The current Custom Speech REST API supports uploading data from local filesystem, in the form of .zip files for acoustic customisation, and .txt for language models. We are seeing if there are ways to automatically upload a batch of data from Azure Blob Storage to the custom speech portal.
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@kishan19 You can follow the steps mentioned here to generate the swagger API reference.

Hope this helps!!
Also, see this quickstart that shows how to do batch with blob storage. Note, that you'd have to change the code a bit to handle multiple files -- but the idea is the same.
@kishan19 We will now proceed to close this thread. If there are further questions regarding this matter, please tag @RohitMungi-MSFT in your reply.
Thank you, this has been super helpful! Solved a long time roadblock for us.