When images are generated they are not automatically saved into your asset library. This is to enable you to maintain an asset library that only contains the assets that you want and not have it filled with discarded assets. This is especially important given the AI models draw upon your asset library when responding to prompts.
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Unless generated images are manually saved/added to the Asset Library, they will remain in the relevant projects that you have created.

Generated images can be easily added to the Asset Library and there are two ways to add a generated image to your Asset Library:

Select the desired image(s) in the thumbnails (highlighted in blue) and select the ‘Add to Assets’ button above.

Or

On the relevant image, click on the 3 dots in the right-hand corner of the thumbnail image and select ‘Save to Assets’.

Once you have selected either pathway, you will need to add it to the relevant Product (or no product) within the Asset Library.