In cultivated tetraploid potato (Solanum tuberosum), reduction to diploidy (dihaploidy) allows for hybridization to diploids and introgression breeding and may facilitate the production of inbreds. Pollination with haploid inducers (HIs) yields maternal dihaploids, as well as triploid and tetraploid hybrids. Dihaploids may result from parthenogenesis, entailing the development of embryos from unfertilized eggs, or genome elimination, entailing missegregation and the loss of paternal chromosomes. A sign of genome elimination is the occasional persistence of HI DNA in some dihaploids. We characterized the genomes of 919 putative dihaploids and 134 hybrids produced by pollinating tetraploid clones with three HIs: IVP35, IVP101, and PL-4. Whole-chromosome or segmental aneuploidy was observed in 76 dihaploids, with karyotypes ranging from 2n = 2x − 1 = 23 to 2n = 2x + 3 = 27. Of the additional chromosomes in 74 aneuploids, 66 were from the non-inducer parent and 8 from the inducer parent. Overall, we detected full or partial chromosomes from the HI parent in 0.87% of the dihaploids, irrespective of parental genotypes. Chromosomal breaks commonly affected the paternal genome in the dihaploid and tetraploid progeny, but not in the triploid progeny, correlating instability to sperm ploidy and to haploid induction. The residual HI DNA discovered in the progeny is consistent with genome elimination as the mechanism of haploid induction.