I have an update for those that may still be having this issue and found this via google.
If you are using this app on a mac, for some reason the app doesn’t have permission to download the models into the .app package itself. Giving it permission to do this is not possible because of gatekeeper. This is not related to internet, firewall or antivirus. It’s a Security “feature” of MacOS.
My solution is to download all the models manually. You can find the links in the app logs.
/Users/USERNAME/Library/Application Support/Topaz Labs LLC/Topaz Gigapixel AI/Logs/
Look for one that ends in main, and open it in Console. Run the install missing models option in the help menu of the app. copy and Paste the link that it errors out in the log on into a browser and download the .tz file somewhere on your computer.
Find the topaz gigapixel app on your computer and right click, show package contents and then navigate to: /Applications/Topaz Gigapixel AI.app/Contents/Resources/local/tgrc
Add the model you downloaded to this folder. then here is the crapy part, if the models need updates, you have to do this again and again after clicking the install missing models option in the help menu and repeat, over and over…
If you would like to not spend an hour doing this, how about 30 minutes of pasting 22 links one by one? 
Just know, if these get updated or moved, you will have to manually go into the logs and get the new missing model.
REMOVE THE SPACE AFTER HTTP, could not paste links…
https ://models.topazlabs.com/v1/gclc-v1-fp16-192x192-1x-mlc.tz
https ://models.topazlabs.com/v1/gfp-s-v1-fp32-1024x1024-mlc.tz
https ://models.topazlabs.com/v1/gclc-v1-fp16-192x192-2x-mlc.tz
https ://models.topazlabs.com/v1/gfs-v1-fp32-64x64-1x-mlc.tz
https ://models.topazlabs.com/v1/gclc-v1-fp16-192x192-4x-mlc.tz
https ://models.topazlabs.com/v1/gfs-v1-fp32-64x64-2x-mlc.tz
https ://models.topazlabs.com/v1/gclc-v1-fp16-96x96-1x-mlc.tz
https ://models.topazlabs.com/v1/gfs-v1-fp32-64x64-4x-mlc.tz
https ://models.topazlabs.com/v1/gclc-v1-fp16-96x96-2x-mlc.tz
https ://models.topazlabs.com/v1/ggi-v1-fp16-192x192-1x-mlc.tz
https ://models.topazlabs.com/v1/gclc-v1-fp16-96x96-4x-mlc.tz
https ://models.topazlabs.com/v1/ggi-v1-fp16-192x192-2x-mlc.tz
https ://models.topazlabs.com/v1/gclc-v1-fp32-192x192-1x-mlc.tz
https ://models.topazlabs.com/v1/ggi-v1-fp16-192x192-4x-mlc.tz
https ://models.topazlabs.com/v1/gclc-v1-fp32-192x192-2x-mlc.tz
https ://models.topazlabs.com/v1/ggn-v3-fp16-96x96-1x-mlc.tz
https ://models.topazlabs.com/v1/gclc-v1-fp32-192x192-4x-mlc.tz
https ://models.topazlabs.com/v1/ggn-v3-fp16-96x96-2x-mlc.tz
https ://models.topazlabs.com/v1/gde-v1-fp16-192x192-1x-mlc.tz
https ://models.topazlabs.com/v1/ggn-v3-fp16-96x96-4x-mlc.tz
https ://models.topazlabs.com/v1/gde-v1-fp16-192x192-2x-mlc.tz
https ://models.topazlabs.com/v1/ghc-v2-fp32-192x192-1x-mlc.tz
https ://models.topazlabs.com/v1/gde-v1-fp16-192x192-4x-mlc.tz
https ://models.topazlabs.com/v1/ghc-v2-fp32-192x192-2x-mlc.tz
https ://models.topazlabs.com/v1/gfclc-v1-fp32-512x512-mlc.tz
https ://models.topazlabs.com/v1/ghc-v2-fp32-192x192-4x-mlc.tz
https ://models.topazlabs.com/v1/gfd-v1-fp16-64x64-mlc.tz
https ://models.topazlabs.com/v1/ghq-v1-fp16-96x96-1x-mlc.tz
https ://models.topazlabs.com/v1/gfg-v1-fp16-512x512-mlc.tz
https ://models.topazlabs.com/v1/ghq-v1-fp16-96x96-2x-mlc.tz
https ://models.topazlabs.com/v1/gfl-v1-fp32-192x192-1x-mlc.tz
https ://models.topazlabs.com/v1/ghq-v1-fp16-96x96-4x-mlc.tz
https ://models.topazlabs.com/v1/gfl-v1-fp32-192x192-2x-mlc.tz
https ://models.topazlabs.com/v1/gmp-v1-fp16-192x192-1x-mlc.tz
https ://models.topazlabs.com/v1/gfl-v1-fp32-192x192-4x-mlc.tz
https ://models.topazlabs.com/v1/gmp-v1-fp16-192x192-2x-mlc.tz
https ://models.topazlabs.com/v1/gfm-v1-fp32-512x512-mlc.tz
https ://models.topazlabs.com/v1/gmp-v1-fp16-192x192-4x-mlc.tz
https ://models.topazlabs.com/v1/gfp-l-v1-fp32-2048x2048-mlc.tz
I did this, added them to the .app and it works. Not sure why this is not included in the initial install of the app, or why these are in the .app and not the Application support folder… meh, it works now.
TL:DR, download all the links and save them to this directory. /Applications/Topaz Gigapixel AI.app/Contents/Resources/local/tgrc
Hope this helps that one person with a deadline and helps make their day better. 
