# Error distribution for Huber Regression

For linear regression there's an assumption that error terms come from normal distribution. so that $$Y = aX + b + \epsilon$$, where $$\epsilon$$ has normal distribution with mean zero and certain variance.

Is there an analogous assumption for Huber loss (or MAE which should be easier)? So that for a variable described by relation $$Y = aX + b + \epsilon$$ with $$\epsilon$$ from this distribution huber regression (or theoretically minimization of MAE) gives a and b parameters?