DeepSpeed Stage 3 in lightning leads to Nan and Inf values in the model parameters.

Nobody has claimed this yet.

### Bug description

I try to use lightning with DeepSpeed stage 3 to train a model under the precision "16-mixed". However, I find that the model parameters includes Nan and Inf values at the first step. When I change it to DDP, this issue does not exist.

I initialize my trainer as:

```
trainer = Trainer(
max_epochs=max_epochs,
logger=logger,
callbacks=[checkpoint_callback, lr_monitor],
sync_batchnorm=sync_batchnorm,
check_val_every_n_epoch=None,
val_check_interval=every_n_train_steps * accumulate_grad_batches,
devices="auto",
accelerator="gpu",
precision="16-mixed",
strategy=deepspeed_stage_3，
accumulate_grad_batches=accumulate_grad_batches,
)
```

### What version are you seeing the problem on?

v2.5

### How to reproduce the bug

```python
trainer = Trainer(
max_epochs=max_epochs,
logger=logger,
callbacks=[checkpoint_callback, lr_monitor],
sync_batchnorm=sync_batchnorm,
check_val_every_n_epoch=None,
val_check_interval=every_n_train_steps * accumulate_grad_batches,
devices="auto",
accelerator="gpu",
precision="16-mixed",
strategy=deepspeed_stage_3，
accumulate_grad_batches=accumulate_grad_batches,
)
```

### Error messages and logs

```
# Error messages and logs here please
```

### Environment

Current environment

```
#- PyTorch Lightning Version (e.g., 2.5.0):
#- PyTorch Version (e.g., 2.5):
#- Python version (e.g., 3.12):
#- OS (e.g., Linux):
#- CUDA/cuDNN version:
#- GPU models and configuration:
#- How you installed Lightning(`conda`, `pip`, source):
```

### More info

_No response_

Start by reproducing the reported Trainer configuration with DeepSpeed Stage 3 and 16-mixed precision, then compare its first training step with DDP. The report does not name files or tests and omits environment details and logs; done means identifying why parameters become NaN or Inf under Stage 3 and confirming they remain finite after the fix.

Written by the indexing model from the issue text.