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 At this time, diffuse interstellar bands (DIBs) have been known for a little more than 100 years, since their first detection by Heger (1922). They originate from material, most probably large molecules in the gas phase, populating the interstellar medium and show a good but not perfect correlation with interstellar extinction. Close to 600 DIBs are known at this time, but only four have an unambiguously identified carrier molecule, the Buckminster fullerene cation C60+. There have been many attempts to identify families of DIBs with perfectly correlating band strengths. Such DIBs would be very likely to be caused by common carrier molecules. Although major efforts have been made to classify broadly based DIB families and important insights have been gained, no family has been identified with sufficient accuracy or statistical significance to prove that a series of selected DIBs originates from the same carrier. This can be attributed in part to the exclusive use of equivalent widths to establish DIB families. In a change of strategy, we search for DIBs that are highly correlated in both band strength and profile shape. This approach increases the chance of correlating DIBs being members of one family and originating from the same carrier molecule. We also search for correlations between DIB profile families and atomic interstellar lines, with the goal of further chemically constraining possible DIB carriers. We adapted the well-known method of time-series alignment to perform a spectral alignment; that is, DIB alignment. In a second step, we analysed the alignment results using a clustering analysis. This method required a statistically significant data set of DIB sight lines. The ESO Diffuse Interstellar Bands Large Exploration Survey (EDIBLES) data were perfectly suited for this application. We report eight DIB families with correlating strengths and profiles, as well as four previously unreported DIBs in the visual range, found using DIB alignment. All profile family members show Pearson correlation coefficients in band strength higher than 0.9. In particular, we report the 6614 - 6521 Ã?? DIB pair, in which both DIBs show the same triple-peak substructure and an unprecedented band strength Pearson correlation coefficient of 0.9935. The presented approach opens up new perspectives that can guide the laboratory search for DIB carriers. The identified DIB profile families show energy differences of several hundreds of wave numbers, which is in the energy regime of vibrational modes. It may be possible to link those energy differences to vibrational modes of chemical bonds that are part of the carrier molecules. Further, one C2 DIB profile family shows a strong correlation with interstellar iron in the gas phase. This correlation draws attention to new types of carriers for DIBs. For example, complexes of iron with aromatic hydrocarbons are expected to exhibit strong bands in the visible region. The discovery of DIB profile families is an important step towards a better understanding of DIB carrier molecules. Detailed studies of specific DIB profile families or DIB pairs involving contour fitting and vibrational progressions will enhance our understanding of their carriers and test the hypothesis of common carriers. In particular, subtle profile shape differences between DIB profile family members can provide more information about their carrier molecules. 
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