The wider application of end-to-end learning methods to embodied decision-making domains remains bottlenecked by their reliance on a superabundance of training data representative of the target domain. Meta-reinforcement learning (meta-RL) approaches abandon the aim of zero-shot generalization--the goal of standard reinforcement learning (RL)--in favor of few-shot adaptation, and thus hold promise for bridging larger generalization gaps. While learning this meta-level adaptive behavior still requires substantial data, efficient environment simulators approaching real-world complexity are growing in prevalence. Even so, hand-designing sufficiently diverse and numerous simulated training tasks for these complex domains is prohibitively labor-intensive. Domain randomization (DR) and procedural generation (PG), offered as solutions to this problem, require simulators to possess carefully-defined parameters which directly translate to meaningful task diversity--a similarly prohibitive assumption. In this work, we present DIVA, an evolutionary approach for generating diverse training tasks in such complex, open-ended simulators. Like unsupervised environment design (UED) methods, DIVA can be applied to arbitrary parameterizations, but can additionally incorporate realistically-available domain knowledge--thus inheriting the flexibility and generality of UED, and the supervised structure embedded in well-designed simulators exploited by DR and PG. Our empirical results showcase DIVA's unique ability to overcome complex parameterizations and successfully train adaptive agent behavior, far outperforming competitive baselines from prior literature. These findings highlight the potential of such semi-supervised environment design (SSED) approaches, of which DIVA is the first humble constituent, to enable training in realistic simulated domains, and produce more robust and capable adaptive agents.