DDI is a sector-based disk image format created with the DiskDupe program. The files are probably not the same as the DDI files commonly found and used in some MSX emulators.
DiskDupe by Micro System Designs is a DOS program that was used in 1990s to create images of floppy disks. A DiskDupe image consists of a header and a raw disk image. The header formats are different for versions 5 and 7 of DiskDupe: Version 7 header is 9216 bytes long and seems to be fixed (it was the same for all images we looked at); Version 5 header is 1280 bytes long and differs from image to image.
It is currently unknown what is stored in the headers. Supposedly, version 7 headers are just placeholders, because they are identical for all images we looked at. Version 5 headers might contain some metadata. By skipping the headers we can get raw images of the disks.
A list of tools that work with the DDI format.
ddi2raw is a Python 3 script that converts a floppy disk image in a DDI (DiskDupe) format to a raw floppy disk image. The script can convert images created with DiskDupe version 5 and 7 and probably with other versions too. It was tested on images of 1.44MB 3.5" floppies.
There is a Pascal program floating around the internet which includes source code and can convert DDI files to raw sector dumps. It is called DOSIMG and can be found mainly on various Chinese websites. However, the program works only on DOS formatted disk images, as it relies on reading the BPB from the boot sector.