diff --git a/deepspeed/runtime/engine.py b/deepspeed/runtime/engine.py
index 892394e049ad3f77f67b8193e8193edac5b9bf96..6fd84a6aa0730718f4b96bf2b6639ff1378c99f6 100644
--- a/deepspeed/runtime/engine.py
+++ b/deepspeed/runtime/engine.py
@@ -1089,6 +1089,8 @@ class DeepSpeedEngine(Module):
                     logger.warning(
                         "**** You are using ZeRO with an untested optimizer, proceed with caution *****"
                     )
+            # This optimizer in engine is ZeRO optimizer of stage1_2 or stage3 based on the 'stage' config,
+            # while ZeRO optimizer itself wraps the original optimizer.
             self.optimizer = self._configure_zero_optimizer(basic_optimizer)
         elif self.amp_enabled():
             assert not (self.fp16_enabled() or self.bfloat16_enabled()), "Cannot enable both amp with (legacy) fp16 or bfloat16 mode"
diff --git a/deepspeed/runtime/zero/stage_1_and_2.py b/deepspeed/runtime/zero/stage_1_and_2.py
index c6a2e26aac8fdc4c4fc94b4fb4f627046959437c..20f92956a3a5372aca2c5026b9f4d79e56ff3e96 100755
--- a/deepspeed/runtime/zero/stage_1_and_2.py
+++ b/deepspeed/runtime/zero/stage_1_and_2.py
@@ -346,7 +346,9 @@ class DeepSpeedZeroOptimizer(ZeROOptimizer):
                 assert (partitioned_data.data_ptr() %
                         (2 * self.nccl_start_alignment_factor) == 0)
 
-            # a partition of the fp32 master weights that will be updated by this process
+            # A partition of the fp32 master weights that will be updated by this process.
+            # Note that the params in single_partition_of_fp32_groups is cloned and detached
+            # from the origin params of the model.
             if not fp16_master_weights_and_gradients:
                 self.single_partition_of_fp32_groups.append(
                     self.parallel_partitioned_bit16_groups[i][partition_id].to(
@@ -356,7 +358,9 @@ class DeepSpeedZeroOptimizer(ZeROOptimizer):
                     self.parallel_partitioned_bit16_groups[i][partition_id].to(
                         self.device).clone().half().detach())
 
-            # modify optimizer of have flat master weight
+            # Set local optimizer to have flat params of its own partition.
+            # After this, the local optimizer will only contain its own partition of params.
+            # In that case, the local optimizer only saves the states(momentum, variance, etc.) related to its partition's params(zero stage1).
             self.single_partition_of_fp32_groups[
                 i].requires_grad = True  # keep this in case internal optimizer uses it
             param_group['params'] = [self.single_partition_of_fp32_groups[i]]
@@ -1426,7 +1430,7 @@ class DeepSpeedZeroOptimizer(ZeROOptimizer):
         partitions = []
 
         dp = dist.get_world_size(group=self.real_dp_process_group[group_id])
-        dp_id = dist.get_rank(group=self.real_dp_process_group[group_id])
+        # dp_id = dist.get_rank(group=self.real_dp_process_group[group_id])
 
         total_num_elements = tensor.numel()
 
@@ -1691,7 +1695,7 @@ class DeepSpeedZeroOptimizer(ZeROOptimizer):
         self.start_timers([OPTIMIZER_GRADIENTS])
         norm_groups = []
         single_partition_grad_groups = []
-        skip = False
+        # skip = False
         for i, group in enumerate(self.bit16_groups):
             partition_id = dist.get_rank(group=self.real_dp_process_group[i])
             if self.cpu_offload:
@@ -1704,7 +1708,7 @@ class DeepSpeedZeroOptimizer(ZeROOptimizer):
                     self.get_grad_norm_direct(self.averaged_gradients[i],
                                               self.params_in_partition[i]))
 
-                # free gradients for all the parameters that are not updated by this process
+                # free gradients for all the parameters that are not updated by this process(ZeRO stage2)
                 self.free_grad_in_param_list(self.params_not_in_partition[i])
 
                 # create a flat gradients for parameters updated by this process
@@ -1723,7 +1727,7 @@ class DeepSpeedZeroOptimizer(ZeROOptimizer):
                         single_grad_partition.numel(), self.partition_size[i], i, partition_id)
 
                 self.single_partition_of_fp32_groups[i].grad = single_grad_partition
-                # release all the gradient since we have already created a necessary copy in dp_grad_partition
+                # release all the gradient since we have already created a necessary copy in dp_grad_partition(ZeRO stage2)
                 self.free_grad_in_param_list(self.params_in_partition[i])
 
                 self.averaged_gradients[i] = None
@@ -1752,6 +1756,7 @@ class DeepSpeedZeroOptimizer(ZeROOptimizer):
                 self.optimizer.step(fp16_param_groups=bit16_param_groups)
             else:
                 self.optimizer.step()
+                # after step(), single_partition_of_fp32_groups has the local optimizer's own partition of updated params
                 for bit16_partitions, fp32_partition in zip(self.parallel_partitioned_bit16_groups, self.single_partition_of_fp32_groups):
                     bit16_partitions[partition_id].data.copy_(fp32_partition.data)
         else:
@@ -1772,7 +1777,8 @@ class DeepSpeedZeroOptimizer(ZeROOptimizer):
             self.reset_cpu_buffers()
 
         self.start_timers([OPTIMIZER_ALLGATHER])
-        # gather the updated weights from everyone
+        # Gather the updated weights from everyone.
+        # Then all partitions of the model parameters are updated and ready for next round forward.
         all_gather_dp_groups(
             partitioned_param_groups=self.parallel_partitioned_bit16_groups,
             dp_process_group=self.real_dp_process_group,