Flux training seems not to update the transformer model

### Describe the bug

When I loaded the checkpoint of the transformer saved using the training script train_dreambooth_flux.py, I found it exactly the same as the pretrained flux-dev model. So I suspect that the model is not updating the parameters. Meanwhile, I notice that the optimizer.bin in the checkpoint save dir is very small, only 1.3K. This could be abnormal. The saved checkpoint works using the training script train_dreambooth_sd3.py. However, it fails with train_dreambooth_flux.py.

### Reproduction

A testing script is like this:
```
import torch
from diffusers import FluxPipeline
from accelerate import Accelerator
import diffusers
from diffusers import (
AutoencoderKL,
FlowMatchEulerDiscreteScheduler,
FluxPipeline,
FluxTransformer2DModel,
)

transformer1 = FluxTransformer2DModel.from_pretrained(
"black-forest-labs/FLUX.1-dev", subfolder="transformer", torch_dtype=torch.bfloat16
)
transformer1.eval()
initial_params = {name: param.data.clone() for name, param in transformer1.named_parameters()}
# the folder that saves the checkpoint of the transformer using accelerator.save_state()
transformer_path = '/xxx/checkpoint-2/transformer'
transformer2 = FluxTransformer2DModel.from_pretrained(
transformer_path, torch_dtype=torch.bfloat16,
)
for name, param in transformer2.named_parameters():
if not torch.equal(initial_params[name], param.data):
print(name, ' not match')
```

### Logs

```shell
Using the test script above, we can find that the saved transformer is exactly the same as the pretrained transformer.
```

### System Info

- 🤗 Diffusers version: 0.32.0.dev0
- Platform: Linux
- Running on Google Colab?: No
- Python version: 3.12.7
- PyTorch version (GPU?): 2.5.1+cu124 (True)
- Flax version (CPU?/GPU?/TPU?): not installed (NA)
- Jax version: not installed
- JaxLib version: not installed
- Huggingface_hub version: 0.26.2
- Transformers version: 4.46.1
- Accelerate version: 1.0.1
- PEFT version: not installed
- Bitsandbytes version: 0.44.1
- Safetensors version: 0.4.5
- xFormers version: not installed
- Accelerator: NVIDIA A100-SXM4-80GB, 81920 MiB
NVIDIA A100-SXM4-80GB, 81920 MiB
NVIDIA A100-SXM4-80GB, 81920 MiB
NVIDIA A100-SXM4-80GB, 81920 MiB
NVIDIA A100-SXM4-80GB, 81920 MiB
NVIDIA A100-SXM4-80GB, 81920 MiB
NVIDIA A100-SXM4-80GB, 81920 MiB
NVIDIA A100-SXM4-80GB, 81920 MiB
- Using GPU in script?:
- Using distributed or parallel set-up in script?:

### Who can help?

@sayakpaul

Start with train_dreambooth_flux.py and compare its checkpoint handling with train_dreambooth_sd3.py, focusing on accelerator.save_state() and the saved transformer directory. Reproduce the report with the provided parameter-comparison script and inspect checkpoint-2/transformer and optimizer.bin. Done means a Flux training checkpoint reflects updated transformer parameters and can be reloaded successfully.

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