How do set y neq x

[bentoayr]

Hello,
I am trying to build a denoising auto encoder.
Is there a way to make the target data be different from the input data?
In particular, I want the input data to be noisy and the target data to be clean data.
In math, instead of having min_f L(x,f(x)) for some loss function I want to have min_f L(x,f(x + noise))?
Cheers !