Feature engineering on distributions
At the end each distribution can be described by a function with parameters. Can be a Gaussian, polynomial etc. In principle you can choose functions that only have one free parameter and fit this one. Depending on your data you might be able to guess a function class that seems to fit the underlying distributions. You can then use the fit parameters as input for your data set. Example: Fit a Gaussian and use mean, normalization and sigma = 3 parameters for your model.