Evolutionary diversification can occur in allopatry or sympatry, can be driven by selection or unselected, and can be phenotypically manifested immediately or remain latent until realised in a newly encountered environment. Diversification of host-parasite interactions is frequently studied in the context of intrinsically selective coevolution, but the potential for host-parasite interaction phenotypes to diversify latently during parasite-blind host evolution is rarely considered. Here we use a social bacterium experimentally adapted to several environments in the absence of phage to analyse allopatric diversification of host quality - the degree to which a host population supports a viral epidemic. Phage-blind evolution reduced host quality overall, with some bacteria becoming completely resistant to growth suppression by phage. Selective-environment differences generated only mild divergence in host-quality. However, selective environments nonetheless played a major role in shaping evolution by determining the degree of stochastic diversification among replicate populations within treatments. Ancestral motility genotype was also found to strongly shape patterns of latent host-quality evolution and diversification. These outcomes show that i) adaptive landscapes can differ in how they constrain stochastic diversification of a latent phenotype and ii) major effects of selection on biological diversification can be missed by focusing on trait means. Collectively, our findings suggest that latent-phenotype evolution (LPE) should inform host-parasite evolution theory and that diversification should be conceived broadly to include latent phenotypes.