The budding yeast Saccharomyces cerevisiae is a long-standing model for the three-dimensional organization of eukaryotic genomes. However, even in this well-studied model, it is unclear how homolog pairing in diploids or environmental conditions influence overall genome organization. Here, we performed high-throughput chromosome conformation capture on diverged Saccharomyces hybrid diploids to obtain the first global view of chromosome conformation in diploid yeasts. After controlling for the Rabl-like orientation using a polymer model, we observe significant homolog proximity that increases in saturated culture conditions. Surprisingly, we observe a localized increase in homologous interactions between the HAS1-TDA1 alleles specifically under galactose induction and saturated growth. This pairing is accompanied by relocalization to the nuclear periphery and requires Nup2, suggesting a role for nuclear pore complexes. Together, these results reveal that the diploid yeast genome has a dynamic and complex 3D organization.