diff --git a/examples/custom_diffusion/train_custom_diffusion.py b/examples/custom_diffusion/train_custom_diffusion.py
index 8dddcd0ca706..e498ca98b1c7 100644
--- a/examples/custom_diffusion/train_custom_diffusion.py
+++ b/examples/custom_diffusion/train_custom_diffusion.py
@@ -314,11 +314,12 @@ def save_new_embed(text_encoder, modifier_token_id, accelerator, args, output_di
     for x, y in zip(modifier_token_id, args.modifier_token):
         learned_embeds_dict = {}
         learned_embeds_dict[y] = learned_embeds[x]
-        filename = f"{output_dir}/{y}.bin"
 
         if safe_serialization:
+            filename = f"{output_dir}/{y}.safetensors"
             safetensors.torch.save_file(learned_embeds_dict, filename, metadata={"format": "pt"})
         else:
+            filename = f"{output_dir}/{y}.bin"
             torch.save(learned_embeds_dict, filename)
 
 
@@ -1040,17 +1041,22 @@ def main(args):
     )
 
     # Scheduler and math around the number of training steps.
-    overrode_max_train_steps = False
-    num_update_steps_per_epoch = math.ceil(len(train_dataloader) / args.gradient_accumulation_steps)
+    # Check the PR https://github.com/huggingface/diffusers/pull/8312 for detailed explanation.
+    num_warmup_steps_for_scheduler = args.lr_warmup_steps * accelerator.num_processes
     if args.max_train_steps is None:
-        args.max_train_steps = args.num_train_epochs * num_update_steps_per_epoch
-        overrode_max_train_steps = True
+        len_train_dataloader_after_sharding = math.ceil(len(train_dataloader) / accelerator.num_processes)
+        num_update_steps_per_epoch = math.ceil(len_train_dataloader_after_sharding / args.gradient_accumulation_steps)
+        num_training_steps_for_scheduler = (
+            args.num_train_epochs * num_update_steps_per_epoch * accelerator.num_processes
+        )
+    else:
+        num_training_steps_for_scheduler = args.max_train_steps * accelerator.num_processes
 
     lr_scheduler = get_scheduler(
         args.lr_scheduler,
         optimizer=optimizer,
-        num_warmup_steps=args.lr_warmup_steps * accelerator.num_processes,
-        num_training_steps=args.max_train_steps * accelerator.num_processes,
+        num_warmup_steps=num_warmup_steps_for_scheduler,
+        num_training_steps=num_training_steps_for_scheduler,
     )
 
     # Prepare everything with our `accelerator`.
@@ -1065,8 +1071,14 @@ def main(args):
 
     # We need to recalculate our total training steps as the size of the training dataloader may have changed.
     num_update_steps_per_epoch = math.ceil(len(train_dataloader) / args.gradient_accumulation_steps)
-    if overrode_max_train_steps:
+    if args.max_train_steps is None:
         args.max_train_steps = args.num_train_epochs * num_update_steps_per_epoch
+        if num_training_steps_for_scheduler != args.max_train_steps * accelerator.num_processes:
+            logger.warning(
+                f"The length of the 'train_dataloader' after 'accelerator.prepare' ({len(train_dataloader)}) does not match "
+                f"the expected length ({len_train_dataloader_after_sharding}) when the learning rate scheduler was created. "
+                f"This inconsistency may result in the learning rate scheduler not functioning properly."
+            )
     # Afterwards we recalculate our number of training epochs
     args.num_train_epochs = math.ceil(args.max_train_steps / num_update_steps_per_epoch)