diff --git a/torchtitan/parallelisms/parallel_dims.py b/torchtitan/parallelisms/parallel_dims.py
index 2ee9b87b..15ec8fbd 100644
--- a/torchtitan/parallelisms/parallel_dims.py
+++ b/torchtitan/parallelisms/parallel_dims.py
@@ -60,26 +60,30 @@ def build_mesh(self, device_type):
         ):
             if d > 1:
                 dims.append(d)
-                if (name == "dp_replicate" and self.dp_shard == 1) or (
-                    name == "dp_shard" and self.dp_replicate == 1
-                ):
-                    names.append("dp")
-                else:
-                    names.append(name)
+                names.append(name)
 
         logger.info(f"Building {len(dims)}-D device mesh with {names}, {dims}")
         names = tuple(names)
         mesh = init_device_mesh(device_type, dims, mesh_dim_names=names)
+
         # Create all the submesh here to ensure all required process groups are
-        # initialized
-        if self.dp_replicate > 1 and self.dp_shard > 1:  # HSDP
-            mesh["dp_replicate", "dp_shard"]._flatten(mesh_dim_name="dp")
+        # initialized:
+        # Mesh for data loading
+        dp_mesh_dim_names = []
+        if self.dp_replicate_enabled:
+            dp_mesh_dim_names.append("dp_replicate")
+
+        if self.dp_shard_enabled:
+            dp_mesh_dim_names.append("dp_shard")
+
+        if dp_mesh_dim_names != []:
+            mesh[tuple(dp_mesh_dim_names)]._flatten(mesh_dim_name="dp")
 
         if self.cp > 1:
             if self.dp_replicate > 1 and self.dp_shard > 1:  # HSDP
                 mesh["dp_replicate", "dp_shard", "cp"]._flatten(mesh_dim_name="dp_cp")
             elif self.dp_shard > 1:  # FSDP
-                mesh["dp", "cp"]._flatten(mesh_dim_name="dp_cp")
+                mesh["dp_shard", "cp"]._flatten(mesh_dim_name="dp_cp")
 
         return mesh