diff --git a/python/paddle/incubate/autograd/primx.py b/python/paddle/incubate/autograd/primx.py
index 7a969748208a46b093399684c79d45ed395a208a..1f5c4f9a5cebbbe61bc33334f9883f56ff698170 100644
--- a/python/paddle/incubate/autograd/primx.py
+++ b/python/paddle/incubate/autograd/primx.py
@@ -38,8 +38,7 @@ def topo_path(xs, ys, block=None):
         path, the unused variables in `xs`, and the unreached variables in `ys`
     """
 
-    if block is None:
-        block = default_main_program().current_block()
+    block = default_main_program().current_block() if block is None else block
 
     path = []
     backpath = []
@@ -160,11 +159,14 @@ class VarMap(object):
         return id(value_var) in self.tab.values()
 
 
+# TODO(lml): supporting control flow, nested blocks, and block other than current block of main program.
 class Transform(object):
     """ An object that maintains the state of transformations applied to a 
     primitve program. """
 
     def __init__(self, block):
+        assert block == default_main_program().current_block(
+        ), f'only support transform on current block of main program.'
         self.block = block
         self.vars = self.init_vars(block)
         self.var2dot = VarMap('var2dot', self.vars)
@@ -400,6 +402,7 @@ class Transform(object):
         return ys_bar, xs_bar
 
 
+# TODO(lml): supporting control flow, nested blocks, and block other than current block of main program.
 def _lower(block, reverse):
     # Some functions which are only used in _lower.
     def bind(args, to_bind, value_table):
@@ -430,10 +433,6 @@ def _lower(block, reverse):
     # Step1: Do some preparatory work for lower
     lower_fn = _prim2orig if reverse else _orig2prim
     lookup_fn = lookup_prim2orig if reverse else lookup_orig2prim
-    if block is None:
-        program = default_main_program()
-        assert program.num_blocks == 1, "The lower transform is designed to process only one block."
-        block = program.current_block()
 
     value_table = {}
     to_bind = {}
@@ -516,6 +515,7 @@ def orig2prim(block=None):
     """ 
     .. note::
         **This API is ONLY available in the static mode.**
+        **Args block must be None or current block of main program.**
 
     All operators in the target block are processed as follows.
     If it is an original operator, it will be transformed into
@@ -523,13 +523,14 @@ def orig2prim(block=None):
     equivalent function.
     
     Args:
-        block(paddle.fluid.framework.Variable|None, optional): The
+        block(paddle.static.Block|None, optional): The
             target block to process on. Default None, and will
             process on the current block of main program.
-    
-    Returns:
-        None
     """
+
+    block = default_main_program().current_block() if block is None else block
+    assert block == default_main_program().current_block(
+    ), f'block is neither None nor current block of main program'
     _lower(block, reverse=False)
 
 
@@ -538,6 +539,7 @@ def prim2orig(block=None):
     """
     .. note::
         **ONLY available in the static mode.**
+        **Args block must be None or current block of main program.**
 
     All operators in the target block are processed as follows.
     If it is an automatic differential basic operator, it will be
@@ -545,10 +547,10 @@ def prim2orig(block=None):
     equivalent function to support execution.
     
     Args:
-        block(paddle.static.Variable|None, optional): The
+        block(paddle.static.Block|None, optional): The
             target block to process on. Default None, and will
             process on the current block of main program.
-       
+    
     Examples:
 
         .. code-block:: python
@@ -566,6 +568,10 @@ def prim2orig(block=None):
             if prim_enabled():
                 prim2orig()
     """
+
+    block = default_main_program().current_block() if block is None else block
+    assert block == default_main_program().current_block(
+    ), f'block is neither None nor current block of main program'
     _lower(block, reverse=True)
 
 
@@ -583,7 +589,9 @@ def _gradients(ys, xs, ys_bar=None):
     """
 
     ys, xs = to_tensors(ys), to_tensors(xs)
-    block = ys[0].block
+    block = default_main_program().current_block()
+    for el in xs + ys:
+        assert el is None or el.block == block, f'variable in xs and ys should be None or in current block of main program'
     # TODO(Tongxin) without any prior knowledge about whether the program
     # is completely lowered to primitive ops, it's mandatory to run the lowering
     # pass once and again. This is obviously inefficient and needs to be 
diff --git a/python/paddle/optimizer/optimizer.py b/python/paddle/optimizer/optimizer.py
index 9dfec3947e95f82fb8239455c156d4fe1470d30a..cf180fccc48576f1ccd53e3e78845d1896f73e51 100644
--- a/python/paddle/optimizer/optimizer.py
+++ b/python/paddle/optimizer/optimizer.py
@@ -58,6 +58,8 @@ def append_backward_new(loss_list,
     program = default_main_program()
     assert program.num_blocks == 1, "The append_backward_new interface is designed to process only one block."
     block = program.current_block()
+    for el in loss_list:
+        assert el.block == block, f'variable in loss_list should be in current block of main program'
 
     orig2prim(block)
     ad = Transform(block)