Integrating Google's Generative AI image generation capabilities into a Kotlin-based Android application can be achieved by utilizing the MediaPipe Image Generator task for on-device image generation or by accessing cloud-based models like Imagen 3 through Vertex AI in Firebase. 
Here is the code snippet you can refer to:

In the above code we are using the following key points:
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On-Device Image Generation: Utilizes MediaPipe's Image Generator task to perform image generation directly on the device, reducing latency and enhancing privacy. 
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Customizable Options: Allows setting base options such as the number of threads to optimize performance based on device capabilities. 
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Direct Integration: Seamlessly integrates into Android applications using Kotlin, leveraging Google's AI capabilities. 
Hence, by implementing MediaPipe's Image Generator task, developers can effectively integrate Google's Generative AI image generation capabilities into Kotlin-based Android applications, enabling on-device image creation from text prompts.