Distribution with parameter dependent on given X

Hi all - I am a beginner PyMC3 user. Recently I have a modeling question and find PyMC3 may be the tool.
I am not even sure this is a valid question. Anyway, here it is:

Given data (X, Y), I want to formulate the model as Y = f(X; a, b, c). Within f(X), there is a parameter following a certain distribution with parameters dependent on X.
An example would be that “c” follows a normal distribution, in which std depends on X,

c = pm.Normal(‘c’, 0, sd = X)

How could I make such a model happen? Many thanks!

Depending on the function f(), if you can rewrite it in theano usually this should be straightforward.
Maybe you can share some code example?