A new feature introduced in version 2.5.9 for iOS allows users to optimize local device storage by storing full-resolution photos in the cloud and downloaded on demand.
Open Day One > Settings > Sync > and choose either Optimize Device Storage or Download All Media.
After enabling "Optimize Device Storage", you can clear local media storage by navigating to Day One > Settings > Sync > Storage Used > Clear Local Photo Storage.
Open Day One > Preferences (in the file menu) > Sync > and choose either Optimize Device Storage or Download All Media.
Photos are optimized when imported to Day One for Basic and Plus users for a more efficient storage and sync. Premium users can now store higher resolution photos. See here.