Generative adversarial networks for multiple distribution noise removal
The task is denoising, so I think you can go with many-to-one mapping between distribution, and then I would probably try changes in generatr architecture if it won't learn properly.
With multiple models, you'd have to classify the type of noise to select correct trained model for particular noise distribution.

And about the CycleGAN...

CycleGAN is for unpaired images. It tries to learn generally more complex problem, because it does not require paired images. 

Since you have paired images, you should utilize that fact and go for pix2pix which needs paired images. Also, CycleGAN mas 2 generators and 2 discriminators, so you have bigger model and thus you need more computational power.