Understanding the coevolution of hosts and parasites is one of the key challenges for evolutionary biology. In particular, it is important to understand the processes that generate and maintain variation. Here, we examine a coevolutionary model of hosts and parasites where infection does not depend on absolute rates of transmission and defense but is approximately all-or-nothing, depending on the relative levels of defense and infectivity of the host and the parasite. We show that considerable diversity can be generated and maintained because of epidemiological feedbacks, with strains differing in the range of host and parasite types they can respectively infect or resist. Parasites with broad and narrow ranges therefore coexist, as do broadly and narrowly resistant hosts, but this diversity occurs without the assumption of highly specific gene interactions. In contrast to gene-for-gene models, cycling in strain types is found only under a restrictive set of circumstances. The generation of diversity in both hosts and parasites is dependent on the shape of the trade-off relationships but is more likely in long-lived hosts and chronic disease with long infectious periods. Overall, our model shows that significant diversity in infectivity and resistance range can evolve and be maintained from initially monomorphic populations.