output_names(m);
     auto mod_output_debug_symbols = get_output_debug_symbols(m);
     for(auto ins : iterator_for(m))