In this paper, we generate conceptual engineering designs of electric vertical take-off and landing (eVTOL) aircraft. We follow the paradigm of simulation-based inference (SBI), whereby we look to learn a posterior distribution over the full eVTOL design space. To learn this distribution, we sample over discrete aircraft configurations (topologies) and their corresponding set of continuous parameters. Therefore, we introduce a hierarchical probabilistic model consisting of two diffusion models. The first model leverages recent work on Riemannian Diffusion Language Modeling (RDLM) and Unified World Models (UWMs) to enable us to sample topologies from a discrete and continuous space. For the second model we introduce a masked diffusion approach to sample the corresponding parameters conditioned on the topology. Our approach rediscovers known trends and governing physical laws in aircraft design, while significantly accelerating design generation.

Data Augmentation through generating pseudo data has been proven effective in mitigating the challenge of data scarcity in the field of Grammatical Error Correction (GEC). Various augmentation strategies have been widely explored, most of which are motivated by two heuristics, i.e., increasing the distribution similarity and diversity of pseudo data. However, the underlying mechanism responsible for the effectiveness of these strategies remains poorly understood. In this paper, we aim to clarify how data augmentation improves GEC models. To this end, we introduce two interpretable and computationally efficient measures: Affinity and Diversity. Our findings indicate that an excellent GEC data augmentation strategy characterized by high Affinity and appropriate Diversity can better improve the performance of GEC models. Based on this observation, we propose MixEdit, a data augmentation approach that strategically and dynamically augments realistic data, without requiring extra monolingual corpora. To verify the correctness of our findings and the effectiveness of the proposed MixEdit, we conduct experiments on mainstream English and Chinese GEC datasets. The results show that MixEdit substantially improves GEC models and is complementary to traditional data augmentation methods.