[Docs] Add basic usage examples for diffusion

[SamitHuang]

PLEASE FILL IN THE PR DESCRIPTION HERE ENSURING ALL CHECKLIST ITEMS (AT THE BOTTOM) HAVE BEEN CONSIDERED.

Purpose

Provide a simpler example with less arguments to run image generatin with vllm-omni

Test Plan

run the basic usage code in the docs

Test Result

INFO 12-06 05:42:21 [parallel_state.py:1208] rank 0 in world size 1 is assigned as DP rank 0, PP rank 0, TP rank 0, EP rank 0
Loading checkpoint shards: 100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 3/3 [00:08<00:00,  2.76s/it]
WARNING 12-06 05:42:36 [__init__.py:755] Current vLLM config is not set.
INFO:vllm_omni.model_executor.model_loader.weight_utils:Using model weights format ['*']
INFO:vllm_omni.model_executor.model_loader.weight_utils:Time spent downloading weights for Tongyi-MAI/Z-Image-Turbo: 0.561067 seconds
INFO:vllm_omni.diffusion.worker.gpu_worker:Worker 0: Initialized device, model, and distributed environment.
INFO:vllm_omni.diffusion.worker.gpu_worker:Worker 0: Model loaded successfully.
INFO:vllm_omni.diffusion.worker.gpu_worker:Worker 0: Scheduler loop started.
INFO:vllm_omni.diffusion.worker.gpu_worker:Worker 0 ready to receive requests via shared memory
INFO:vllm_omni.diffusion.scheduler:SyncScheduler initialized result MessageQueue
INFO:vllm_omni.diffusion.omni_diffusion:Prepared 1 requests for generation.
INFO:vllm_omni.diffusion.diffusion_engine:Generation completed successfully.
Image saved to coffee.png
/usr/lib/python3.12/multiprocessing/resource_tracker.py:254: UserWarning: resource_tracker: There appear to be 1 leaked semaphore objects to clean up at shutdown
  warnings.warn('resource_tracker: There appear to be %d '
/usr/lib/python3.12/multiprocessing/resource_tracker.py:254: UserWarning: resource_tracker: There appear to be 2 leaked shared_memory objects to clean up at shutdown
  warnings.warn('resource_tracker: There appear to be %d '

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Essential Elements of an Effective PR Description Checklist

• The purpose of the PR, such as "Fix some issue (link existing issues this PR will resolve)".
• The test plan, such as providing test command.
• The test results, such as pasting the results comparison before and after, or e2e results
• (Optional) The necessary documentation update, such as updating supported_models.md and examples for a new model.
• (Optional) Release notes update. If your change is user facing, please update the release notes draft.

BEFORE SUBMITTING, PLEASE READ https://github.com/vllm-project/vllm-omni/blob/main/CONTRIBUTING.md (anything written below this line will be removed by GitHub Actions)

[hsliuustc0106]

I think in the quickstart, we may need to provide two examples:

1. Qwen-Image example: Text-to-image generation quickstart with vllm-omni
2. Qwen3-Omni example: Omni-modality understanding and generation quickstart with vllm-omni
   we need to make it better for users to undestand the usage of our API at the first glance.

[Gaohan123]

Agreed. Maybe this PR can be merged first. Then I will supplement a example for Qwen3-Omni in both offline and online. Besides, an online example for image generation is also needed.

[SamitHuang]

agreed. thanks for helping supplement

[Gaohan123]

LGTM, thanks!