Pairwise differences between rolling average values for different window widths

This code aims to compute the rolling average of a signal for a range of window widths (i.e. how many points are averaged), and then calculate the sum of all pairwise differences between averages at each window width.

import numpy as nptestData = np.random.normal(0,1,10000)windowWidths = np.arange(1,1000)sliding_averages = []diffs = []for windowWidth in windowWidths:    # Rolling average using convolution    sliding_average = np.convolve(testData, np.ones(windowWidth) / windowWidth, mode='valid')     # All pairwise differences    pairwiseDiffs = (sliding_average[:,None] - sliding_average[None,:])     # Define mask to extract only one corner of difference matrix    mask = np.triu(np.ones_like(pairwiseDiffs, dtype=bool), k=1)     pairwiseDiffs = pairwiseDiffs[mask]    pairwiseDiffsSqrd = pairwiseDiffs**2    diffs.append(np.sum(pairwiseDiffsSqrd))

This is aiming to be a component in reproducing the computation described in this section of a paper:

Calculation:

My question is whether there is a more efficient way to run this calculation.

I have tried vectorizing further and replacing convolution steps with other approaches, but am not confident in the result.