docs(openai): clarify codex oauth image generation

docs/tools/image-generation.md

@@ -1,5 +1,5 @@
 ---
-summary: "Generate and edit images using configured providers (OpenAI, Google Gemini, fal, MiniMax, ComfyUI, Vydra, xAI)"
+summary: "Generate and edit images using configured providers (OpenAI, OpenAI Codex OAuth, Google Gemini, fal, MiniMax, ComfyUI, Vydra, xAI)"
 read_when:
   - Generating images via the agent
   - Configuring image generation providers and models
@@ -10,12 +10,12 @@ title: "Image generation"
 The `image_generate` tool lets the agent create and edit images using your configured providers. Generated images are delivered automatically as media attachments in the agent's reply.
 
 <Note>
-The tool only appears when at least one image generation provider is available. If you don't see `image_generate` in your agent's tools, configure `agents.defaults.imageGenerationModel` or set up a provider API key.
+The tool only appears when at least one image generation provider is available. If you don't see `image_generate` in your agent's tools, configure `agents.defaults.imageGenerationModel`, set up a provider API key, or sign in with OpenAI Codex OAuth.
 </Note>
 
 ## Quick start
 
-1. Set an API key for at least one provider (for example `OPENAI_API_KEY` or `GEMINI_API_KEY`).
+1. Set an API key for at least one provider (for example `OPENAI_API_KEY` or `GEMINI_API_KEY`) or sign in with OpenAI Codex OAuth.
 2. Optionally set your preferred model:
 
 ```json5
@@ -30,6 +30,20 @@ The tool only appears when at least one image generation provider is available.
 }
 ```
 
+Use Codex OAuth instead of an OpenAI API key:
+
+```json5
+{
+  agents: {
+    defaults: {
+      imageGenerationModel: {
+        primary: "openai-codex/gpt-image-2",
+      },
+    },
+  },
+}
+```
+
 3. Ask the agent: _"Generate an image of a friendly lobster mascot."_
 
 The agent calls `image_generate` automatically. No tool allow-listing needed — it's enabled by default when a provider is available.
@@ -59,7 +73,7 @@ Use `action: "list"` to inspect available providers and models at runtime:
 | ------------- | -------- | ------------------------------------------------------------------------------------- |
 | `prompt`      | string   | Image generation prompt (required for `action: "generate"`)                           |
 | `action`      | string   | `"generate"` (default) or `"list"` to inspect providers                               |
-| `model`       | string   | Provider/model override, e.g. `openai/gpt-image-2`                                    |
+| `model`       | string   | Provider/model override, e.g. `openai/gpt-image-2` or `openai-codex/gpt-image-2`      |
 | `image`       | string   | Single reference image path or URL for edit mode                                      |
 | `images`      | string[] | Multiple reference images for edit mode (up to 5)                                     |
 | `size`        | string   | Size hint: `1024x1024`, `1536x1024`, `1024x1536`, `2048x2048`, `3840x2160`            |
@@ -125,9 +139,11 @@ OpenAI, Google, and xAI support up to 5 reference images via the `images` parame
 
 ### OpenAI `gpt-image-2`
 
-OpenAI image generation defaults to `openai/gpt-image-2`. The older
-`openai/gpt-image-1` model can still be selected explicitly, but new OpenAI
-image-generation and image-editing requests should use `gpt-image-2`.
+OpenAI image generation defaults to `openai/gpt-image-2` with `OPENAI_API_KEY`.
+Use `openai-codex/gpt-image-2` to generate or edit images with the same Codex
+OAuth sign-in used by `openai-codex` chat models. The older `openai/gpt-image-1`
+model can still be selected explicitly, but new OpenAI image-generation and
+image-editing requests should use `gpt-image-2`.
 
 `gpt-image-2` supports both text-to-image generation and reference-image
 editing through the same `image_generate` tool. OpenClaw forwards `prompt`,
@@ -153,6 +169,18 @@ Edit one local reference image:
 /tool image_generate action=generate model=openai/gpt-image-2 prompt="Keep the subject, replace the background with a bright studio setup" image=/path/to/reference.png size=1024x1536
 ```
 
+Generate with Codex OAuth:
+
+```
+/tool image_generate action=generate model=openai-codex/gpt-image-2 prompt="A clean editorial poster for OpenClaw image generation" size=3840x2160 count=1
+```
+
+Edit one local reference image with Codex OAuth:
+
+```
+/tool image_generate action=generate model=openai-codex/gpt-image-2 prompt="Keep the subject, replace the background with a bright studio setup" image=/path/to/reference.png size=1024x1536
+```
+
 Edit with multiple references:
 
 ```