For Android users

You may go to Settings - Auto Download - New Episodes - turn that option off, or disable or enable it for the podcasts you would like to have automatically downloaded by clicking the Customize button.

Alternatively, you can go to a channel's show info page - tap the three dots button at the top right-hand side - Settings - Auto Download - select "None".

For iOS users

You may go to the app Personal tab - Settings - Auto Download - Advanced Options - Keep the unplayed episodes at most, and set it as "none". You can also turn off the "Playlist Auto Download" setting, if you do not want to have the episodes added to your playlists downloaded automatically.