  Intermediate dimensions were recently introduced by Falconer, Fraser, and
Kempton [Math. Z., 296, (2020)] to interpolate between the Hausdorff and
box-counting dimensions. In this paper, we show that for every subset $ E $ of
the symbolic space, the intermediate dimensions of the projections of $ E $
under typical self-affine coding maps are constant and given by formulas in
terms of capacities. Moreover, we extend the results to the generalized
intermediate dimensions in several settings, including the orthogonal
projections in Euclidean spaces and the images of fractional Brownian motions.
