*There is always the well-known plunging of diapers in the toilet (rubber gloves make this dirty job not quite so dirty).
*You can attach a diaper sprayer, similar to a kitchen sink sprayer, to the plumbing in your toilet and spray off the waste right into the toilet.
*You can use a biodegradable flushable liner that lays in the diaper, and then after it is soiled, it is dumped into the toilet and flushed prior to washing the diaper.
*Or you can use a combination of the above.
I know some may think it is gross to be washing dirty diapers in the same machine that you wash your other clothes in, but ask yourself this...what do you do when your child is potty training and has an accident in their clothing, it is thrown into the same washing machine that your other clothes go in, isn't it? Same thing goes for clothing or linens that have been vomited on, or bedding that has been wet on. It really is no different.
And there ya go.