diff --git a/imperative/python/test/unit/functional/test_tensor.py b/imperative/python/test/unit/functional/test_tensor.py
index e6f56819d82c30ff9b9016ce73db09e3b4274ec7..e3423a492660dcaf320fcac46ff2b1c1042dcd8d 100644
--- a/imperative/python/test/unit/functional/test_tensor.py
+++ b/imperative/python/test/unit/functional/test_tensor.py
@@ -711,6 +711,35 @@ def test_copy_d2d(is_varnode):
     copy_test("gpu0:0", "gpu0:1", network=network)
 
 
+@pytest.mark.require_ngpu(2)
+@pytest.mark.parametrize(
+    "shape, device_src, device_dst",
+    [
+        ((0,), "cpu0", "cpu0"),
+        ((10, 0), "cpu0", "cpu1"),
+        ((2, 0, 3), "cpu0", "gpu0"),
+        ((1, 0, 1, 0), "gpu0", "cpu0"),
+        ((2, 3, 4, 5, 0), "gpu0", "gpu1"),
+    ],
+)
+@pytest.mark.parametrize("is_symbolic", [None, True, False])
+def test_copy_empty(shape, device_src, device_dst, is_symbolic):
+    inp = tensor(np.random.randn(*shape).astype("float32"), device=device_src)
+
+    def func(inp):
+        return F.copy(inp, device_dst)
+
+    if is_symbolic is not None:
+        func = trace(symbolic=is_symbolic)(func)
+
+    for _ in range(3):
+        out = func(inp)
+        assert out.numpy().shape == shape
+        assert out.device == device_dst
+        if is_symbolic is None:
+            break
+
+
 @pytest.mark.parametrize(
     "shape, repeats, axis",
     [
diff --git a/imperative/src/impl/opr_utility.cpp b/imperative/src/impl/opr_utility.cpp
index 7238f58c4929e280a23fc7e71c1644728fa48a8f..2cbd1da0563a3b45473d550d28703cc05c4b651b 100644
--- a/imperative/src/impl/opr_utility.cpp
+++ b/imperative/src/impl/opr_utility.cpp
@@ -170,6 +170,7 @@ void OutputCallback::init_output_static_infer_desc() {}
 cg::OperatorNodeBase::NodeProp* OutputCallback::do_make_node_prop() const {
     NodeProp* prop = Super::do_make_node_prop();
     prop->add_flag(NodeProp::Flag::NO_AUTOMATIC_DUP);
+    prop->add_flag(NodeProp::Flag::CROSS_COMP_NODE_MEMORY);
     SmallVector<NodeProp::DepType> dep_types(input().size(),
                                              NodeProp::DepType::DEV_COMP_ORDER);
     using IT = cg::static_infer::InferType;
diff --git a/src/opr/impl/io.cpp b/src/opr/impl/io.cpp
index 4a691213d924c11b2f039040be8d609c491919f7..2a6c59f1b9f55c6c9b641988ef34b05ecfd169db 100644
--- a/src/opr/impl/io.cpp
+++ b/src/opr/impl/io.cpp
@@ -708,7 +708,7 @@ Copy::Copy(VarNode *inp, const OperatorNodeConfig &config):
     Super{inp->owner_graph(), config, "copy", {inp}}
 {
     add_input({inp});
-    add_output(None);
+    add_output(None)->add_flag(VarNode::Flag::ALLOW_EMPTY_SHAPE);
 }
 
 SymbolVar Copy::make(SymbolVar inp, const OperatorNodeConfig &config) {
@@ -767,6 +767,8 @@ Copy::NodeProp* Copy::do_make_node_prop() const {
     using F = NodeProp::Flag;
     rst->add_flag(F::CROSS_COMP_NODE_MEMORY);
     rst->add_flag(F::NO_AUTOMATIC_DUP);
+    rst->add_dep_type_existing_var(input(0),
+                                   NodeProp::DepType::VALUE_ALLOW_EMPTY);
     return rst;
 }
 
diff --git a/src/opr/impl/utility.cpp b/src/opr/impl/utility.cpp
index 2aa82fd2bfbf77474b4dcf9df3212be4f75a2f4e..b2413486f7b38d6191e06a1534ce970542a8c701 100644
--- a/src/opr/impl/utility.cpp
+++ b/src/opr/impl/utility.cpp
@@ -423,7 +423,7 @@ Identity::Identity(VarNode* input, const OperatorNodeConfig &config):
     Super(input->owner_graph(), config, "identity", {input})
 {
     add_input({input});
-    add_output(None);
+    add_output(None)->add_flag(VarNode::Flag::ALLOW_EMPTY_SHAPE);
     set_ignore_side_effect();
 }
 
@@ -437,6 +437,13 @@ SymbolVar Identity::make(
     return input.insert_single_output_opr<Identity>(input.node(), config);
 }
 
+Identity::NodeProp* Identity::do_make_node_prop() const {
+    auto ret = Super::do_make_node_prop();
+    ret->add_dep_type_existing_var(input(0),
+                                   NodeProp::DepType::VALUE_ALLOW_EMPTY);
+    return ret;
+}
+
 #if MGB_ENABLE_GRAD
 MGB_IMPL_OPR_GRAD(Identity) {
     return out_grad.at(0);
diff --git a/src/opr/include/megbrain/opr/utility.h b/src/opr/include/megbrain/opr/utility.h
index 8f3cf6b80d2209b5d9adbdf2b413b20b11896521..7112e4f3e056c2e08dcb8e774272054a4e2a30e6 100644
--- a/src/opr/include/megbrain/opr/utility.h
+++ b/src/opr/include/megbrain/opr/utility.h
@@ -277,6 +277,7 @@ MGB_DEFINE_OPR_CLASS(MarkNoBroadcastElemwise, intl::ForwardInputToOutput) // {
  * its gradient can be correctly computed.
  */
 MGB_DEFINE_OPR_CLASS(Identity, intl::ForwardInputToOutput) // {
+        NodeProp* do_make_node_prop() const override;
     public:
         using Param = megdnn::param::Empty;
         Identity(VarNode* input, const OperatorNodeConfig &config);
diff --git a/src/opr/test/io.cpp b/src/opr/test/io.cpp
index 61782789805c29ae8e0359e38d7e0516c8860719..d85439c7a2ac2cb5dea14a720521dd6974f51c4d 100644
--- a/src/opr/test/io.cpp
+++ b/src/opr/test/io.cpp
@@ -406,6 +406,20 @@ TEST(TestOprIO, D2DNonContig) {
     MGB_ASSERT_TENSOR_EQ(host_y, except_y);
 }
 
+TEST(TestOprIO, D2DCopyEmpty) {
+    auto cns = load_multiple_xpus(2);
+    HostTensorGenerator<> gen;
+    auto host_x = gen({2,0,3,0,4}, cns[0]);
+    auto graph = ComputingGraph::make();
+    auto x = opr::Host2DeviceCopy::make(*graph, host_x).rename("x"),
+         y = (opr::Copy::make(x, {cns[1]})).rename("y");
+    HostTensorND host_y;
+    auto func = graph->compile({make_callback_copy(y, host_y)});
+    func->execute();
+    ASSERT_TRUE(host_y.layout().is_empty());
+    ASSERT_EQ(host_y.layout(), host_x->layout());
+}
+
 TEST(TestOprIO, MultipleDeviceTensorHolder) {
     auto cns = load_multiple_xpus(2);
     HostTensorGenerator<> gen0;