diff --git a/deepspeed/runtime/zero/partition_parameters.py b/deepspeed/runtime/zero/partition_parameters.py
index 05825fc90688..e6cb9199899a 100755
--- a/deepspeed/runtime/zero/partition_parameters.py
+++ b/deepspeed/runtime/zero/partition_parameters.py
@@ -807,8 +807,12 @@ def _partition_gradient(self, param, partition_buffer=None, accumulate=False):
         if start < param.ds_numel:
             elements = min(param.ds_numel - start, partition_size)
 
-            dest_tensor = partition_buffer.view(-1).narrow(0, 0, elements)
+            dest_tensor_full_buffer = partition_buffer.view(-1).narrow(
+                0,
+                0,
+                partition_size)
 
+            dest_tensor = dest_tensor_full_buffer.narrow(0, 0, elements)
             src_tensor = param.grad.view(-1).narrow(0, start, elements)
 
             # just copy the grad partition to the buffer
@@ -841,7 +845,7 @@ def _partition_gradient(self, param, partition_buffer=None, accumulate=False):
             #                                             elements))
 
         #print("after partition gradients")
-        param.grad.data = dest_tensor.data
+        param.grad.data = dest_tensor_full_buffer.data
         see_memory_usage("After partitioning gradients", force=False)
 
 
diff --git a/deepspeed/runtime/zero/stage3.py b/deepspeed/runtime/zero/stage3.py
index f840de15c57d..99b4916aef3c 100755
--- a/deepspeed/runtime/zero/stage3.py
+++ b/deepspeed/runtime/zero/stage3.py
@@ -961,10 +961,9 @@ def _create_fp16_partitions_with_defragmentation(self):
 
                     #create flat buffer in CPU and move to GPU
                     self.fp16_partitioned_groups_flat.append(
-                        flatten_dense_tensors_aligned(
-                            self.fp16_partitioned_groups[i],
-                            dist.get_world_size(group=self.dp_process_group)).cuda(
-                                torch.cuda.current_device()))
+                        flatten_dense_tensors_aligned(self.fp16_partitioned_groups[i],
+                                                      1).cuda(
+                                                          torch.cuda.current_device()))
                     see_memory_usage(
                         f"After flattening and moving param group {i} to GPU",
                         force=False)
@@ -976,10 +975,12 @@ def _create_fp16_partitions_with_defragmentation(self):
                                   flat_offset,
                                   total_elements)
                     self.fp16_partitioned_groups_flat.append(fp16_partitioned_group_flat)
-                    self._move_to_flat_buffer(self.fp16_partitioned_groups[i],
-                                              self.fp16_partitioned_groups_flat[i])
                     flat_offset += total_elements
 
+                # move param to flat buffer for both param offload on/off
+                self._move_to_flat_buffer(self.fp16_partitioned_groups[i],
+                                          self.fp16_partitioned_groups_flat[i])
+
                 see_memory_usage(f"After Flattening param group {i}", force=False)
 
     def _create_fp32_partitions(self):
@@ -1036,6 +1037,14 @@ def setup_zero_stage3_hooks(self):
         self.hierarchy = 0
         self._register_hooks_recursively(self.module)
 
+        #reset step if in inference mode
+        def _end_of_forward_hook(module, *args):
+
+            if not torch._C.is_grad_enabled():
+                self.param_coordinator.reset_step()
+
+        self.module.register_forward_hook(_end_of_forward_hook)
+
     def persistent_parameters(self):
         persistent_params = []
         total_persistent_parameters = 0
diff --git a/tests/unit/test_fp16.py b/tests/unit/test_fp16.py
index 5012614f97b0..dbd40c322be9 100755
--- a/tests/unit/test_fp16.py
+++ b/tests/unit/test_fp16.py
@@ -347,9 +347,6 @@ def test_zero_static_scale(tmpdir, zero_stage, use_cpu_offload):
     if use_cpu_offload and not deepspeed.ops.__compatible_ops__[CPUAdamBuilder.NAME]:
         pytest.skip("cpu-adam is not compatible")
 
-    if zero_stage == 3:
-        pytest.skip("skip for now")
-
     config_dict = {
         "train_batch_size": 4,
         "steps_per_print": 1,
@@ -371,8 +368,9 @@ def test_zero_static_scale(tmpdir, zero_stage, use_cpu_offload):
     args = args_from_dict(tmpdir, config_dict)
 
     @distributed_test(world_size=2)
-    def _test_zero_static_scale(args, zero_stage):
-        hidden_dim = 10
+    def _test_zero_static_scale(args, zero_stage, hidden_dim):
+        #making hidden size not divisible by DP for covering this scenario
+        hidden_dim = hidden_dim
         model = SimpleModel(hidden_dim)
 
         model, optim, _, _ = deepspeed.initialize(args=args,
@@ -393,7 +391,10 @@ def _test_zero_static_scale(args, zero_stage):
             model.backward(loss)
             model.step()
 
-    _test_zero_static_scale(args=args, zero_stage=zero_stage)
+    #test when hidden_dim is not aligned with world size
+    _test_zero_static_scale(args=args, zero_stage=zero_stage, hidden_dim=9)
+    #test when hidden_dim is aligned with world size
+    _test_zero_static_scale(args=args, zero_stage=zero_stage, hidden_dim=10)
 
 
 def test_zero_static_scale_deprecated_format(tmpdir):