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Thumbdata files are hidden by default, so unless you have the option for showing hidden files enabled, (Menu ► Settings ► Show Hidden Files) you might not even be aware of them and that they are eating up your free space. You can find them in /DCIM/.thumbnails folder on your SD card or internal storage, depending on where your images are saved by default.
Considering *.thumbdata files are generated in the DCIM folder where the digital camera saves photos, it is likely that the *.thumbdata files are generated by apps related to the digital camera, image preview or editing. From what we could gather, the general consensus is that these files are created by any of the media gallery apps.
THUMBDATA format is used for indexing and caching purpose and probably also contains thumbnails of processed images as well. They are generated so image previews (thumbnails) are quickly loaded on the display and users do not experience any sluggish behavior when they browse through their images, especially if they have a huge library.
The problem with these .thumbdata files is that they grow with each image the gallery/camera app encounters, and thus THUMBDATA indexes can even potentially store data about images that were deleted from the device. So a situation may happen, that even if you would delete all images from your storage, one or more .thumbdata files would still take up space.

how to disable thumbdata from regeneration

How to prevent .thumbdata files to grow big in size?

There is one, pretty reliable solution to solve the "thumbdata problem".
  locate the thumbdata  files  and delete them.  create a new folder with the Root Browser app or ES file explorer.
(check Google Play store)
in the DCIM folder where the .thumbdata file was previously located

create a new empty file called .thumbdata

And that's it. The system will be fooled, and no more .thumbdata files will be generated and eating up your free space.
Some users also tried to create an empty file with the same file name and restrict it for reading, but it apparently does not always work and some apps that synchronize images will remove the "read only" attribute. That means the "folder way" is probably the only choice at the moment how to reliably disable .thumbdata file growth.

note, it's totally safe to delete thumbnails as it has no effect to the storage.